On Spin-Statistics and Bogoliubov Transformations in Flat Spacetime With Acceleration Conditions

TL;DR

This paper explores how acceleration and boundary conditions in flat spacetime influence the spin-statistics connection of a scalar field, revealing that acceleration can manifest the fundamental relation between spin and statistics.

Contribution

It demonstrates that acceleration and boundary conditions can reveal the spin-statistics connection through Bogoliubov transformations in flat spacetime.

Findings

Particles obey the same statistics in in- and out-modes.

Acceleration can manifest the spin-statistics connection.

Boundary conditions lead to thermal radiation emission.

Abstract

A single real scalar field of spin zero obeying the Klein-Gordon equation in flat space-time under external conditions is considered in the context of the spin-statistics connection. An imposed accelerated boundary on the field is made to become, in the far future, (1) asymptotically inertial and (2) asymptotically non-inertial (with an infinite acceleration). The constant acceleration Unruh effect is also considered. The systems involving non-trivial Bogoliubov transformations contain dynamics which point to commutation relations. Particles described by in-modes obey the same statistics as particles described by out-modes. It is found in the non-trivial systems that the spin-statistics connection can be manifest from the acceleration. The equation of motion for the boundary which forever emits thermal radiation is revealed.