Valid for Much of "Realistic" Fields: A Non-Generational Conjecture For Deriving All First-Class Constraints at Once

TL;DR

This paper introduces a single-step conjecture for deriving all first-class constraints in realistic gauge singular field theories, verified across several fundamental physical models.

Contribution

It proposes a non-generational, one-step conjecture for first-class constraints, simplifying the traditional multi-step Dirac algorithm, with validation on key physical theories.

Findings

Reproduces constraints obtained by Dirac's algorithm

Validated on electromagnetic, Yang-Mills, and gravitational fields

Shows applicability to a wide range of realistic physical theories

Abstract

We propose a single-step non-generational conjecture of all first class constraints,(involving only variables compatible with canonical Poisson brackets), for a realistic gauge singular field theory. We verify our proposal for the free electromagnetic field, Yang-Mills fields in interaction with spinor and scalar fields, and we also verify our proposal in the case gravitational field. We show that the first class constraints which were reached at using the standard Dirac's multi-generational algorithm will be reproduced using the proposed conjecture. We make no claim that our conjecture will be valid for all mathematically plausible Lagrangians; but, nevertheless the examples we consider here show that this conjecture is valid for wide range or much of realistic fields of physical interest that are know to exist and are manifested in nature