M1L2f.txt

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If you're interested in the subject
and I couldn't do full justice to it,
you may want to look at this book from Claude
Cohen-Tannoudji, Jacques Dupont-Roc, and Gilbert
Grynberg about photons and atoms.
The whole book is dedicated how to describe
the interaction of atoms with electromagnetic fields.
In this book, they go through different ways
of formulating the electromagnetic field
classically.
They use a Lagrange formalism for the electromagnetic fields
and show that the Euler-Lagrange equation, Maxwell's equation.
So there are lots of different approaches,
and also one can say that what we
did here is-- which is the simplest way of describing
light atom intersection, has of-- how
to say-- we work in the Coulomb gauge, which is not
the gauge you would choose when you want to describe
relativistic physics.
There is the other gauge, the Logens gauge.
It makes the field quantization much more difficult.
But when you ever wondered why is the quantization done
in the way I did, and you think something I did was arbitrary.
Why did they pick the Coulomb gauge?
Read this book.
There are hundreds of pages which explain it to you.
And I'm not joking here, it's a wonderful reading.
I mean I got the book and just looked up a few things,
and I almost got hooked on it, and read more and more.
It's a fascinating story how deeply people have thought
about how to describe this aspect of the course,
and how profound their thoughts are.

What this book will emphasize, about this
is what I want to tell you in closing
about the quantization of the electromagnetic field
is the following.
We were really working hard with classical field equations
to describe the electromagnetic field, classically,
by completely eliminating redundant variables.
We started with six components of the electric and magnetic
field, and reduced it to two components,
the two components of the [INAUDIBLE] vector potentials.
And as those masters say, as a result
the field can be quantized with the great economy
and the formalism.
If you want to have more sumetric formulations where
you don't eliminate the variables using the Coulomb
gauge, the problem is you have variables
which are not independent.
And now I think if you quantize, you
have to formulate auxiliary conditions between the not
independent operators.
It's aesthetically maybe pleasing
because the approach is more sumetric,
but mathematically it's much more involved.
Anyway, if you're interested, this book
has a wonderful discussion on the different ways how
you can approach interactions of atoms