Deformed symmetries on canonical noncommutative spaces

2007 ◽  
Author(s):  
Kuldeep Kumar ◽  
Aalok Misra
Keyword(s):  
Noncommutative Spaces ◽  
Deformed Symmetries

A Gravity Theory on Noncommutative Spaces

2007 ◽  
Author(s):  
Frank Meyer ◽  
P. Aschieri ◽  
C. Blohmann ◽  
M. Dimitrijevic ◽  
P. Schupp ◽  
...  
Keyword(s):  
Gravity Theory ◽  
Noncommutative Spaces

scholarly journals Noncommutative spaces and covariant formulation of statistical mechanics

2015 ◽  
Vol 92 (2) ◽  
Author(s):  
V. Hosseinzadeh ◽  
M. A. Gorji ◽  
K. Nozari ◽  
B. Vakili
Keyword(s):  
Statistical Mechanics ◽  
Covariant Formulation ◽  
Noncommutative Spaces

scholarly journals Codes as Fractals and Noncommutative Spaces

2012 ◽  
Vol 6 (3) ◽  
pp. 199-215 ◽  
Author(s):  
Matilde Marcolli ◽  
Christopher Perez
Keyword(s):  
Noncommutative Spaces

scholarly journals ON TIME-SPACE NONCOMMUTATIVITY FOR TRANSITION PROCESSES AND NONCOMMUTATIVE SYMMETRIES

2005 ◽  
Vol 20 (27) ◽  
pp. 2023-2034 ◽  
Author(s):  
A. P. BALACHANDRAN ◽  
ALEKSANDR PINZUL
Keyword(s):  
Quantum Physics ◽  
Rotational Symmetry ◽  
Time Dependent ◽  
Commutative Case ◽  
Transition Processes ◽  
Time Space ◽  
Deformed Symmetries ◽  
Moyal Plane ◽  
Spatial Rotations ◽  
Space Noncommutativity

We explore the consequences of time-space noncommutativity in the quantum mechanics of atoms and molecules, focusing on the Moyal plane with just time-space noncommutativity [Formula: see text]. Space rotations and parity are not automorphisms of this algebra and are not symmetries of quantum physics. Still, when there are spectral degeneracies of a time-independent Hamiltonian on a commutative spacetime which are due to symmetries, they persist when θ0i≠0: they do not depend at all on θ0i. They give no clue about rotation and parity violation when θ0i≠0. The persistence of degeneracies for θ0i≠0 can be understood in terms of invariance under deformed noncommutative "rotations" and "parity". They are not spatial rotations and reflection. We explain such deformed symmetries. We emphasize the significance of time-dependent perturbations (for example, due to time-dependent electromagnetic fields) to observe noncommutativity. The formalism for treating transition processes is illustrated by the example of nonrelativistic hydrogen atom interacting with quantized electromagnetic field. In the tree approximation, the 2s→1s + γ transition for hydrogen is zero in the commutative case. As an example, we show that it is zero in the same approximation for θ0i≠0. The importance of the deformed rotational symmetry is commented upon further using the decay Z0→2γ as an example.

scholarly journals NONCOMMUTATIVE METAFLUID DYNAMICS

2006 ◽  
Vol 21 (03) ◽  
pp. 505-516 ◽  
Author(s):  
A. C. R. MENDES ◽  
C. NEVES ◽  
W. OLIVEIRA ◽  
F. I. TAKAKURA
Keyword(s):  
Phase Space ◽  
Nonlinear Equations ◽  
Equations Of Motion ◽  
Additional Term ◽  
Dissipative Force ◽  
Covariant Form ◽  
Covariant Quantization ◽  
Noncommutative Spaces ◽  
Classical Phase Space

In this paper we define a noncommutative (NC) metafluid dynamics.1,2 We applied the Dirac's quantization to the metafluid dynamics on NC spaces. First class constraints were found which are the same obtained in Ref. 4. The gauge covariant quantization of the nonlinear equations of fields on noncommutative spaces were studied. We have found the extended Hamiltonian which leads to equations of motion in the gauge covariant form. In addition, we show that a particular transformation3 on the usual classical phase space (CPS) leads to the same results as of the ⋆-deformation with ν = 0. Besides, we have shown that an additional term is introduced into the dissipative force due to the NC geometry. This is an interesting feature due to the NC nature induced into model.

scholarly journals COMPLEX GRAVITY AND NONCOMMUTATIVE GEOMETRY

2001 ◽  
Vol 16 (05) ◽  
pp. 759-766 ◽  
Author(s):  
ALI H. CHAMSEDDINE
Keyword(s):  
Noncommutative Geometry ◽  
Space Time ◽  
Specific Form ◽  
Antisymmetric Tensor ◽  
Gauge Invariant ◽  
Diffeomorphism Invariance ◽  
Open Strings ◽  
Noncommutative Spaces

The presence of a constant background antisymmetric tensor for open strings or D-branes forces the space-time coordinates to be noncommutative. An immediate consequence of this is that all fields get complexified. By applying this idea to gravity one discovers that the metric becomes complex. Complex gravity is constructed by gauging the symmetry U(1, D-1). The resulting action gives one specific form of nonsymmetric gravity. In contrast to other theories of nonsymmetric gravity the action is both unique and gauge invariant. It is argued that for this theory to be consistent one must prove the existence of generalized diffeomorphism invariance. The results are easily generalized to noncommutative spaces.

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