Non-trivial classical backgrounds with vanishing quantum corrections

TL;DR

This paper investigates classical electromagnetic and gravitational backgrounds with zero scalar invariants, proposing that such configurations do not produce quantum effects like vacuum polarization or particle creation, and verifies this through explicit calculations.

Contribution

It introduces and verifies a conjecture that backgrounds with all scalar invariants zero have no quantum corrections, expanding understanding of quantum effects in classical fields.

Findings

Effective lagrangian vanishes for these backgrounds

No particle production occurs in these configurations

Results apply to both electromagnetic and gravitational fields

Abstract

Vacuum polarization and particle production effects in classical electromagnetic and gravitational backgrounds can be studied by the effective lagrangian method. Background field configurations for which the effective lagrangian is zero are special in the sense that the lowest order quantum corrections vanishes for such configurations. We propose here the conjecture that there will be neither particle production nor vacuum polarization in classical field configurations for which all the scalar invariants are zero. We verify this conjecture, by explicitly evaluating the effective lagrangian, for non-trivial electromagnetic and gravitational backgrounds with vanishing scalar invariants. The implications of this result are discussed.