scholarly journals Emergence of maximal acceleration from non-commutativity of spacetime

2021 ◽  
pp. 2150069
Author(s):  
E. Harikumar ◽  
Leela Ganesh Chandra Lakkaraju ◽  
Vishnu Rajagopal
Keyword(s):  
Deformation Parameter ◽  
Line Element ◽  
Minkowski Spacetime ◽  
Geodesic Equation ◽  
Newtonian Limit ◽  
First Order ◽  
Maximal Acceleration

In this paper, we show that the causally connected four-dimensional line element of the [Formula: see text]-deformed Minkowski spacetime induces an upper cut-off on the proper acceleration and derive this maximal acceleration, valid up to first order in the deformation parameter. We find a contribution to maximal acceleration which is independent of [Formula: see text] and thus signals effect of the non-commutativity alone. We also construct the [Formula: see text]-deformed geodesic equation and obtain its [Formula: see text]-deformed Newtonian limit, valid up to first order in deformation parameter. Using this, we constrain non-commutative parameters present in the expression for maximal acceleration. We analyze different limits of the maximal acceleration and also discuss its implication to maximal temperature. We also obtain a bound on the deformation parameter.

Feshbach–Villars equation in a κ-Minkowski spacetime

2020 ◽  
Vol 35 (37) ◽  
pp. 2050307
Author(s):  
B. Hamil ◽  
M. Merad
Keyword(s):  
Experimental Data ◽  
Perturbation Theory ◽  
Deformation Parameter ◽  
Order Approximation ◽  
Minkowski Spacetime ◽  
Magnetic Interaction ◽  
Relativistic Limit ◽  
First Order ◽  
Klein Gordon ◽  
First Order Approximation

In this paper, by using the Dirac derivatives the Klein–Gordon (K-G) equation is determined in a [Formula: see text]-Minkowski spacetime. The dispersion relation and the first-order approximation case are deduced. The Feshbach–Villars (FV) equation is derived by applying the new linearization process to the time. We then study the effect of magnetic interaction on energies spectrum in a [Formula: see text]-Minkowski spacetime as an application, as a result we found that the energies spectrum are not symmetrical. We also study the case of hydrogen atom in non-relativistic limit by using perturbation theory. The upper bound of the [Formula: see text]-deformation parameter is evaluate, on the basis of the experimental data for [Formula: see text] transition frequency.

scholarly journals UNIFORMLY ACCELERATED DETECTOR IN THE κ-DEFORMED DIRAC VACUUM

2013 ◽  
Vol 28 (15) ◽  
pp. 1350063 ◽  
Author(s):  
E. HARIKUMAR ◽  
RAVIKANT VERMA
Keyword(s):  
Response Function ◽  
Deformation Parameter ◽  
Minkowski Spacetime ◽  
Vacuum State ◽  
Dirac Field ◽  
Unruh Effect ◽  
Wightman Function ◽  
Dirac Theory ◽  
First Order ◽  
Poincaré Algebra

In this paper, we investigate how a uniformly accelerated detector responds to vacuum state of a Dirac field in the κ-Minkowski spacetime. Starting from κ-deformed Dirac theory, which is invariant under κ-Poincaré algebra, we derive κ-deformed Wightman function for Dirac field, which is valid up to first-order in the deformation parameter a. Using this, we calculate the response function of the uniformly accelerated detector, which is coupled to massless Dirac field in κ-spacetime. From this, we obtain the modification to Unruh effect for the κ-deformed Dirac field, valid up to first-order in the deformation parameter.

scholarly journals Oseen's correction to stokes drag on axially symmetric arbitrary particle in transverse flow: A new approach

2014 ◽  
Vol 41 (3) ◽  
pp. 177-212
Author(s):  
Deepak Srivastava ◽  
Nirmal Srivastava
Keyword(s):  
Reynolds Number ◽  
General Expression ◽  
Deformation Parameter ◽  
Axial Flow ◽  
Transverse Flow ◽  
Axially Symmetric ◽  
New Approach ◽  
First Order ◽  
Stokes Drag ◽  
Axis Of Symmetry

In this paper, Oseen?s correction to Stokes drag experienced by axially symmetric particle placed in a uniform stream perpendicular to axis of symmetry(i.e. transverse flow) is obtained. For this, the linear relationship between axial and transverse Stokes drag is utilized to extend the Brenner?s formula for axial flow to transverse flow. General expression of Oseen?s correction to Stokes drag on axially symmetric particle placed in transverse flow is found to be new. This general expression is applied to some known axially symmetric bodies and obtained values of Oseen?s drag, up to first order terms in Reynolds number ?R?, are also claimed to be new and never exist in the literature. Numerical values of Oseen drag are also evaluated and their variations with respect to Reynolds number, eccentricity and deformation parameter are depicted in figures and compared with some known values. Some important applications are also highlighted.

TWISTED SYMMETRY AND NONCOMMUTATIVE FIELD THEORY

2012 ◽  
Vol 13 ◽  
pp. 54-65
Author(s):  
MARIJA DIMITRIJEVIĆ ◽  
LARISA JONKE
Keyword(s):  
Field Theory ◽  
Effective Action ◽  
Degrees Of Freedom ◽  
Deformation Parameter ◽  
Field Theories ◽  
Gauge Field Theory ◽  
Noncommutative Field Theory ◽  
First Order ◽  
Minkowski Space Time ◽  
Noncommutative Spaces

Although the meaning of twisted symmetry is still not fully understood, the twist approach has its advantages in the construction of field theories on noncommutative spaces. We discuss these advantages on the example of κ-Minkowski space-time. We construct the noncommutative U(1) gauge field theory. Especially the action is written as an integral of a maximal form, thus solving the cyclicity problem of the integral in κ-Minkowski. Using the Seiberg-Witten map to relate noncommutative and commutative degrees of freedom the effective action with the first order corrections in the deformation parameter is obtained.

