This course is on nuclear and particle physics.
Today, we shall give an overview of the topics
that would be covered in the course. In short,
this course is on the basic constituents of
all matter around us. We will discuss what
are the properties of these constituents,
and we will also discuss what are their dynamics,
and what are the guiding forces that dictate
their interactions.
We shall start in the second half of the 19th
century. We had good understanding of what
is the constitution of the universe by then.
At least considering all matter that we are
familiar with, it was established that we
can think about something like less than 100
basic chemical elements, which make all this
matter around us. So, we have the understanding
of chemical elements, and the smallest unit
of that was called atom. Experiments to understand
further what are the properties of these chemical
elements, what are their constituents, etcetera
had been going on.
So, by 1897 experiments of J. J. Thomson led
to the discovery of presence of electron in
the atoms. He studied the cathode rays closely;
did try to understand what their properties
are; how do they behave under electric field,
how do they behave under magnetic field, etcetera,
and established that they have: firstly, electric
charge. Atoms of the chemical elements were
known to be electrically neutral, but, now,
we have an electrically charged particle present
in matter.
He proposed an atomic model. Rather, he, working
with Lord Kelvin and other collaborators and
other leading people in the field, suggested
(but it is basically, mostly due to Thomson)
that atom looks like a positively charged
sphere. Kind of positively charged matter
and of a somewhat uniformly distributed positive
charge.
(time: 4:50-5:10) So, I have positively charged
sphere with negatively charged electrons embedded
in it.
Where are this negatively charged particles
that is coming out as part of the cathode
ray? They are there in the atom, distributed
in this positively charged matter. That is
Thomson铆s model of an atom. So, these are
the electrons.
Then in the early years of 20th century, a
series of experiments by Rutherford and collaborators
had something slightly different to say. What
did they do?
They had alpha particles.
In Rutherford铆s experiment, they took a
thin gold foil and send this alpha particle
on to it. If Thomson铆s atomic model was
correct, the scattering of this alpha particle
due to the positively charged uniform sphere
(atom) would be, kind of, a mild scattering.
Thin gold foil, we can assume that the gold
atoms are there in the line or in a plane
of the paper. Take the plane of this is the
gold foil.
(time: 7:14) Then, alpha particles bombard
it. They will see this thin plane of gold
is made of atoms of gold. The alpha particles
will see this; there will be electromagnetic
repulsion, and they will scatter. This scattering
is (if it is something like a uniformly spread
out in their sphere) then it will be kind
of a mild scattering. . That is what was expected.
But then, Rutherford and his team looked closely
and specifically looked for things like the
large angle scattering of the alpha particles.
By which we mean, this (angle) becomes large;
more than 90 degrees. And then, what happens?
They will comeback. They specifically looked
for whether there are alpha particles, which
are scattering back. And they did indeed find
a small fraction of these alpha particles,
which are sent to the gold foil, do come back.
Now, there is a little bit of a trouble that
Thomson铆s atomic model will face in explaining
this large angle scattering. Rutherford proposed
that it may not be the case like this, and
by 1911, he kind of proposed this in a clear
way. Look at it in this fashion. Think about
as if all the positive charges in an atom
are concentrated in a small volume or a small
core of the atom. So, atom as a whole has
a small, much smaller than the atom itself,
tiny core inside it, which contain all positive
charge.
The concentration or the density of the positive
charge in the atom is very large in that small
core. Outside; there is no positive charge.
So, you have a positively charged core. And
he said electrons are not that orderly, they
are moving around. That had its own problems.
But, basically, he said we will worry about
the problems (later).
(Time: 10:32) But at least his experiments
the alpha particle scattering experiment could
be explained in a way, that whenever you send
alpha particles close to this core; the fraction
of the alpha particles in the beam, which
fall close to this nucleus, will return. They
will not be able to go at small angles. Other
things can actually go with some angle and
then further smaller angle here.
But when it is going to kind of go directly
towards the core, positively charged core,
then they will have a large angle scattering
and return. So, this core is basically called
the nucleus. So, there is a positively charged
nucleus, and electrons (let me denote it by
e), revolve around this. Problem with this
model is that, classically, electrodynamics
tells us that accelerated charge particle
emit energy; lose energy.
