Lecture 4 - Non covariant quantization of EM field

Question 1

What is the gauge condition for the Coulomb gauge

Answer 1

nabla cdot A(r,t) = 0

Question 2

For each time t the vector potential A(x,t) is a sum over two variables, what?

Answer 2

Sum over k and r, making up the modes.

Question 3

How is non-covariant quantization of the electromagnetic field done?

Answer 3

1. Introduce a infinitely large volume L^3
2. Impose periodic boundary conditions for vector potential A
3. Impose expressions for a and a* in terms of new coordinates p and q.
4. Impose canonical commutation relations on q and p (these are equivalent to those of a and a-dagger)

Question 4

Is the number operator definite positive?

Answer 4

Yes

Question 5

What are the eigenvalues of the number operators?

Answer 5

Positive integers and zero

Question 6

For what purpose is Ferm’s golden rule used?

Answer 6

To calculate the probability for a transition