Gauge Interaction as Periodicity Modulation

TL;DR

This paper offers a geometric interpretation of gauge invariance using compact space-time dimensions, linking gauge interactions to boundary deformations and exploring quantum behavior through periodic boundary conditions, with a focus on abelian theories.

Contribution

It introduces a novel geometric framework connecting gauge invariance to boundary deformations in compact space-time, and relates local symmetries to space-time transformations, providing insights into quantum gauge interactions.

Findings

Maxwell's gauge invariance derived from variational principle

Periodic boundary conditions serve as semi-classical quantization

Formal correspondence with scalar QED in abelian case

Abstract

The paper is devoted to a geometrical interpretation of gauge invariance in terms of the formalism of field theory in compact space-time dimensions [arXiv:0903.3680]. In this formalism, the kinematic information of an interacting elementary particle is encoded on the relativistic geometrodynamics of the boundary of the theory through local transformations of the underlying space-time coordinates. Therefore, gauge interaction is described as invariance of the theory under local deformations of the boundary, the resulting local variations of field solution are interpreted as internal transformations, and the internal symmetries of the gauge theory turn out to be related to corresponding local space-time symmetries. In the case of local infinitesimal isometric transformations, Maxwell's kinematics and gauge invariance are inferred directly from the variational principle. Furthermore we explicitly impose periodic conditions at the boundary of the theory as semi-classical quantization condition in order to investigate the quantum behavior of gauge interaction. In the abelian case the result is a remarkable formal correspondence with scalar QED.