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

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, $θ$ and $β,$ are introduced. It should be emphasized, the effects of $β$ which is related to momentum sector has more key role in comparison to $θ$ which is related to space sector. Also the different boundary conditions and mathematical interpretations of non-commutativity are explored.

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