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

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, $\hat{I}¸$ and ${\hat{I}}^2,$ are introduced. It should be emphasized, the effects of ${\hat{I}}^2$ which is related to momentum sector has more key role in comparison to $\hat{I}¸$ which is related to space sector. Also the different boundary conditions and mathematical interpretations of non-commutativity are explored.

10 pages, Accepted for publication in Physics Letters B (July/30/2015)