Reply by author to A. I. Bayoumi and E. M. Abdelrahman

Riad, S.

doi:10.1190/1.1486925

Cited by 14 publications

(24 citation statements)

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“…It should be noted that the form of the latter equation depend essentially on the point of view how to write the action of the spinor field in an external background in the noncommutative space. We consider two possible actions, one obtained from simple Moyal modification [13] (introducing Moyal products into the ordinary Dirac field action [1,2,15,14,16,17,18,19,11,20]) and another action obtained by the so-called Seiberg-Witten (SW) map, see [21,22,23,24,25,26].…”

Section: Introductionmentioning

confidence: 99%

Quantum and pseudoclassical descriptions of nonrelativistic spinning particles in noncommutative space

2010

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We construct a nonrelativistic wave equation for spinning particles in the noncommutative space (in a sense, a θ-modification of the Pauli equation). To this end, we consider the nonrelativistic limit of the θ-modified Dirac equation. To complete the consideration, we present a pseudoclassical model (à la Berezin-Marinov) for the corresponding nonrelativistic particle in the noncommutative space. To justify the latter model, we demonstrate that its quantization leads to the θ-modified Pauli equation. We extract θ-modified interaction between a nonrelativistic spin and a magnetic field from such a Pauli equation and construct a θ-modification of the Heisenberg model for two coupled spins placed in an external magnetic field. In the framework of such a model, we calculate the probability transition between two orthogonal EPR (Einstein-Podolsky-Rosen) states for a pair of spins in an oscillatory magnetic field and show that some of such transitions, which are forbidden in the commutative space, are possible due to the space noncommutativity. This allows us to estimate an upper bound on the noncommtativity parameter. * adorno@dfn.if.usp.br † baldiott@fma.if.usp.br ‡ gitman@dfn.if.usp.br

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Section: Introductionmentioning

confidence: 99%

Quantum and pseudoclassical descriptions of nonrelativistic spinning particles in noncommutative space

2010

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“…(16). One of the most popular approaches of NC theories [13] is the one ruled by the well known Moyal-Weyl product [14]. In this approach, the standard product of two NC objects is substituted by the so-called star-product given by…”

Section: A Noncommutativity In Space-time: a Few Wordsmentioning

confidence: 99%

“…We will use (− + ++) and the summation notation for repeated indices is assumed from now on. Since we know that for two objects within an integral [14] the Moyal-Weyl product can be substituted by an ordinary product, we can write Eq. (18) as…”

Section: B the Nc Space-time Podolsky Modelmentioning

confidence: 99%

Faddeev–Jackiw approach of noncommutative space–time electromagnetic theories

Abreu

Fernandes

Mendes

et al. 2018

Int. J. Mod. Phys. A

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The interest in higher derivatives field theories has its origin mainly in their influence concerning the renormalization properties of physical models and to remove ultraviolet divergences. The noncommutative Podolsky theory is a constrained system that cannot by directly quantized by the canonical way. In this work we have used the Faddeev-Jackiw method in order to obtain the Dirac brackets of the NC Podolsky theory.

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“…and the θ αβ term is the NC contribution. One basic property in NC theory [1] is that the integral over the star product of two quantities is equal to the corresponding integral over the ordinary product [15], leading the action (4) be rewritten in the form…”

Section: Noncommutative Proca Modelmentioning

confidence: 99%

Gauge-invariant extensions of the Proca model in a noncommutative space–time

Abreu

Neto

Fernandes

et al. 2016

Int. J. Mod. Phys. A

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The gauge invariance analysis of theories described in noncommutative (NC) space-times can lead us to interesting results since noncommutativity is one of the possible paths to investigate quantum effects in classical theories such as general relativity, for example. This theoretical possibility has motivated us to analyze the gauge invariance of the NC version of the Proca model, which is a second-class system, in Dirac's classification, since its classical formulation (commutative space-time) has its gauge invariance broken thanks to the mass term. To obtain such gauge invariant model, we have used the gauge unfixing method to construct a first-class NC version of the Proca model. We have also questioned if the gauge symmetries of NC theories, are affected necessarily or not by the NC parameter. In this way, we have calculated its respective symmetries in a standard way via Poisson brackets.

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Reply by author to A. I. Bayoumi and E. M. Abdelrahman

Cited by 14 publications

References 0 publications

Quantum and pseudoclassical descriptions of nonrelativistic spinning particles in noncommutative space

Quantum and pseudoclassical descriptions of nonrelativistic spinning particles in noncommutative space

Faddeev–Jackiw approach of noncommutative space–time electromagnetic theories

Gauge-invariant extensions of the Proca model in a noncommutative space–time

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