Relativistic corrections to the Moyal-Weyl spacetime

2019

Rev. Escuela Física

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Generators of the Poincaré group, for a free massive scalar field, are usually expressed in the momentum space. In this work we perform a transformation of these generators into the coordinate space. This (spatial)-position space is spanned by eigenvectors of the Newton-Wigner-Pryce operator. The motivation is twofold. First, we want to investigate the localization of a relativistic particle. Furthermore, we need a deeper understanding of the commutative spatial coordinate space in QFT, in order to investigate the non-commutative version thereof.

Section: Poincaré Groupsupporting

confidence: 73%

Remarks on QFT in the Coordinate Space

2019

Rev. Escuela Física

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“…This is stems from the fact that ladder operators do not explicitly depend on the mass. The commutation relations between the spatialmomentum operator and the NWP-operator are given by, see [SS09] or [Muc15],…”

Section: Massless Nwp-operatormentioning

confidence: 99%

Massless QFT and the Newton-Wigner Operator

2019

Rev. Escuela Física

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“…In particular the question that is answered in this context is the following: Can we obtain a noncommutative spacetime in a addition to the Snyder type one, by a strict deformation quantization? And if so, will there be terms resembling additional relativistic corrections like in example for [Muc15a]? To answer these questions, we need to evaluate the commutator of the deformed Coleman-Mandula operators.…”

Section: Extending Snyder-spacetime By Deformationmentioning

confidence: 99%

“…To answer these questions, we need to evaluate the commutator of the deformed Coleman-Mandula operators. The generators of deformation are in this context (as in [And13], [Muc14] and [Muc15a]) the momentum operators. Moreover, in order to preform the deformation quantization we need to prove that the deformation of these unbounded operators is well-defined.…”

Section: Extending Snyder-spacetime By Deformationmentioning

confidence: 99%

A Poincaré covariant noncommutative spacetime

Int. J. Geom. Methods Mod. Phys.

Vergara

2018

We interpret, in the realm of relativistic quantum field theory, the tangential operator given by Coleman, Mandula [CM67] (see also [MPS16]) as an appropriate coordinate operator. The investigation shows that the operator generates a Snyder-like noncommutative spacetime with a minimal length that is given by the mass. By using this operator to define a noncommutative spacetime, we obtain a Poincaré invariant noncommutative spacetime and in addition solve the soccer-ball problem. Moreover, from recent progress in deformation theory we extract the idea how to obtain, in a physical and mathematical well-defined manner, an emerging noncommutative spacetime. This is done by a strict deformation quantization known as Rieffel deformation (or warped convolutions). The result is a noncommutative spacetime combining a Snyder and a Moyal-Weyl type of noncommutativity that in addition behaves covariant under transformations of the whole Poincaré group. Discussion 16Conventions 0.1. We use d = n + 1, for n ∈ N and the Greek letters are split into µ, ν = 0, . . . , n. Moreover, we use Latin letters for the spatial components which run from 1, . . . , n and we choose the following convention for the Minkowski scalar product of d-dimensional vectors, a · b = a 0 b 0 + a k b k = a 0 b 0 − a · b. Furthermore, we use the common symbol S (R n,d ) for the Schwartz-space and H for a Hilbert space. * amuch@matmor.unam.mx † vergara@nucleares.unam.mx 2