Quantisation of Lorentz invariant scalar field theory in noncommutative spacetime and its consequence
Abstract
Quantisation of Lorentz invariant scalar field theory in DoplicherFredenhagenRoberts (DFR) spacetime, a Lorentz invariant, noncommutative spacetime is studied. We use an approach to quantisation that is based on the equations of motion alone and derive the equal time commutation relation between DoplicherFredenhagenRobertsAmorim (DFRA) scalar field and its conjugate, which has noncommutative dependent modifications, but the corresponding creation and annihilation operators obey usual algebra. We show that imposing the condition that the commutation relation between the field and its conjugate is same as that in the commutative spacetime leads to a deformation of the algebra of quantised oscillators. Both these deformed commutation relations derived are valid to all orders in the noncommutative parameter. By analysing the first nonvanishing terms which are θ^{3} order, we show that the deformed commutation relations scale as 1 /λ^{4}, where λ is the length scale set by the noncommutativity of the spacetime. We also derive the conserved currents for DFRA scalar field. Further, we analyse the effects of noncommutativity on Unruh effect by analysing a detector coupled to the DFRA scalar field, showing that the Unruh temperature is not modified but the thermal radiation seen by the accelerated observer gets correction due to the noncommutativity of spacetime.
 Publication:

Nuclear Physics B
 Pub Date:
 January 2022
 DOI:
 10.1016/j.nuclphysb.2021.115633
 arXiv:
 arXiv:2110.03897
 Bibcode:
 2022NuPhB.97415633H
 Keywords:

 High Energy Physics  Theory
 EPrint:
 25 pages