Revisiting Quantization of Gauge Field Theories: Sandwich Quantization Scheme

TL;DR

This paper revisits gauge field theory quantization, proposing a novel 'sandwich' scheme that imposes constraints between physical states, revealing new solutions and insights into the structure of gauge systems.

Contribution

It introduces the 'sandwich quantization scheme' for gauge theories, providing a new perspective on constraint implementation and uncovering previously unrecognized solutions.

Findings

Sandwich constraints can be solved with new solutions.

The scheme offers a different understanding of gauge constraints.

Potential implications for physical state characterization.

Abstract

Quantization of field theories with gauge symmetry is an extensively discussed and well-established topic. In this short note, we revisit this old problem. While we confirm all details of the existing literature, we highlight a potentially important point which may provide a better understanding of and insights on the quantization of gauged systems. The gauge degrees of freedom have vanishing momenta, and hence their equations of motion appear as constraints on the system. We argue that to ensure consistency of quantization one can impose these constraints as ``sandwich conditions'': The physical Hilbert space of the theory consists of all states for which the constraints sandwiched between any two physical states vanish. We solve the sandwich constraints and show they have solutions not discussed in the gauge field theory literature. We briefly discuss the physical meaning of these solutions and the implications of the "sandwich quantization scheme".