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2 votes
1 answer
877 views

Hermitian conjugate of 4-derivative $\partial_\mu$

I want to find the hermitian conjugate of 4-derivative $\partial_\mu$ for the real scalar Lagrangian defined as $$\mathcal{L} = \frac{1}{2} (\partial_\mu \phi)^\dagger(\partial^\mu\phi) - \frac{1}{2}...
3 votes
1 answer
165 views

Schwartz QFT coupling to the photon

I am reading Schwartz's QFT textbook. In Eq. (10.104) he writes: $$ \left[i\partial_\mu-eA_\mu,i\partial_\nu-eA_\nu\right]~=~-e i[\partial_\mu A_{\nu}-\partial_\nu A_{\mu}]~=~ -e i F_{\mu \nu}. \tag{...