The Treatment of conformable systems with second class constraints

TL;DR

This paper extends the Dirac theory to conformable singular systems with second-class constraints, introducing a conformable Poisson bracket and demonstrating the approach with an example that aligns with classical results when a parameter equals one.

Contribution

It develops a conformable Dirac theory for singular systems with second-class constraints, including a new conformable Poisson bracket and an illustrative example.

Findings

The conformable Poisson bracket is successfully defined.

The conformable Dirac theory is consistent with classical results when alpha=1.

An example demonstrates the applicability of the developed theory.

Abstract

In this work, a conformable singular system with second-class constraints is discussed. The conformable Poisson bracket (CDB) of two functions is defined. and, the Dirac theory is developed to be applicable to conformable singular systems. In addition, to demonstrate the theory an illustrative example is given and solved, the results are found to be in agreement with ref \cite{rabei1992hamilton} when $\alpha=1$.