Signatures of minimal length from Casimir–Polder forces with neutrons

2020 ◽  
Vol 29 (14) ◽  
pp. 2043026 ◽  
Author(s):  
Fabrizio Pinto
Keyword(s):  
Deformation Parameter ◽  
Zero Point ◽  
Minimal Length ◽  
Dispersion Forces ◽  
Heuristic Argument ◽  
First Order ◽  
Energy Neutron ◽  
Point Field ◽  
Interparticle Potentials ◽  
Physics Experiments

In this paper, dispersion forces between neutrons are suggested as a probe of the fundamental structure of spacetime. Corrections to standard expressions for the interparticle potentials are obtained through computer algebra system strategies and a novel heuristic argument for comparison with field theory computations. It is confirmed that, to first order in the deformation parameter, the unretarded ([Formula: see text]) van der Waals potential is unchanged. The modified retarded Casimir–Polder potential, obtained from the minimal length zero-point field, compares satisfactorily in both sign and magnitude with rigorous calculations. It is shown that low energy neutron scattering can provide a gain in excess of [Formula: see text] orders of magnitude over atomic physics experiments in constraining corrections due to the existence of a minimal length.

scholarly journals Effects of Noncommutativity on the Black Hole Entropy

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Kumar S. Gupta ◽  
E. Harikumar ◽  
Tajron Jurić ◽  
Stjepan Meljanac ◽  
Andjelo Samsarov
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Deformation Parameter ◽  
Black Hole Entropy ◽  
Brick Wall ◽  
Btz Black Hole ◽  
First Order ◽  
Hole Geometry ◽  
Wall Method

The BTZ black hole geometry is probed with a noncommutative scalar field which obeys theκ-Minkowski algebra. The entropy of the BTZ black hole is calculated using the brick wall method. The contribution of the noncommutativity to the black hole entropy is explicitly evaluated up to the first order in the deformation parameter. We also argue that such a correction to the black hole entropy can be interpreted as arising from the renormalization of the Newton’s constant due to the effects of the noncommutativity.

scholarly journals Geodesic equation inκ-Minkowski spacetime

2012 ◽  
Vol 86 (4) ◽  
Author(s):  
E. Harikumar ◽  
T. Jurić ◽  
S. Meljanac
Keyword(s):  
Minkowski Spacetime ◽  
Geodesic Equation

Diffusion in κ-deformed space and spectral dimension

2016 ◽  
Vol 31 (09) ◽  
pp. 1650056 ◽  
Author(s):  
V. Anjana
Keyword(s):  
Diffusion Equation ◽  
Laplace Operator ◽  
Deformation Parameter ◽  
Minkowski Spacetime ◽  
Spectral Dimension ◽  
Topological Dimension ◽  
High Energies ◽  
Large Diffusion ◽  
Beltrami Laplace Operator

In this paper, we derive the expression for spectral dimension using a modified diffusion equation in the [Formula: see text]-deformed spacetime. We start with the Beltrami–Laplace operator in the [Formula: see text]-Minkowski spacetime and obtain the deformed diffusion equation. From the solution of this deformed diffusion equation, we calculate the spectral dimension which depends on the deformation parameter “[Formula: see text]” and also on an integer “[Formula: see text]”, apart from the topological dimension. Using this, we show that, for large diffusion times the spectral dimension approaches the usual topological dimension whereas spectral dimension diverges to [Formula: see text] for [Formula: see text] and [Formula: see text] for [Formula: see text] at high energies.

scholarly journals κ-DEFORMED DIRAC EQUATION

2011 ◽  
Vol 26 (15) ◽  
pp. 1103-1115 ◽  
Author(s):  
E. HARIKUMAR ◽  
M. SIVAKUMAR ◽  
N. SRINIVAS
Keyword(s):  
Perturbation Theory ◽  
Hydrogen Atom ◽  
Dirac Equation ◽  
Power Series ◽  
Time Reversal ◽  
Deformation Parameter ◽  
Generalized Uncertainty Principle ◽  
Minkowski Spacetime ◽  
Planck Length ◽  
Conjugation Invariance

We construct a Dirac equation in κ-Minkowski spacetime and analyze its implications. This κ-deformed Dirac equation is expanded as a power series involving derivatives with respect to commutative coordinates and the deformation parameter, a. We show that the κ-deformation breaks the charge conjugation invariance but preserves parity and time reversal. We then study how the hydrogen atom spectrum is modified due to the κ-deformation, applying perturbation theory. Using this, we obtain bounds on the deformation parameter a, which are a few orders higher than the Planck length. We also show that the effects of deformation on the spectrum are distinct from that of Moyal deformation and generalized uncertainty principle.

scholarly journals Consequences of minimal length discretization on line element, metric tensor, and geodesic equation

2021 ◽  
Author(s):  
Abdel Nasser Tawfik ◽  
Abdel Magied Diab ◽  
Sameh Shenawy ◽  
Eiman Abou El Dahab
Keyword(s):  
Line Element ◽  
Geodesic Equation ◽  
Minimal Length ◽  
Metric Tensor ◽  
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