Generalized Heisenberg-Euler formula in Abelian gauge theory with parity violation

Kimiko Yamashita, Xing Fan, Shusei Kamioka, Shoji Asai, Akio Sugamoto

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


A generalized Heisenberg-Euler formula is given for an Abelian gauge theory having vector as well as axial vector couplings to a massive fermion. So, the formula is applicable to a parity-violating theory. The gauge group is chosen to be U(1). The formula is quite similar to that in quantum electrodynamics, but there is a complexity in which one factor (related to spin) is expressed in terms of the expectation value. The expectation value is evaluated by the contraction with the one-dimensional propagator in a given background field. The formula affords a basis to the vacuum magnetic birefringence experiment, which aims to probe the dark sector, where the interactions of the light fermions with the gauge fields are not necessarily parity conserving.

Original languageEnglish (US)
Article number123B03
JournalProgress of Theoretical and Experimental Physics
Issue number12
StatePublished - Dec 1 2017


  • B30

ASJC Scopus subject areas

  • General Physics and Astronomy


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