This electrons, which are moving around, let
us say, are accelerated, because whenever
something moves or deviate from a straight
line (that is what is happening here when
they move in a circle or any closed orbits
or circular orbit or curved paths; they deviate
from the straight line), then that deviation
means there is an acceleration.
This acceleration will cost the electron.
Accelerating electron is going to lose its
energy, and what happens then? It has to keep
on losing its energy and then it will fall.
As it moves around you will lose balance between
the centripetal acceleration and then this
thing unless you come closer. The radius has
to keep on reducing for smaller and smaller
energy electrons. Then ultimately it will
fall inside. The stability of this model is
in question. I mean it is not possible classically.
Later on, quantum mechanics takes over and
then gives a way out of this. But that is
not going to be our story. We will go further
focusing on this core, the nucleus. So, that
is the kind of beginning of this picture of
atomic nucleus.
Now, let us look closer and then see what
are the further developments there. We are
talking about early 20th century, when Rutherford
and team had been (working on it). Many people,
but mainly Rutherford. By 1920 he established
something remarkable. They could understand
nucleus of different atoms. Understand meaning,
they could figure hydrogen atom has its nucleus,
helium atom has its nucleus, atoms of heavier
elements of heavier nuclei, etcetera.
Now, his experiments established that this
nucleus is kind of not a single unit. Apparently,
nucleus of heavier elements contains nucleus
of hydrogen atom. So, this is the atom; electron;
nucleus. And then if you look at this closely,
they contain nucleus of hydrogen atom. Let
me fill that for clarity. Hydrogen atom (nucleus).
I will not fill all of it. I will come to
that. But, this is something which is remarkable
and then we call that; the nucleus of the
hydrogen atom, as proton.
So, proton is established as part of all the
nucleus. Experimentally it was seen that it
is there in many atoms that Rutherford studied,
and then he suggested that its part of all
atoms. That is one thing, and then later on
other experiments led Chadwick to discover
in 1932 another constituent, which is electrically
neutral, present in the nucleus along with
the proton. Now proton is electrically charged
neutron is electrically neutral. In a sense,
the way I have made this cartoon, we have
the proton and neutrons let me denoted by
n in the atomic nucleus.
So, that is kind of the modern picture of
atom, along with the quantum mechanics and
the rules of the quantum mechanics put in.
Now, let me look at this nucleus more closely.
Some of you who are been closely looking at
what we are doing must have already noticed
one peculiar thing happening here. Look at
this nucleus, it has protons. Many protons.
Heavier nuclei like the nucleus of gold atom,
etcetera is expected to have more protons.
They are confined to a small volume. I can
also indicate what is the size of this, although
we will come to this size of nucleus etcetera
later. Basically, it is of the order of 10
-15 meters. That is the kind of size of nucleus,
whereas the size of atom in something like
5 orders of magnitude larger.
So, this picture is highly zoomed into the
(nucleus) and not to the scale at all; all
the constituents. So, in this 10 -10 meter
atoms, the positive charges are focused, or
concentrated or put in a small volume, which
has a size, or a radius of 10 -15 meters.
So, very small.
Now, you look at it. You have this positively
charged protons coming together, sitting together.
There must be a repulsive coulomb force or
electric repulsive force between them. What
about that? They may be repelling each other;
pushing each other. Suddenly, that is a question.
That is a question that has to be addressed
by Rutherford铆s atomic model.
When we come to the nucleus stability of the
nucleus against electromagnetic 
force of repulsion between the protons. Neutrons
are there, but they are electrically neutral;
they do not take part in this electromagnetic
interaction. So, then protons will repel each
other. So, how are they grouped together?
We need something which is attractive or which
is going to attract these two protons together.
there has to be an attractive force.
So, that tells you that there is some attractive
force between the protons then only they will
sit together; stay together, and maybe also
between the protons and neutrons, and neutrons
and neutrons.
Now, let us look at two protons, separated
by a distance between these two. There is
an electric force. I will write only the magnitude.
Direction is along the line joining the centers
of these protons. So, electromagnetic force
is 1 over 4 pi epsilon 0, the charge of the
proton times the charge of the other proton
is q2, divided by r2, (square of) the distance
between these two.
What kind of attractive force that we are
familiar with? We are familiar with the gravitational
force, which we know is attractive in nature.
Now, see whether that can fit in here. What
is the gravitational force between two protons?,
It is the Newtonian gravitational constant
then the square of the mass of this. and then
this r square. Let us compare these two, and
then see which one is bigger. We need some
attractive force, which is bigger than or
larger than the repulsive electric force.
