Extending Hamilton's principle to quantize classical fields

TL;DR

This paper extends Hamilton's principle to classical fields with specific boundary conditions, deriving quantization conditions akin to Bohr-Sommerfeld rules, and applies this to angular momentum measurements of a scalar field.

Contribution

It introduces a novel extension of Hamilton's principle to certain boundary conditions, leading to a new perspective on quantization in classical fields.

Findings

Quantization conditions are derived for classical scalar fields.

The approach is analogous to Bohr-Sommerfeld quantization.

Application to angular momentum measurements demonstrates the theory.

Abstract

Hamilton's principle does not formally apply to systems whose boundary conditions lie outside configuration space, but extensions are possible using certain "natural" boundary conditions that allow action extremization. With the single conjecture that only such action-extremizing boundaries can be physically realized, the classical relativistic scalar field becomes subject to certain quantization conditions upon measurement. These conditions appear to be analogous to Bohr-Sommerfeld quantization, and are derived explicitly for the case of angular momentum measurements of a classical scalar field.