Harmonic analysis on phase space and Born's metric for space time

2005 ◽  
pp. 477-482
Author(s):  
S. Twareque Ali
Keyword(s):  
Phase Space ◽  
Harmonic Analysis ◽  
Space Time

The phase space time evolution method

1971 ◽  
Vol 1 (2) ◽  
pp. 115-143
Author(s):  
Morton A. Tavel ◽  
Martin S. Zucker
Keyword(s):  
Phase Space ◽  
Time Evolution ◽  
Space Time ◽  
Space Time Evolution

Quantum harmonic analysis on phase space

1984 ◽  
Vol 25 (5) ◽  
pp. 1404-1411 ◽  
Author(s):  
R. Werner
Keyword(s):  
Phase Space ◽  
Harmonic Analysis

Mathematical problems of stochastic quantum mechanics: Harmonic analysis on phase space and quantum geometry

1986 ◽  
Vol 6 (1) ◽  
pp. 1-18 ◽  
Author(s):  
S. Twareque Ali ◽  
Eduard Prugovečki
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Harmonic Analysis ◽  
Quantum Geometry ◽  
Mathematical Problems

COSMIC DEFECT COSMOLOGY

2009 ◽  
Vol 24 (08n09) ◽  
pp. 1620-1624
Author(s):  
A. TARTAGLIA
Keyword(s):  
Phase Space ◽  
Cold Dark Matter ◽  
Displacement Vector ◽  
Empty Space ◽  
Space Time ◽  
Point Particle ◽  
Accelerated Expansion ◽  
Displacement Vector Field ◽  
Type Ia ◽  
Ia Supernovae

The accelerated expansion of the universe is interpreted as an effect of a defect in space-time treated as a four-dimensional continuum endowed with physical properties. The analogy is with texture defects in material continua, like dislocations and disclinations, described in terms of a singular displacement vector field. A Lagrangian for empty space-time is proposed exploiting one further analogy between the phase space of a Robertson-Walker universe and the phase space of a point particle moving across an homogeneous isotropic medium. The model, named Cosmic Defect theory, produces, as a byproduct, also inflation near the initial singularity. The theory has been applied to fit the luminosity data of 192 type Ia supernovae. The results are satisfying and comparable with the ones obtained by means of the Λ Cold Dark Matter standard model.

scholarly journals NON-COMMUTATIVE SPACE–TIME OF DOUBLY SPECIAL RELATIVITY THEORIES

2003 ◽  
Vol 12 (02) ◽  
pp. 299-315 ◽  
Author(s):  
J. KOWALSKI-GLIKMAN ◽  
S. NOWAK
Keyword(s):  
Phase Space ◽  
Special Relativity ◽  
Space Time ◽  
Kinematic Structure ◽  
Doubly Special Relativity ◽  
Minkowski Space Time ◽  
Space Time Structure ◽  
Commutative Space ◽  
Intrinsic Length ◽  
Heisenberg Double

Doubly Special Relativity (DSR) theory is a recently proposed theory with two observer-independent scales (of velocity and mass), which is to describe a kinematic structure underlining the theory of Quantum Gravity. We observe that there are infinitely many DSR constructions of the energy–momentum sector, each of whose can be promoted to the κ-Poincaré quantum (Hopf) algebra. Then we use the co-product of this algebra and the Heisenberg double construction of κ-deformed phase space in order to derive the non-commutative space–time structure and the description of the whole of DSR phase space. Next we show that contrary to the ambiguous structure of the energy momentum sector, the space–time of the DSR theory is unique and related to the theory with non-commutative space–time proposed long ago by Snyder. This theory provides non-commutative version of Minkowski space–time enjoying ordinary Lorentz symmetry. It turns out that when one builds a natural phase space on this space–time, its intrinsic length parameter ℓ becomes observer-independent.

GRAVITY IN CURVED PHASE-SPACES, FINSLER GEOMETRY AND TWO-TIMES PHYSICS

2012 ◽  
Vol 27 (12) ◽  
pp. 1250069 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Phase Space ◽  
Tangent Bundle ◽  
Finsler Geometry ◽  
Space Time ◽  
Vacuum Field ◽  
Field Equations ◽  
Problem Of Time ◽  
Gravitational Field Equations ◽  
Cotangent Space ◽  
Kaluza Klein

The generalized (vacuum) field equations corresponding to gravity on curved 2d-dimensional (dim) tangent bundle/phase spaces and associated with the geometry of the (co)tangent bundle TMd-1, 1(T*Md-1, 1) of a d-dim space–time Md-1, 1 are investigated following the strict distinguished d-connection formalism of Lagrange–Finsler and Hamilton–Cartan geometry. It is found that there is no mathematical equivalence with Einstein's vacuum field equations in space–times of 2d dimensions, with two times, after a d+d Kaluza–Klein-like decomposition of the 2d-dim scalar curvature R is performed and involving the introduction of a nonlinear connection [Formula: see text]. The physical applications of the 4-dim phase space metric solutions found in this work, corresponding to the cotangent space of a 2-dim space–time, deserve further investigation. The physics of two times may be relevant in the solution to the problem of time in quantum gravity and in the explanation of dark matter. Finding nontrivial solutions of the generalized gravitational field equations corresponding to the 8-dim cotangent bundle (phase space) of the 4-dim space–time remains a challenging task.

scholarly journals TENSIONLESS BRANES AND THE NULL STRING CRITICAL DIMENSION

1998 ◽  
Vol 13 (32) ◽  
pp. 2571-2583 ◽  
Author(s):  
P. BOZHILOV
Keyword(s):  
Phase Space ◽  
Brst Quantization ◽  
Critical Dimension ◽  
Space Time ◽  
Operator Ordering ◽  
Vacuum States ◽  
Constraint Algebra ◽  
The One ◽  
Null String

BRST quantization is carried out for a model of p-branes with second-class constraints. After extension of the phase space, the constraint algebra coincides with the one of null string when p =1. It is shown that in this case one can or cannot obtain critical dimension for the null string, depending on the choice of the operator ordering and the corresponding vacuum states. When p>1, operator orderings leading to critical dimension in the p=1 case are not allowed. Admissible orderings give no restrictions on the dimension of the embedding space–time. Finally, a generalization to supersymmetric null branes is proposed.

Stochastic localization, quantum mechanics on phase space and quantum space-time

1985 ◽  
Vol 8 (11) ◽  
pp. 1-128 ◽  
Author(s):  
S. Twareque Ali
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Space Time ◽  
Quantum Space

scholarly journals Outage Capacity of Two-Phase Space-Time Coded Cooperative Multicasting

2006 ◽  
Author(s):  
Aitor del Coso ◽  
Osvaldo Simeone ◽  
Yeheskel Bar-ness ◽  
Christian Ibars
Keyword(s):  
Phase Space ◽  
Space Time ◽  
Outage Capacity ◽  
Two Phase
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