On Verification of the Non-Generational Conjectural- Derivation of First Class constraints: HP Monopole's Field case

TL;DR

This paper extends the verification of a non-generational conjectural method for deriving first class constraints to the case of the 't Hooft-Polyakov monopole's field, aligning with results obtained via Dirac's algorithm.

Contribution

It provides further validation of the conjectural derivation method for gauge field theories, specifically applying it to the HP monopole's field in the Higgs vacuum.

Findings

Reproduces results consistent with Dirac's algorithm

Validates the conjecture for the 't Hooft-Polyakov monopole case

Supports the method's applicability to complex gauge fields

Abstract

In [7] we proposed a non-generational conjectural derivation of all first class constraints (involving, only, variables compatible with canonical Poisson brackets) for realistic gauge (singular) field theories; and we verified the conjecture in cases of electromagnetic field, Yang Mills fields interacting with scalar and spinor fields, and the gravitational field. Here we will further verify our conjecture for the case of 't Hooft- Polyakov (HP) monopole's field (i.e. in the Higgs Vacuum); and show that we will reproduce the results in Ref.[6], which we reached at using Dirac's standard multi-generational algorithm.