A state description of pair production from Dirac sea in gravitational field --physical interpretation of Weyl anomaly--

TL;DR

This paper presents a novel interpretation of Weyl anomaly as resulting from pair production in a gravitational field, using a Fock space approach to connect vacuum states before and after Weyl transformations.

Contribution

It introduces a new physical mechanism linking pair production to Weyl anomaly via the Dirac sea and Fock space states in curved spacetime.

Findings

Weyl symmetry breaking is linked to pair production in the Dirac sea.

The vacuum in curved spacetime can be viewed as a pair-produced state after Weyl transformation.

The Ricci scalar R relates to the trace of the energy-momentum tensor, explaining Weyl anomaly.

Abstract

We present the method that the pair production of particles is described as a Fock space state vector, where the pair production stems from receiving energy from, as an example, gravitational background field. At the same time we show a sort of new mechanism that in the diffeomorphism-invariant Dirac sea the Weyl symmetry is broken due to the pair production and this provides us a new physical interpretation of the origin of Weyl anomaly. In the present paper at the first place, we consider two kinds of background space-time which are connected each other by the Weyl transformation. It is shown that the vacuum, i.e. Dirac sea, in the "curved" space-time \underline{after} making Weyl transformation is nothing but the pair produced state provided we consider the state in terms of the Fock space basis in the "flat" space-time \underline{before} making the Weyl transformation. When summing up with respect to the time the contribution of pair production of each time-slice we obtain the Ricci scalar $R$ and then it is related to the trace part $\left\langle T^{\mu}_{\> \mu}\right\rangle$ of the energy-momentum tensor to produce Weyl anomaly.