• DOI:10.1007/s00023-022-01157-1
• Corpus ID: 235731989

Almost Radial Gauge

@article{Herdegen2022AlmostRG,
  title={Almost Radial Gauge},
  author={Andrzej Herdegen},
  journal={Annales Henri Poincar{\'e}},
  year={2022}
}

• A. Herdegen
• Published 5 July 2021
• Mathematics, Physics
• Annales Henri Poincaré

An almost radial gauge $$A^\mathrm {ar}$$

A
ar

of the electromagnetic potential is constructed for which $$x\cdot A^\mathrm {ar}(x)$$

x
·

A
ar

(
x
)

vanishes arbitrarily fast in timelike directions. This potential is in the class introduced by Dirac with the purpose of forming gauge-invariant quantities in quantum electrodynamics. In the quantum case, the construction of smeared operators $$A^\mathrm {ar}(K)$$

A
ar

(
K
)

is enabled by a natural extension of the free electromagnetic field algebra introduced earlier (represented in a Hilbert space). The space of possible smearing functions K includes vector fields with the asymptotic spacetime behavior typical for scattered currents (the conservation condition in the whole spacetime need not be assumed). This construction is motivated by a possible application to the infrared problem in QED.