Kinetic theory in curved space: a first quantised approach

TL;DR

This paper develops a first quantised real-time formalism for non-equilibrium many-body theory in curved spacetime, unifying thermal and cosmological fluxes and ensuring covariance under particle definition changes.

Contribution

It introduces a novel path integral regulation method for relativistic particles, unifies different flux scenarios, and extends the formalism to curved space and string backgrounds.

Findings

Regulation of propagators yields Feynman and complex conjugate propagators.

Mixing propagator regulations models particle flux in curved spacetime.

Formalism applies to both thermal and cosmological fluxes, maintaining covariance.

Abstract

We study the real time formalism of non-equilibrium many-body theory, in a first quantised language. We argue that on quantising the relativistic scalar particle in spacetime with Minkowski signature, we should study both propagations $e^{i(p^2-m^2)\tilde \lambda}$ and $e^{-i(p^2-m^2)\tilde \lambda}$ on the particle world line. The path integral needs regulation at the mass shell $p^2=m^2$. If we regulate the two propagations independently we get the Feynman propagator in the vacuum, and its complex conjugate. But if the regulation mixes the two propagations then we get the matrix propagator appropriate to perturbation theory in a particle flux. This formalism unifies the special cases of thermal fluxes in flat space and the fluxes `created' by Cosmological expansion, and also gives covariance under change of particle definition in curved space. We comment briefly on the proposed application to closed strings, where we argue that coherent fields and `exponential of quadratic' particle fluxes must {\it both} be used to define the background for perturbation theory.