2015/01/08 by Éverton M. C. Abreu, M. J. Neves, Abreu, Everton M. C. +3
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Analysis and Transform Methods #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.1501.01912
openalex publication_date 2015/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The so-called canonical noncommutativity is based on a constant noncommutative parameter (θ). However, this formalism breaks Lorentz invariance and one way to recover it is to define the NC parameter as a variable, an extra coordinate of the system. One approach that uses the variable θ was developed by Doplicher, Fredenhagen and Roberts (DFR) and hence, their phase-space is formed by (x,p,θ) with extra-dimensions. In this work we have demonstrated precisely that this phase-space is incomplete because the variable θ requires an associated momentum and the so-called DFR phase-space is in fact formed by (x, p, θ, π), where π is an useful object. One of the models used here to demonstrate this fact brought other interesting results. We have used this complete phase-space to explain some undefined results in the θ-variable literature. Finally, we have shown the importance of this DFR-momentum since with it we could fill the gap that exist in θ-variable results. In other words, we have computed the field commutation relations of a QFT in this DFR phase-space. The results obtained here match exactly with the postulated (not demonstrated) values that dwell in the DFR literature.