scholarly journals Some Properties of Massless Particles in Arbitrary Dimensions

1998 ◽  
Vol 10 (08) ◽  
pp. 1079-1109 ◽  
Author(s):  
Mourad Laoues
Keyword(s):  
Tensor Product ◽  
Arbitrary Spin ◽  
Space Time ◽  
De Sitter ◽  
Sitter Group ◽  
Massless Particles ◽  
Arbitrary Dimensions ◽  
The One

Various properties of two kinds of massless representations of the n-conformal (or (n+1)-De Sitter) group [Formula: see text] are investigated for n≥2. It is found that, for space-time dimensions n≥3, the situation is quite similar to the one of the n=4 case for Sn-massless representations of the n-De Sitter group [Formula: see text]. These representations are the restrictions of the singletons of [Formula: see text]. The main difference is that they are not contained in the tensor product of two UIRs with the same sign of energy when n>4, whereas it is the case for another kind of massless representations. Finally some examples of Gupta–Bleuler triplets are given for arbitrary spin and n≥3.

scholarly journals The Accurate Modification of Tunneling Radiation of Fermions with Arbitrary Spin in Kerr-de Sitter Black Hole Space-Time

2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Bei Sha ◽  
Zhi-E Liu ◽  
Xia Tan ◽  
Yu-Zhen Liu ◽  
Jie Zhang
Keyword(s):  
Black Hole ◽  
Dispersion Relation ◽  
String Theory ◽  
Event Horizon ◽  
Quantum Tunneling ◽  
Gravitational Theory ◽  
Arbitrary Spin ◽  
Space Time ◽  
De Sitter ◽  
Tunneling Radiation

The quantum tunneling radiation of fermions with arbitrary spin at the event horizon of Kerr-de Sitter black hole is accurately modified by using the dispersion relation proposed in the study of string theory and quantum gravitational theory. The derived tunneling rate and temperature at the black hole horizons are analyzed and studied.

scholarly journals Dimensionally Compactified Chern-Simon Theory in 5D as a Gravitation Theory in 4D

2017 ◽  
Vol 45 ◽  
pp. 1760005 ◽  
Author(s):  
Ivan Morales ◽  
Bruno Neves ◽  
Zui Oporto ◽  
Olivier Piguet
Keyword(s):  
Dimensional Space ◽  
Cosmological Solution ◽  
Space Time ◽  
Gravitation Theory ◽  
Simons Theory ◽  
De Sitter ◽  
Field Equations ◽  
Sitter Group ◽  
Dimensional Space Time ◽  
Chern Simons

We propose a gravitation theory in 4 dimensional space-time obtained by compacting to 4 dimensions the five dimensional topological Chern-Simons theory with the gauge group SO(1,5) or SO(2,4) – the de Sitter or anti-de Sitter group of 5-dimensional space-time. In the resulting theory, torsion, which is solution of the field equations as in any gravitation theory in the first order formalism, is not necessarily zero. However, a cosmological solution with zero torsion exists, which reproduces the Lambda-CDM cosmological solution of General Relativity. A realistic solution with spherical symmetry is also obtained.

scholarly journals RESONANCE SOLITONS AS BLACK HOLES IN MADELUNG FLUID

2002 ◽  
Vol 17 (24) ◽  
pp. 1601-1619 ◽  
Author(s):  
O. K. PASHAEV ◽  
JYH-HAO LEE
Keyword(s):  
Reaction Diffusion ◽  
Space Time ◽  
Coupling Constant ◽  
De Sitter ◽  
Bilinear Method ◽  
Envelope Solitons ◽  
Gauge Fixing ◽  
Arbitrary Strength ◽  
Madelung Fluid ◽  
The One

