Uniformly accelerating observer in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>κ</mml:mi></mml:math>-deformed space-time

Harikumar, E.; Kapoor, A. K.; Verma, Ravikant

doi:10.1103/physrevd.86.045022

Cited by 27 publications

(43 citation statements)

References 38 publications

(92 reference statements)

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“…As considered in Ref. [28], the interaction Hamiltonian representing the interaction between the detector and scalar field up to first order in the parameter 1/κ can be described by the conventional Hermitian interaction Hamiltonian…”

Section: Dynamical Evolution Of a Two-level Detector Interactsmentioning

confidence: 99%

“…It is worthy noting that the κ-deformed Klein-Gordon theory can be written in the commutative spacetime [28]. Since the relevant model is constructed in the commutative spacetime, it allows us to unambiguously define the trajectory of the motional detector, that is needed for the study of the influence of the relativistic motion on the κ parameter estimation.…”

Section: κ-Deformed Klein-gordon Theorymentioning

confidence: 99%

“…[28]. During the concrete calculation of Green function, we just take an approximate value up to second order in 1/κ.…”

Section: κ-Deformed Klein-gordon Theorymentioning

confidence: 99%

“…To derive the κ-deformed Klein-Gordon equation which is invariant under the κ-Poincaré algebra, it is natural to introduce the Dirac derivatives D μ transforming like a vector under M μν as follows [24][25][26][27][28] …”

Section: κ-Deformed Klein-gordon Theorymentioning

confidence: 99%

“…We consider a two-level atom as a probe coupled to a κ-deformed massless scalar field which is defined in the commutative spacetime [28]. In this paper, the authors started with the κ-deformed KleinGordon equation, which is invariant under the action of κ-Poincaré algebra and written in the commutative spacetime itself.…”

Section: Introductionmentioning

confidence: 99%

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Relativistic motion enhanced quantum estimation of $$\kappa $$ κ -deformation of spacetime

et al. 2018

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We probe the κ-deformation of spacetime using a two-level atom as a detector coupled to a κ-deformed massless scalar field which is invariant under a κ-Poincaré algebra and written in commutative spacetime. To address the quantum bound to the estimability of the deformation parameter κ, we perform measurements on the two-level detector and maximize the value of quantum Fisher information over all possible detector preparations. We prove that the population measurement is the optimal measurement in the estimation of the deformation parameter κ. In particular, we show that the relativistic motion of the detector affects the precision in the estimation of the parameter κ, which can effectively improve this precision comparing to that of the static detector case by many orders of magnitude.

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Section: Dynamical Evolution Of a Two-level Detector Interactsmentioning

confidence: 99%

Section: κ-Deformed Klein-gordon Theorymentioning

confidence: 99%

“…[28]. During the concrete calculation of Green function, we just take an approximate value up to second order in 1/κ.…”

Section: κ-Deformed Klein-gordon Theorymentioning

confidence: 99%

Section: κ-Deformed Klein-gordon Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Relativistic motion enhanced quantum estimation of $$\kappa $$ κ -deformation of spacetime

et al. 2018

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Resonance Interaction Energy in κ‐Minkowski Spacetime

2023

Annalen der Physik

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If gravity is quantized, one of the consequences may be that the spacetime coordinates are quantized and become noncommutative. The κ‐Minkowski spacetime is such kind of noncommutative spacetime. In this paper, the resonance interaction energy of a two‐atom system coupled with a fluctuating vacuum scalar field in the κ‐Minkowski spacetime is studied. It is found that the resonance interaction energy is dependent on the interatomic separation, the transition wavelength of the atoms, and the spacetime non‐commutativity. When the interatomic separation is small compared with a characteristic length determined by the spacetime non‐commutativity parameter and the transition wavelength, the resonance interaction energy is that in the Minkowski spacetime plus a correction due to the spacetime non‐commutativity. When the interatomic separation is comparable to or larger than the characteristic length, the resonance interaction energy cannot be organized in the form of a Minkowski term plus a correction, which indicates that the long‐range behavior of the vacuum in the κ‐Minkowski spacetime is fundamentally different from that in the Minkowski spacetime.

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Effect of non-commutativity of space-time on thermodynamics of photon gas

Verma¹,

Nandi²

2019

Gen Relativ Gravit

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Doubly special relativity(DSR) introduce a minimal length scale i.e. the Planck length scale, which is independent length scale in addition to the speed of light in the normal special theory of relativity(STR). Doubly special relativity leads to study the κ-Minkowski space-time. In this paper, we present the result of our investigation on the thermodynamics of photon gas in the κ-Minkowski space-time. For studying this, we start with the κ-deformed dispersion relation and keep terms upto first order in the deformation parameter a and we study that how does κ-deformed dispersion relation affect the thermodynamics of photon gas. In the limit, deformation parameter a → 0, we get back the all results in the special theory of relativity(STR) [1].

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Uniformly accelerating observer inκ-deformed space-time

Cited by 27 publications

References 38 publications

Relativistic motion enhanced quantum estimation of $$\kappa $$ κ -deformation of spacetime

Relativistic motion enhanced quantum estimation of $$\kappa $$ κ -deformation of spacetime

Resonance Interaction Energy in κ‐Minkowski Spacetime

Effect of non-commutativity of space-time on thermodynamics of photon gas

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