- #1
Vic Sandler
- 4
- 3
The problem is on pages 323 and 324 of the second edition.
Given the lagrangian
[tex]\mathcal{L} = -\frac{1}{4}F_{\mu\nu}(x)F^{\mu\nu}(x) - \frac{1}{2}(n_{\mu}A^{\mu})^2[/tex]
show that the momentum space photon propoagator is given by
[tex]D_F^{\mu\nu}(k) = \frac{-g^{\mu\nu} - k^{\mu}k^{\nu}(n^2 + k^2)/(kn)^2 + (n^{\mu}k^{\nu} + n^{\nu}k^{\mu})/(kn)}{k^2 + i\epsilon}[/tex]
I can solve this problem if I replace the factor [itex](n^2 + k^2)[/itex] with [itex](n^2 - k^2)[/itex].
My question is this:
Should the book say [itex](n^2 - k^2)[/itex] and not [itex](n^2 + k^2)[/itex]?
This question and this question only. The meat of the answer will be one word.
Homework Statement
Given the lagrangian
[tex]\mathcal{L} = -\frac{1}{4}F_{\mu\nu}(x)F^{\mu\nu}(x) - \frac{1}{2}(n_{\mu}A^{\mu})^2[/tex]
show that the momentum space photon propoagator is given by
[tex]D_F^{\mu\nu}(k) = \frac{-g^{\mu\nu} - k^{\mu}k^{\nu}(n^2 + k^2)/(kn)^2 + (n^{\mu}k^{\nu} + n^{\nu}k^{\mu})/(kn)}{k^2 + i\epsilon}[/tex]
Homework Equations
The Attempt at a Solution
I can solve this problem if I replace the factor [itex](n^2 + k^2)[/itex] with [itex](n^2 - k^2)[/itex].
My question is this:
Should the book say [itex](n^2 - k^2)[/itex] and not [itex](n^2 + k^2)[/itex]?
This question and this question only. The meat of the answer will be one word.