The QED(0+1) model and a possible dynamical solution of the strong CP problem

TL;DR

This paper studies a simplified quantum mechanical model analogous to the Schwinger model, showing how boundary conditions and theta sectors can dynamically resolve the strong CP problem by selecting a specific theta value.

Contribution

It introduces a QED(0+1) model as a prototype for gauge theories, demonstrating a natural dynamical mechanism for solving the strong CP problem through boundary conditions and theta-sector analysis.

Findings

The model reproduces standard results for massless fermions in infinite volume.

For non-zero mass, the sector with theta = theta_M is dynamically selected.

The approach exploits theta-dependence of free energy to find a unique minimum.

Abstract

The QED(0+1) model describing a quantum mechanical particle on a circle with minimal electromagnetic interaction and with a potential -M cos(phi - theta_M), which mimics the massive Schwinger model, is discussed as a prototype of mechanisms and infrared structures of gauge quantum field theories in positive gauges. The functional integral representation displays a complex measure, with a crucial role of the boundary conditions, and the decomposition into theta sectors takes place already in finite volume. In the infinite volume limit, the standard results are reproduced for M=0 (massless fermions), but one meets substantial differences for M not = 0: for generic boundary conditions, independently of the lagrangean angle of the topological term, the infinite volume limit selects the sector with theta = theta_M, and provides a natural "dynamical" solution of the strong CP problem. In comparison with previous approaches, the strategy discussed here allows to exploit the consequences of the theta-dependence of the free energy density, with a unique minimum at theta = theta_M.