The direction of time in quantum field theory

TL;DR

This paper explores how the algebra of observables in quantum field theory inherently breaks time-reversal symmetry, suggesting that such symmetry breaking can be understood through classical random fields when considering covariance.

Contribution

It proposes that the algebra of observables should be time-reversal invariant, with symmetry breaking described by states, leading to a classical continuous random field representation.

Findings

Algebra of observables is invariant under Lorentz and parity but not time reversal.

Time-reversal symmetry breaking is represented by states over the algebra.

Modified algebra corresponds to a classical continuous random field.

Abstract

The algebra of observables associated with a quantum field theory is invariant under the connected component of the Lorentz group and under parity reversal, but it is not invariant under time reversal. If we take general covariance seriously as a long-term goal, the algebra of observables should be time-reversal invariant, and any breaking of time-reversal symmetry will have to be described by the state over the algebra. In consequence, the modified algebra of observables is a presentation of a classical continuous random field.