So, let us take the ratio of the electric
force and gravitational force. You will get
1 over 4 pi epsilon 0 q square in the numerator;
r square cancels, when you take the ratio
between these two; GN in the denominator;
m square in the denominator. So, epsilon 0
is equal to 8.85 X 10-12 in SI units; q, charge
is 1.602 X 10 -19 Coulomb; masses 1.67 X 10-27
kilogram; GN, Newtonian gravitational constant
is 6.67 X 10-11 Newton meter square over (kilogram
square). Put all these things together and
you get the ratio of electrostatic repulsive
force between two protons and gravitational
attractive force between the same protons
at the same distance is of the order of 10
36 positive 10 36.
So, electric force apparently is much much
much stronger than the gravitational force.
It is something like 1036 times larger than
the gravitational force. So, definitely that
is not going to help us.
Therefore, for the stability of the nucleus
(let me just write it as N, denote this thing
by N) against the electromagnetic repulsion
of the protons which are close together. We
require some strong force. And it is a it
is found in nucleus. This strong nuclear force
is not seen otherwise. We have not come across
with that. It was there all through, but we
were not aware of that.
Now, looking at the nucleus we see that there
has to be something there to glue these protons
together. Now, this is something which we
just call as strong nuclear force, and we
will come to the properties of this as we
go on. We will see that the nuclear force
is confined to small distances within the
nucleus or at the size of the nucleus, and
that is why we do not see the presence of
these outside at large distances.
So, they should have that property; that as
we look at things at large distances these
are negligibly small. That is one thing. Then,
another property that is coming from the observed
radio activity of the nucleus. This is basically
the spontaneous disintegration of nuclei.
Some nuclei are not stable; they disintegrate.
they split, emit certain radiations. Alpha
radiation is one of those. (And) beta and
gamma (rays). These are the normal radioactive
emissions.
We will come to the specific details of those
later. But now, this has to be again caused
by some interaction. How does this happen?
If there is a strong interaction and then
its there, gluing together the protons and
neutrons. Then what happens when something
disintegrates? How does that happen?
So, to explain that we need another force,
which is simply called the weak nuclear force.
So, beta decay or any other nuclear decay
happens because of the weak nuclear force.
We will come to this and the properties of
these, as we go on. That is, kind of, the
purpose of our course. The starting point
of our course would be to, kind of, look at
the a nucleus closely and then properties
of the nucleus like mass, charge, size of
this. Then there is one another thing.
(Time: 30:55) Let us look at the helium nucleus
helium, the second element. It has two protons
and two neutrons. So, if you take two free
protons and two neutrons and bring them together,
they should ideally form this kind of a thing.
so, the conditions are set so, that they can
come close to each other. So, that the nucleus
strong nuclear force will be binding them
together and then they will form helium atom.
Now, when you look at this, and look at the
mass of the helium atom and the mass of two
protons plus mass of two neutrons; Then there
is a difference between the sum of the constituent
masses. Or, sum of the masses of protons and
neutrons inside this helium atom is larger
than the mass of the helium. So, when they
come together and make a nucleus they lose
some mass. Some energy is lost; some mass
is lost. This is called mass defect, or this
is basically called the binding energy.
We will come to the details of this binding
energy and whether we can kind of make a estimate
of these for a nucleus specifically. What
are the different things that make the binding
energy large so that the nucleus is stable.
We will come to that later. Then we will talk
about radioactive decays, nuclear reactions
(some of these we will discuss in some details)
and models of nucleus.
We have only said that they come together
and then form (nucleus). That is their constituents.
But, like in the case of atoms, we have to
actually give again specific details of how
the nucleus is formed, and then what are the
properties of that, etcetera, when they are
there. And what are the kind of energy levels
of these or what is the kind of general picture
of the nucleus, or the model of the nucleus.
So, there are these nuclear models that we
will discuss.
Now, we will continue talk about the nuclear
force; we will talk a little more about the
nuclear force and nuclear force. There was
a hypothesis put forward by Yukawa in 1934
to understand the nuclear strong nuclear force.
He said think about the nuclear force between
two nucleons or two nuclei as if happening
with the exchange of some particles. So, he
predicted the existence of (they have to have
mass. We will come to some of the details
later) massive bosons. Bosons are integers
spin particles.
