Non-commutative and commutative vacua effects in a scalar torsion scenario

TL;DR

This paper investigates how non-commutative and commutative vacua influence the phase space of a scalar field within a scalar torsion framework, comparing classical and quantum effects and emphasizing the role of non-commutative parameters.

Contribution

It introduces a detailed analysis of non-commutative parameters in scalar torsion scenarios, highlighting the dominant influence of momentum-related non-commutativity over space-related effects.

Findings

Non-commutative parameter β significantly impacts phase space dynamics.

Comparison between classical and quantum regimes reveals notable differences.

Boundary conditions and interpretations of non-commutativity are thoroughly examined.

Abstract

In this work, the effects of non-commutative and commutative vacua on the phase space generated by a scalar field in a scalar torsion scenario are investigated. For both classical and quantum regimes, the commutative and non-commutative cases are compared. To take account the effects of non-commutativity, two well known non-commutative parameters, $\theta$ and $\beta,$ are introduced. It should be emphasized, the effects of $\beta$ which is related to momentum sector has more key role in comparison to $\theta$ which is related to space sector. Also the different boundary conditions and mathematical interpretations of non-commutativity are explored.