Discrete time evolution and energy nonconservation in noncommutative physics

Balachandran, A. P.; Martins, Andrey Gomes; Teotonio-Sobrinho, P.

doi:10.1088/1126-6708/2007/05/066

Cited by 10 publications

(9 citation statements)

References 13 publications

(22 reference statements)

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“…However, it is not clear at all what are the physical consequences of translational symmetry breaking. These consequences should be carefully investigated, especially the possible violation of energy-momentum conservation [73]. Even if this situation with translational symmetry breaking could cause violation of energy-momentum conservation, we point out that in the case of the star product (91), this violation would be so minute, that one could safely neglect it.…”

Section: Concluding Remarks and Discussionmentioning

confidence: 95%

SCALAR FIELD THEORY ON Κ-Minkowski SPACE–TIME AND TRANSLATION AND LORENTZ INVARIANCE

Meljanac

Samsarov

2011

Int. J. Mod. Phys. A

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We investigate the properties of κ-Minkowski spacetime by using representations of the corresponding deformed algebra in terms of undeformed Heisenberg-Weyl algebra. The deformed algebra consists of κ-Poincaré algebra extended with the generators of the deformed Weyl algebra. The part of deformed algebra, generated by rotation, boost and momentum generators, is described by the Hopf algebra structure. The approach used in our considerations is completely Lorentz covariant. We further use an adventages of this approach to consistently construct a star product which has a property that under integration sign it can be replaced by a standard pointwise multiplication, a property that was since known to hold for Moyal, but not also for κ-Minkowski spacetime. This star product also has generalized trace and cyclic properties and the construction alone is accomplished by considering a classical Dirac operator representation of deformed algebra and by requiring it to be hermitian. We find that the obtained star product is not translationally invariant, leading to a conclusion that the classical Dirac operator representation is the one where translation invariance cannot simultaneously be implemented along with hermiticity. However, due to the integral property satisfied by the star product, noncommutative free scalar field theory does not have a problem with translation symmetry breaking and can be shown to reduce to an ordinary free scalar field theory without nonlocal features and tachionic modes and basicaly of the very same form. The issue of Lorentz invariance of the theory is also discussed.

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Section: Concluding Remarks and Discussionmentioning

confidence: 95%

SCALAR FIELD THEORY ON Κ-Minkowski SPACE–TIME AND TRANSLATION AND LORENTZ INVARIANCE

Meljanac

Samsarov

2011

Int. J. Mod. Phys. A

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“…We show that time translation gets quantized on B χ n in units of χ. Elsewhere this effect has been discussed in detail [24,25,26] and it has been proved that energy is conserved only mod 2π χ in scattering processes. A formal scattering theory has also been developed.…”

Section: Jhep00(2009)000mentioning

confidence: 99%

“…The algebra B χ n leads to time-quantization in units of χ and therefore [24,25] energy nonconservation: it is conserved only mod 2π χ . An effect of this sort was first discovered by Chaichian [26] for a cylindrical noncommutative spacetime.…”

Section: Time Quantizationmentioning

confidence: 99%

“…An effect of this sort was first discovered by Chaichian [26] for a cylindrical noncommutative spacetime. Quantum physics on such spacetime including scattering theory was later developed in [25].…”

Section: Time Quantizationmentioning

confidence: 99%

“…As explained in [25,24], a quantum field ψ is defined only on the spectrum of time operator x 0 . Time translations are from one point of this spectrum to another, so that only the time translations (e iχP 0 ) N , N ∈ Z exist on quantum fields.…”

Section: Jhep00(2009)000mentioning

confidence: 99%

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Non-Pauli effects from noncommutative spacetimes

Balachandran

Padmanabhan

2010

J. High Energ. Phys.

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Noncommutative spacetimes lead to nonlocal quantum field theories (qft's) where spin-statistics theorems cannot be proved. For this reason, and also backed by detailed arguments, it has been suggested that they get corrected on such spacetimes leading to small violations of the Pauli principle. In a recent paper [1], Pauli-forbidden transitions from spacetime noncommutativity were calculated and confronted with experiments. Here we give details of the computation missing from this paper. The latter was based on a spacetime B χ n different from the Moyal plane. We argue that it quantizes time in units of χ. Energy is then conserved only mod 2π χ . Issues related to superselection rules raised by non-Pauli effects are also discussed in a preliminary manner.

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Some features of scattering problem in a κ‐Deformed minkowski spacetime

Khodadi

2016

Annalen der Physik

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The doubly special relativity (DSR) theories are suggested in order to incorporate an observerindependent length scale in special theory of relativity. The Magueijo-Smolin proposal of DSR is realizable through a particular form of the noncommutative (NC) spacetime (known as κ-Minkowski spacetime) in which the Lorentz symmetry is preserved. In this framework, the NC parameter κ provides the origin of natural cutoff energy scale. Using a nonlinear deformed relativistic dispersion relation along with the Lorentz transformations, we investigate some phenomenological facets of two-body collision problem (without creation of new particles) in a κ-Minkowski spacetime. By treating an elastic scattering problem, we study effects of the Planck scale energy cutoff on some relativistic kinematical properties of this scattering problem. The results are challenging in the sense that as soon as one turns on the κ-spacetime extension, the nature of the two-body collision alters from elastic to inelastic one. It is shown also that a significant kinematical variable involving in heavy ion collisions, the rapidity, is not essentially an additive quantity under a sequence of the nonlinear representation of the Lorentz transformations. 4 In the framework of Newtonian kinematics and for the case of two equal masses m1 = m2, the ratio K 1,a K 1,b in terms of ψ results in the simple relation K 1,a K 1,b = cos 2 ψ which the laboratory scattering angle ψ is limited to the interval 0 ≤ ψ ≤ π 2 . For more details one can see "Classical Mechanics" text book such as Ref. [86]. If ψ = 0 then K 1,a K 1,b = 1, namely, no collision takes place since the speed remains constant before and after the collision and no momentum is transferred to particle-2. However, if ψ → π

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Discrete time evolution and energy nonconservation in noncommutative physics

Cited by 10 publications

References 13 publications

SCALAR FIELD THEORY ON Κ-Minkowski SPACE–TIME AND TRANSLATION AND LORENTZ INVARIANCE

SCALAR FIELD THEORY ON Κ-Minkowski SPACE–TIME AND TRANSLATION AND LORENTZ INVARIANCE

Non-Pauli effects from noncommutative spacetimes

Some features of scattering problem in a κ‐Deformed minkowski spacetime

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