MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Spacetime Dependence of Local Temperature in Relativistic Quantum Field Theory

Michael Gransee


The spacetime dependence of the inverse temperature four-vector $\boldsymbol{\beta}$ for certain states of the quantized Klein-Gordon field on (parts of) Minkowski spacetime is discussed. These states fulfill a recently proposed version of the Kubo-Martin-Schwinger (KMS) boundary value condition, the so-called "local KMS (LKMS) condition". It turns out that, depending on the mass parameter $m\geq 0$, any such state can be extended either
(i) to a LKMS state on some forward or backward lightcone, with $\boldsymbol{\beta}$ depending linearily on spacetime, or
(ii) to a thermal equilibrium (KMS) state on all of Minkowski space with constant $\boldsymbol{\beta}$.

This parallels previously known results for local thermal equilibrium (LTE) states of the quantized Klein-Gordon field. Furthermore, in the case of a massless field our results point to a discrepancy with some classic results in general approaches to (non-quantum) relativistic thermodynamics.

MSC Codes:
81T28, 81T05, 82C10
local KMS condition, local equilibrium, thermal quantum field theory

Related publications

2016 Repository Open Access
Michael Gransee

Spacetime dependence of local temperature in relativistic quantum field theory