So, massive bosons mediate 
strong nuclear force. That is in a sense the
Yukawa hypothesis. And what are these bosons?
People looked for those and finally, in 1947
some such scalar particles were discovered.
Spin-0 particles were discovered. They are
called the Pions. (Time: from 36:16 to 36:31
帽 no subtitles needed). (from Time 36:32)
One can understand this Yukawa hypothesis
of exchange of Pions between protons as the,
kind of, mediating the interaction or making
the interaction happen.
Then they were many other particles were discovered
in the cosmic rays. Examples are muons. In
a very short description muons are particles
similar to electrons, but much heavier than
electrons. Then there are other particles.
Pions come in different charges. Neutral pions,
plus minus pions. Rho-0, rho plus minus (heavier
particles. something similar to pions). Then
K-meson, then lambda particle, etcetera. All
these happened towards the middle of the 20th
century.
So, we had many particles which are not really
otherwise seen in the day to day normal matter.
Now, this had been one of the difficulties,
one of the difficult periods to classify them
and understand such many different particles.
So, now, let us say the classification of
particles had to be done.
Many different ways were tried and then there
is something particularly called the Eightfold
way of Gellmann, Nishijima and Ne铆eman.
Some of this now what we do is kind of give
information. We will definitely get back to
these and then tell the details; some of the
details at least, of all these that yes. So,
today we are actually trying to say; what
are the things that we are going to do in
the course of time that is going to come in
the next lecture onwards. We will spend sufficient
time on each of these and then discuss further.
We will definitely look at these, and that
is why we are just mentioning that here. So,
the classification of this in a proper way
had been done and this is now thought of as
a good turning point of understanding of these
particles. And this led to what is called
the Quark model. Which is established by 1964,
again by Gall-mann and Zweig. In some kind
of a short way, this means that when you look
at the protons they have constituents. They
are made of tinier particles; tinier constituents.
Also the substructure of proton was 
proposed by Feynman in what is called the
Parton Model 
by 1969. He was trying to explain the experimental
results; scattering experiments. How that
can fit in, and then he suggested that we
can actually think about protons as if made
of smaller constituents, which we simply called
partons. Partons are tiny things inside the
protons.
Now, that is what the classification and the
eightfold way leads to. Saying that there
must be basic units; small constituents, which
make these protons. Not only these protons;
according to the quark model; but many other
such particles like pions and rho mesons,
etcetera, which we mentioned just before.
And they all are made of smaller units called
quarks.
So, this is the proton; proton is made of
these quarks. Neutron is also made of quarks.
There must be a different combination. There
must be many different types of these quarks,
and different combinations of them, etcetera.
So that proton is a proton and it is different
from the neutron. Otherwise if it is all the
same type of quarks and then same number of
these things, then how will this differ from
each other?
We will come to the properties of that later.
Now look at what is the summary of the situation.
So, summarizing, that we have the modern picture
of the atom.
We have the nucleus, positively charged. And
electrons moving around this. Negatively charged
electrons. When we zoom in, we get a larger
picture. That is basically the 
nucleus being made of protons and neutrons;
many of them. Then again, in turn each of
these we look at, and then they, say a proton,
is made of quarks. That is how it goes.
Now, we can ask the questions; what exactly
is this? What are the properties of these;
what are these called; how many of them are
there; etcetera. At the moment we can actually
consider these quads as elementary particles.
Meaning, at least to the level that we have
probed, quarks are without any sub structure;
they are elementary.
And there are other types (of elementary particles),
like electrons, which are called leptons.
There are 6 different types of quarks, and
each of these come in 3 different varieties;
6 different types of 
electron-like particles or 
the leptons. They are actually put together
in groups usually, because of reasons for
this. We will come to this kind of grouping
later.
There are electrons, muons and tau leptons.
All of these particles are negatively charged;
different in masses. And then there are what
are called the neutrinos. They are electrically
neutral. When it comes to quarks, there are
u, d, c, s, t, b; 6 different types of this.
Each of these actually come in 3 different
varieties. u itself comes in uR uB uG; different
labels; 3 labels. It is conventionally called
color charge. Again, there are reasons to
call it color, it has nothing to do with the
photons or the light or the color that we
see in our common day-to-day life. Nothing
to do with that. But they come in different
varieties.
