Feynman path integral on the non-commutative plane

Smailagić, Anais; Spallucci, Euro

doi:10.1088/0305-4470/36/33/101

Cited by 289 publications

(354 citation statements)

References 15 publications

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“…Then, solving the Einstein equations (3 ) we find Reissner-Nordstrøm like the metric : The line element (6) shows an interesting asymptotic behavior for small r. By using the asymptotic form of the lower incomplete gamma-function one sees that F ( r ) ∼ O ( r 6 ) and the metric (6) is of the deSitter type…”

mentioning

confidence: 92%

“…Putting gravity aside for a moment, let us consider the effect of non-commuting coordinates on an elementary charge. We have shown that the coordinate fluctuations can be described, within coherent states approach, as a smearing effect [6], turning point-like mass into a "matter droplet" with a gaussian profile. As coordinate non-commutativity is a property of the spacetime fabric itself, and not of its matter content, the same smearing effect is expected to operate on electric as well as "inertial" charges, i.e.…”

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confidence: 99%

“…6 It may seem surprising that there are no charge contributions to the effective cosmological constant. This is due to the linear behavior of the electric field at short distance, as seen from Fig.…”

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confidence: 99%

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Non-commutative geometry inspired charged black holes

et al. 2007

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We find a new, non-commutative geometry inspired, solution of the coupled EinsteinMaxwell field equations describing a variety of charged, self-gravitating objects, including extremal and non-extremal black holes. The metric smoothly interpolates between deSitter geometry, at short distance, and Reissner-Nordstrøm geometry far away from the origin. Contrary to the ordinary Reissner-Nordstrøm spacetime there is no curvature singularity in the origin neither "naked" nor shielded by horizons. We investigate both Hawking process and pair creation in this new scenario.In a recent paper we obtained a non-commutative geometry inspired solution of the Einstein equation smoothly interpolating between a deSitter core around the origin and an ordinary Schwarzschild spacetime at large distance 1 email: ansoldi@trieste.infn.it 2

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Non-commutative geometry inspired charged black holes

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“…Now, we recall that the fermions are taken to be infinitely massive (static), which means that there is no magnetic field. In such a case, by employing (35) and (27), the lowest-order modification in β 2 of the interaction energy takes the form…”

Section: Born-infeld-like Modelmentioning

confidence: 99%

“…These studies were first made by using a star product (Moyal product). However, in recent years, a novel way to formulate noncommutative quantum field theory (or quantum field theory in the presence of a minimal length) has been initiated in [34][35][36], which define the fields as mean values over coherent states of the noncommutative plane. Later, it has been shown that the coherent state approach can be summarized through the introduction of a new multiplication rule which is known as the Voros star-product [37].…”

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confidence: 99%

Remarks on nonlinear electrodynamics

2014

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We consider both generalized Born-Infeld and exponential electrodynamics. The field energy of a pointlike charge is finite only for Born-Infeld-like electrodynamics. However, both Born-Infeld-type and exponential electrodynamics display the vacuum birefringence phenomenon. Subsequently, we calculate the lowest-order modifications to the interaction energy for both classes of electrodynamics, within the framework of the gauge-invariant path-dependent variables formalism. These are shown to result in longrange (1/r 5 -type) corrections to the Coulomb potential. Once again, for their noncommutative versions, the interaction energy is ultraviolet finite.

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Traversable Wormholes in the Extended Teleparallel Theory of Gravity with Matter Coupling

Mustafa

Ahmad

Овгун

et al. 2021

Fortschritte der Physik

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This study explores the Gaussian and the Lorentzian distributed spherically symmetric wormhole solutions in the f(τ,T) gravity. The basic idea of the Gaussian and Lorentzian noncommutative geometries emerges as the physically acceptable and substantial notion in quantum physics. This idea of the noncommutative geometries with both the Gaussian and Lorentzian distributions becomes more striking when wormhole geometries in the modified theories of gravity are discussed. Here we consider a linear model within f(τ,T) gravity to investigate traversable wormholes. In particular, we discuss the possible cases for the wormhole geometries using the Gaussian and the Lorentzian noncommutative distributions to obtain the exact shape function for them. By incorporating the particular values of the unknown parameters involved, we discuss different properties of the new wormhole geometries explored here. It is noted that the involved matter violates the weak energy condition for both the cases of the noncommutative geometries, whereas there is a possibility for a physically viable wormhole solution. By analyzing the equilibrium condition, it is found that the acquired solutions are stable. Furthermore, we provide the embedded diagrams for wormhole structures under Gaussian and Lorentzian noncommutative frameworks. Moreover, we present the critical analysis on an anisotropic pressure under the Gaussian and the Lorentzian distributions.

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Feynman path integral on the non-commutative plane

Abstract: Abstract. We formulate Feynman path integral on a non commutative plane using coherent states. The propagator for a free particle exhibits UV cut-off induced by the parameter of non commutativity.

Cited by 289 publications

References 15 publications

Non-commutative geometry inspired charged black holes

Non-commutative geometry inspired charged black holes

Remarks on nonlinear electrodynamics

Traversable Wormholes in the Extended Teleparallel Theory of Gravity with Matter Coupling

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