- #1

- 46

- 2

## Homework Statement

https://i.imgur.com/sI3JiB4.jpg

https://i.imgur.com/PLpnPZw.jpg

**I have no idea how to solve the first question about the vacuum energy. I solved the second and third problems, but I'm hopelessly stuck at the first.**

2. Homework Equations

2. Homework Equations

The Hamiltonian can be written as ##H_H=\int \frac{\mathrm{d} k}{2 \pi 2\omega_k}\left(A(k) A^\dagger (k)+A^\dagger (k) A(k) \right)## and the canonical commutation relations apply:

##[A(k), A(k')]=0, [A^\dagger(k), A^\dagger(k')]=0, [A(k), A^\dagger (k')]=2 \pi 2 \omega_k \delta(k-k')##

## The Attempt at a Solution

The trouble is that I have no idea how to begin to solve this question.

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