Rotating fermions inside a cylindrical boundary

TL;DR

This paper investigates quantum fermion fields inside a cylindrical boundary in Minkowski space, analyzing how boundary conditions affect thermal states, expectation values, and Casimir divergences.

Contribution

It introduces a detailed analysis of rotating fermion states with different boundary conditions and computes their thermal expectation values and Casimir divergences.

Findings

Expectation values are finite inside the cylinder.

Boundary conditions influence the divergence rate of Casimir effects.

Thermal expectation values depend on the choice of boundary conditions.

Abstract

We study a quantum fermion field inside a cylinder in Minkowski space-time. On the surface of the cylinder, the fermion field satisfies either spectral or MIT bag boundary conditions. We define rigidly-rotating quantum states in both cases, assuming that the radius of the cylinder is sufficiently small that the speed-of-light surface is excluded from the space-time. With this assumption, we calculate rigidly-rotating thermal expectation values of the fermion condensate, neutrino charge current and stress-energy tensor relative to the bounded vacuum state. These rigidly-rotating thermal expectation values are finite everywhere inside and on the surface of the cylinder and their detailed properties depend on the choice of boundary conditions. We also compute the Casimir divergence of the expectation values of these quantities in the bounded vacuum state relative to the unbounded Minkowski vacuum. We find that the rate of divergence of the Casimir expectation values depends on the conditions imposed on the boundary.