Envelope solitons of the Nonlinear Schrödinger equation (NLS) under quantum potential's influence are studied. Corresponding problem is found to be integrable for an arbitrary strength, s ≠ 1, of the quantum potential. For s < 1, the model is equivalent to the usual NLS with rescaled coupling constant, while for s > 1, to the reaction–diffusion system. The last one is related to the anti-de Sitter (AdS) space valued Heisenberg model, realizing a particular gauge fixing condition of the (1+1)-dimensional Jackiw–Teitelboim gravity. For this gravity model, by the Madelung fluid representation we derive the acoustic form of the space–time metric. The space–time points, where dispersion changes the sign, correspond to the event horizon, while the soliton solution to the AdS black hole. Moving with the above bounded velocity, it describes evolution on the one sheet hyperboloid with nontrivial winding number, and creates under collision, the resonance states which we study by the Hirota bilinear method.

scholarly journals Graphene in curved Snyder space

2020 ◽  
Vol 75 (10) ◽  
pp. 809-817
Author(s):  
Bilel Hamil ◽  
Houcine Aounallah ◽  
Bekir Can Lütfüoğlu
Keyword(s):  
Magnetic Field ◽  
Graphene Layer ◽  
Space Time ◽  
Noncommutative Space ◽  
Dirac Fermions ◽  
De Sitter ◽  
Sitter Group ◽  
Energy Eigenvalues ◽  
Entropy Functions

AbstractThe Snyder-de Sitter (SdS) model which is invariant under the action of the de Sitter group, is an example of a noncommutative space-time with three fundamental scales. In this paper, we considered the massless Dirac fermions in graphene layer in a curved Snyder space-time which are subjected to an external magnetic field. We employed representation in the momentum space to derive the energy eigenvalues and the eigenfunctions of the system. Then, we used the deduced energy function obtaining the internal energy, heat capacity, and entropy functions. We investigated the role of the fundamental scales on these thermal quantities of the graphene layer. We found that the effect of the SdS model on the thermodynamic properties is significant.

scholarly journals Einstein’s E=mc2 Derivable from Heisenberg’s Uncertainty Relations

2019 ◽  
Vol 1 (2) ◽  
pp. 236-251 ◽  
Author(s):  
Sibel Başkal ◽  
Young S. Kim ◽  
and Marilyn E. Noz
Keyword(s):  
Commutation Relation ◽  
Lorentz Group ◽  
Hermitian Matrix ◽  
Uncertainty Relations ◽  
De Sitter ◽  
Oscillator Representation ◽  
Sitter Group ◽  
Hermitian Conjugate ◽  
Step Down ◽  
The One

Heisenberg’s uncertainty relation can be written in terms of the step-up and step-down operators in the harmonic oscillator representation. It is noted that the single-variable Heisenberg commutation relation contains the symmetry of the S p ( 2 ) group which is isomorphic to the Lorentz group applicable to one time-like dimension and two space-like dimensions, known as the O ( 2 , 1 ) group. This group has three independent generators. The one-dimensional step-up and step-down operators can be combined into one two-by-two Hermitian matrix which contains three independent operators. If we use a two-variable Heisenberg commutation relation, the two pairs of independent step-up, step-down operators can be combined into a four-by-four block-diagonal Hermitian matrix with six independent parameters. It is then possible to add one off-diagonal two-by-two matrix and its Hermitian conjugate to complete the four-by-four Hermitian matrix. This off-diagonal matrix has four independent generators. There are thus ten independent generators. It is then shown that these ten generators can be linearly combined to the ten generators for Dirac’s two oscillator system leading to the group isomorphic to the de Sitter group O ( 3 , 2 ) , which can then be contracted to the inhomogeneous Lorentz group with four translation generators corresponding to the four-momentum in the Lorentz-covariant world. This Lorentz-covariant four-momentum is known as Einstein’s E = m c 2 .

scholarly journals On the Group-Theoretical Approach to Relativistic Wave Equations for Arbitrary Spin

