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Canonical quantization of the electromagnetic field in arbitrary xi-gauge

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arxiv 2211.16870 v1 pith:KLCOIG55 submitted 2022-11-30 hep-th

Canonical quantization of the electromagnetic field in arbitrary $\xi$-gauge

classification hep-th
keywords gaugebrstelectromagneticfieldparameterquantizationarbitrarycanonical
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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abstract

We carry out the canonical quantization of the electromagnetic field in arbitrary $\xi$-gauge and compute its propagator. In this way we fill a gap in the literature and clarify some existing confusion about Feynman $i\epsilon$ prescription for the propagator of the electromagnetic field. We also discuss the BRST quantization and investigate the apparent singularities present in the theory when the gauge parameter $\xi$ takes the value -1. We find that this is a mere artifact due to the choice of basic modes and show that in the appropriate basis the commutation relations and the BRST transformation are, in fact, independent of the gauge parameter. The latter only appears as the coefficient of a BRST exact term in the Hamiltonian, which constitutes an extremely simple proof of the independence of any physical process on the gauge parameter $\xi$.

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