Rotating quantum states

Victor E Ambruş,Elizabeth Winstanley

doi:10.1016/j.physletb.2014.05.031

Abstract

We revisit the definition of rotating thermal states for scalar and fermion fields in unbounded Minkowski space–time. For scalar fields such states are ill-defined everywhere, but for fermion fields an appropriate definition of the vacuum gives thermal states regular inside the speed-of-light surface. For a massless fermion field, we derive analytic expressions for the thermal expectation values of the fermion current and stress–energy tensor. These expressions may provide qualitative insights into the behaviour of thermal rotating states on more complex space–time geometries.

Highlights

In the canonical quantisation of a free field, an object of fundamental importance is the vacuum state, from which states containing particles are constructed
For a quantum fermion field, both positive and negative frequency fermion modes have positive Dirac norm, so the split of the field modes into positive and negative frequency is less constrained compared with the scalar field case
This toy model reveals that there are quantum states which can be defined for a fermion field but which have no analogue for scalar fields

Summary

Introduction

In the canonical quantisation of a free field, an object of fundamental importance is the vacuum state, from which states containing particles are constructed. The definition of a vacuum state is dependent on how the field modes are split into positive and negative frequency modes. This split is restricted for a quantum scalar field by the fact that positive frequency modes must have positive Klein-Gordon norm. In this letter we explore this difference between scalar and fermion quantum fields by considering the definition of rotating vacuum and thermal states in Minkowski space. This toy model reveals that there are quantum states which can be defined for a fermion field but which have no analogue for scalar fields

Rotating scalars

Conclusions