There are certain reasons for this. When we
combine these 3 different varieties, then
we will get a color neutral or (some)thing
which is not-going-to-be-interacting-strongly
kind of a combination. We will come to that
later. Of these the top quark, t, was discovered
as late as 1995. So, it is all happening in
our time, and very interesting. We will discuss
some of the interesting facts about this.
We will continue for a little more and then
stop the overview soon.
Now, we talked about the participants 
of this. Then we have what is called fundamental
forces.
What are the forces, which dictates the dynamics
of this? We know about gravitational force,
which is definitely there all around us. Then
we know about electromagnetic force, which
is also there in our common experience, day-to-day
experience. And we talked about the strong
nuclear force, and we also suggested that
there should be some weak nuclear force.
Gravitational force, we already saw that it
is too small compared to the electromagnetic
force, and strong force has to be larger than
that. Electromagnetic force and weak force
actually come in between. So, the gravitational
force as such has not much of a role to play
in the dynamics of elementary particles. It
comes into play in large scale structures
or formation of large scales structures, where
we have large mass; big bodies. So, we will
not really be discussing that in this course.
Rather, we will be talking about only these.
This description is given in a specific theoretical
model, which is called as the standard model
of particle physics; which was in a sense
established by 1970 or 69-70 by Glashow, Weinberg
and Salam.
We will discuss, as we go on, a little bit
about these things; and specifically, we will
actually talk about what is the mathematical
framework of this model. It is essentially
what is called the Gauge Field Theory.
This was the development in kind of 1930 to
1970. People established this as one of the
ways to understand the dynamics of the fundamental
forces that the elementary particles experience.
A short description of this gauge symmetry,
which dictates the gauge field theory can
be understood by looking at how the electromagnetic
potential; or the magnetic vector potential
and the electrostatic potential together;
they behave. They have a kind of an arbitrariness
in it, in the sense that if we transform or
change this A, the magnetic potential to some
other potential;
so that it is some addition of some gradient
of some scalar function; along with saying
that phi (this scalar potential) is changed
to phi minus time derivative of the same function,
where psi is some scalar function.
Then, this together will give you the electric
fields E is equal to minus gradient of phi,
we are familiar with this; minus derivative
of A with respect to time. And magnetic field
is essentially curl of A. So, if you change
A to A prime and phi to phi prime, this E
is not going to be affected according to this.
So, there is an arbitrariness in this. Or
in another sense, it is a symmetry. This transformation
(this change is called the transformation)
of A to A prime is called the gauge transformation.
Do not worry about the terminology now. We
will come to that in slightly more detail
and then try to give a basic introduction
to this in this course.
In a picture of the gauge field theory, essentially,
this boils down to this fact. That is what
I wanted to tell today. When we look at the
interaction between an electron and a positron
or an electron, this can be understood similar
to, (not exactly the way, but something at
least in the way that Yukawa had thought)
by happening through the exchange of some
particles. This particle for electromagnetic
interaction is called the photon, which is
essentially the quantum of 
electromagnetic field; which is symbolized
by the gamma here, is essentially represented
mathematically by the vector potential and
the scalar potential. They describe the photons.
And now there is a very consistent beautiful
way of understanding this interaction between
two charged particles through the exchange
of such photons, mathematically considering
the gauge transformations, gauge symmetry,
and the gauge field theory in general. We
will come to that. Now, this is something
which is talking about the electromagnetic
force; and what Weinberg, Salam and Glashow
their proposals, their studies (and many other
people studies later on) led to the picture
that other forces
(like the) strong and weak nuclear forces
can also be understood as if happening through
the exchange of such particles.
So, for example, electron and electron or
positron can interact, let us take electrons,
through the exchange of what is called a weak
boson, which is similar to the photon. This
has to have a charge. So some neutral particle
will go. The details, we will come to later.
So this is how it goes.
There could also electron going as an electron,
but then interacting. This is very similar
to the photon. Electrically neutral particle.
This is the story with weak force. And strong
force is also, similarly, happening through
exchange of some other mediators, which are
called the gluons. They glue together. This
is basically the strong interaction. That
is kind of the picture of these gauge field
theory or interaction of particles under the
fundamental forces picturized through the
gauge field theory and exchange of quantum
of the fields. That is the kind of thing that
the standard model will be describing.