2021 ◽  
Author(s):  
Luca Nanni
Keyword(s):  
Mass Spectrum ◽  
Wave Equations ◽  
Relativistic Equation ◽  
Physical Nature ◽  
Physical Reality ◽  
Arbitrary Spin ◽  
Theoretical Physics ◽  
De Sitter ◽  
Sitter Group ◽  
Algebraic Approaches

Formulating a relativistic equation for particles with arbitrary spin remains an open challenge in theoretical physics. In this study, the main algebraic approaches used to generalize the Dirac and Kemmer&ndash;Duffin equations for particles of arbitrary spin are investigated. It is proved that an irreducible relativistic equation formulated using spin matrices satisfying the commutation relations of the de Sitter group leads to inconsistent results, mainly as a consequence of violation of unitarity and the appearance of a mass spectrum that does not reflect the physical reality of elementary particles. However, the introduction of subsidiary conditions resolves the problem of unitarity and restores the physical meaning of the mass spectrum. The equations obtained by these approaches are solved and the physical nature of the solutions is discussed.

ONE-LOOP FINITE TEMPERATURE EFFECTIVE ACTION FOR COMPOSITE FIELDS IN CURVED SPACE

1995 ◽  
Vol 10 (03) ◽  
pp. 389-420
Author(s):  
J. BALAKRISHNAN
Keyword(s):  
Effective Action ◽  
Riemann Tensor ◽  
Space Time ◽  
Gauge Condition ◽  
Zero Temperature ◽  
De Sitter ◽  
Abelian Gauge ◽  
Curved Space ◽  
Background Space ◽  
The One

We obtain high temperature results for the one-loop effective action for composite fields in interaction with an Abelian gauge field and minimally coupled to gravity in a curved background space-time, using the Vilkovisky-DeWitt approach, by making a local expansion in the Riemann tensor and its derivatives. We also give results for the fields minimally coupled to gravity in an arbitrary curved background space-time at zero temperature, and for the case where the fields are nonminimally coupled to gravity in Euclidean de Sitter space. The results obtained are gauge-invariant and gauge-condition-independent on-shell as well as off-shell.

scholarly journals Field Theory of Particles with Arbitrary Spin

1977 ◽  
Vol 30 (1) ◽  
pp. 1 ◽  
Author(s):  
HS Green
Keyword(s):  
Field Theory ◽  
Dynamical Symmetry ◽  
Arbitrary Spin ◽  
De Sitter ◽  
Interacting Particles ◽  
Field Equations ◽  
Sitter Group ◽  
Finite Dimensional ◽  
General Field ◽  
Higher Spin

It is pointed out that existing field equations for particles of higher spin are unsuitable' for the formulation of field theories with interaction. ' A generalization of the Dirac and Kemmer matrices is discussed in terms of finite-dimensional representations of the de, Sitter group. ' It is shown how to formulate a general field theory in such a way as to exhibit a corresponding dynamical symmetry. The resulting field equation resembles Bhabha's, but is self-consistent in its applications to interacting particles and has a different type of mass spectrum. In the Appendix, it is shown that'within any'irreducible representation of the Poincare group there are finite-dimensional representations of the'Lorentz group'labelled (s, � s).

scholarly journals Massive-scalar effective actions on anti-de Sitter space-time

1999 ◽  
Vol 77 (2) ◽  
pp. 85-99 ◽  
Author(s):  
M Kamela ◽  
C P Burgess
Keyword(s):  
De Sitter Space ◽  
Space Time ◽  
Massive Scalar ◽  
De Sitter ◽  
Elementary Functions ◽  
Gamma Functions ◽  
Arbitrary Dimensions ◽  
Odd Dimensions

Closed forms are derived for the effective actions for free, massive spinless fields in anti-de Sitter space-times in arbitrary dimensions. The results have simple expressions in terms of elementary functions (for odd dimensions) or multiple Gamma functions (for even dimensions). We use these to argue against the quantum validity of Cruz' recently proposed duality relating such theories with differing masses and cosmological constants.PACS Nos. 11.10- z, 11.90+ t, and 04.60-m.

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