- #1

Judas503

- 23

- 0

## Homework Statement

I have the following massive spin-1 propagator-

$$ D^{\mu\nu}(k)=\frac{\eta^{\mu\nu}-\frac{k^{\mu}k^{\nu}}{m^2}}{k^2 - m^2} $$

I want to write down the propagator in the imaginary time formalism commonly used in thermal field theories.

## Homework Equations

## The Attempt at a Solution

Factorizing the denominator is easy:

$$ k^2 - m^2 = (k^0)^2 - \mathbf{k}^2 - m^2 $$

Then, the following substitution can be used:

$$ \omega_{k}=\mathbf{k}^2 + m^2 $$

and, $$ k^0 = i\omega_{n}=\frac{2n\pi i}{\beta} $$

However, the problem lies in simplifying the numerator. Any help would be really appreciated.