We will discuss some details of this in this
course. If time permits we will also discuss,
I think at least we will give you some flavor
of this, because that is something very topical,
what is happening now. This gauge field theory
description has a little bit of a trouble
in understanding the masses of the particles.
Now, for this we will need something called
Electroweak Symmetry breaking 
and Higgs mechanism. I am just giving you
the words; definitely, without describing
it it does not really make too much sense,
but let me at least just name them. There
is something called electroweak symmetry that
we talked about. The transformation and invariance
of this electric and magnetic field etcetera
under the change of the potential, and similarly
for other forces. It is called the symmetry.
Now, that symmetry has to be broken. The electroweak
symmetry breaking is needed to discuss the
mass of these particles. We will come to a
little bit about that. And the mechanism to
do that, one of the mechanisms, which was
proposed is called the Higgs mechanism named
that the proposer Peter Higgs. This led to,
in 2012, just a few years before, by Large
Hadron Collider or LHC to discover the Higgs
boson.
There are many things that are yet to be known,
experimentally as well as theoretically, about
the Higgs boson, about the electroweak symmetry
breaking, and there are beautiful and many
different interesting ideas that are there
in this thing. So, we will discuss these in
a very short way. At least I will try to give
you a flavor of this.
Then there are also a few things that I want
to discuss. Say, for example, if you look
at the universe as a whole. This will be the
last few minutes of this particular session.
Basically, we have many other things that
is happening, apart from the Higgs boson and
the properties of that.
For example, there are particles called Neutrinos.
And neutrinos, in the standard model description
-- starting from the beta decay, where this
was proposed and then subsequently discovered,
it was thought that the neutrinos have no
mass. They, of course, have very tiny mass
even if they have it at all. Recently we have
established that they do have some mass. They
have to have some mass to describe certain
other phenomena. That is an issue; in the
sense that, it is not an issue to how the
mass, but that understanding of how the neutrinos
generate mass or what type of mass it is,
etcetera are not clear. And that is an active
topic of research currently.
The other thing is; we can ask the question
like what are the constituents of the universe.
Usually what we do is to actually look outside,
look at the universe; get information. And
how do we get information? We look at the
stars and receive information in the form
of light, say. That is how we see the stars.
Then we also have special equipments which
can actually see other electromagnetic radiations
apart from light. The gamma ray and X-ray,
etcetera. Or the whole spectrum of electromagnetic
(radiation). Radio astronomy will probe radio
wave signals, etcetera.
Looking at all these, we can actually try
to ask the question like what do we know about
this universe; and can we make an estimate
of the matter particles there, etcetera. And
there are also cosmological models, which
tells us what is the constituent mass of the
universe, and what is the mass of the universe.
Now, this at the moment gives kind of a picture,
which is something not understood clearly.
So, apparently observations lead to this fact
that only about 5% of the total mass of the
universe is understood through 
the visible observations that we do. When
I say visible, it includes all spectrum of
electromagnetic radiations that we can see
with our naked eye, with our instruments,
etcetera.
Something like 27% is again supposed to be
matter, and that is not seen. That is called
the dark matter. So let me write it as dark
matter. Rest of it, something around 68% is
essentially not even matter. It is some form
of energy, and it is dark energy, something
which is not understood. So, dark matter and
dark energy. This is something which is not
included in the standard model and not known.
There is also the other question of Baryon
asymmetry, which is in a senses, like there
are matter and antimatter like electrons and
protons 帽 (those of you who do not know
do not worry about it, but we will describe
it later). So, basically there is a large
number of particles against antiparticles.
So, when you look at the universe it is all
made of particles -- electrons, protons etcetera.
There are antiparticles corresponding to every
particle, like positron is the antiparticle
of electron, anti-proton is an antiparticular
proton, etcetera. These are to be there for
consistency of standard model and our theoretical
understanding. And we have also seen them
in the laboratory. So, we can make them we
can actually study them. But when you look
at the universe as a whole we do not see any
of them naturally. So, naturally we see only
particles not antiparticles. This asymmetry
is not understood. In a way that is big active
the topic of research today. In general then
all these things lead to the question of,
how do we actually extend our theoretical
understanding going beyond the standard model?
That is the one of the basic research that
is going on in the currently. We will discuss
some of these special topics in an appropriate
way.
That is the kind of overview that I can give
you as what would happen in this course, as
we go along starting from the next lecture.
