Noncommutative geometry induced by spin effects

Colatto, L. P.; Penna, A. L. A.; Santos, Wytler Cordeiro dos

doi:10.1103/physrevd.73.105007

Cited by 10 publications

(13 citation statements)

References 71 publications

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“…In this work we shall derive quantum mechanics from an action for electrodynamics formulated on a noncommutative spacetime taking the fields in the enveloping algebra. The case of Lie algebra valued fields has been treated in the literature [4][5][6][7][8][9][10]. Our main motivation to study quantum mechanics using the enveloping algebra approach [11][12][13][14] is that this approach allows a formulation of the standard model on a noncommutative spacetime [14].…”

Section: Introductionmentioning

confidence: 99%

Quantum mechanics on noncommutative spacetime

Calmet¹,

Selvaggi²

2006

Phys. Rev. D

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We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a non-relativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical noncommutative spacetime. An interesting new feature of quantum mechanics formulated on a noncommutative spacetime is an intrinsic electric dipole moment. We note however that noncommutative intrinsic dipole moments are not observable in present experiments searching for an EDM of leptons or nuclei such as the neutron since they are spin independent. These experiments are sensitive to the energy difference between two states and the noncommutative effect thus cancels out. Bounds on the noncommutative scale found in the literature relying on such intrinsic electric dipole moment are thus incorrect. * xcalmet@ulb.ac.be

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Section: Introductionmentioning

confidence: 99%

Quantum mechanics on noncommutative spacetime

Calmet¹,

Selvaggi²

2006

Phys. Rev. D

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“…As to the case without θ 0i components, the two parameters are chosen to be orthogonal to the angular momentum. Hence, the anomaly angular momentum distribution will be naturally modified [10], and the ABJ anomaly produced from noncommutative bosonic gas, with θ ij components, under the product of [ , J θ ] ⋆ emerged into noncommutative departure coupling to commutative field [11]. Otherwise, we show that geometric fluctuations either generates ABJ anomaly in fermion action without taking account of M oyal W eyl product between each particle fields.…”

Section: Introductionmentioning

confidence: 80%

Modulation Field Induces Universe Rotation

Chen

2008

Preprint

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In this paper, we consider a time dependent module field on spacetime extension without modifying commutative relation on noncommutative quantum plane. The significant idea is that Lorentz symmetry is conserved in module and unmodule coordinate. We focus on the redefinition of spacetime structure without considering noncommutative bosonic gas in deforming the product between fields. Which the null vector is a vector on orthogonal D dimensional Hilbert spacetime. In Riemann geometry, the equation of motion is deformed from an induced rotation. Particle field survives on the state composed by two theoretical assumed null vectors, one is commutative, another is anticommutative. In the point of view, neutrino and photon mass are produced by its shift, the rotated effect generates a horizon in redefining particle field.

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“…It would be interesting to uplift our model along these stated directions to uncover fully this surprising hint of a relationship between noncommutative geometry and spin structures. Indeed, in this aspect, a first step was made in [21] and [22] where the noncommutative parameter θ is tied to a local spin structure S = m 2 θ. In contrast, our progagator has a spin-1/2 Pauli Hamiltonian partially emerging as the effective theory.…”

Section: The Free Particlementioning

confidence: 99%

A coherent-state-based path integral for quantum mechanics on the Moyal plane

Tan¹

2006

J. Phys. A: Math. Gen.

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Inspired by a recent work that proposes using coherent states to evaluate the Feynman kernel in noncommutative space, we provide an independent formulation of the path-integral approach for quantum mechanics on the Moyal plane, with the transition amplitude defined between two coherent states of mean position coordinates. In our approach, we invoke solely a representation of the noncommutative algebra in terms of commutative variables. The kernel expression for a general Hamiltonian was found to contain gaussian-like damping terms, and it is non-perturbative in the sense that it does not reduce to the commutative theory in the limit of vanishing θ -the noncommutative parameter. As an example, we studied the free particle's propagator which turned out to be oscillating with period being the product of its mass and θ. Further, it satisfies the Pauli equation for a charged particle with its spin aligned to a constant, orthogonal B field in the ordinary Landau problem, thus providing an interesting evidence of how noncommutativity can induce spin-like effects at the quantum mechanical level. *

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Noncommutative geometry induced by spin effects

Cited by 10 publications

References 71 publications

Quantum mechanics on noncommutative spacetime

Quantum mechanics on noncommutative spacetime

Modulation Field Induces Universe Rotation

A coherent-state-based path integral for quantum mechanics on the Moyal plane

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