scholarly journals Spectral distances on the doubled Moyal plane using Dirac eigenspinors

2018 ◽  
Vol 97 (8) ◽  
Author(s):  
Kaushlendra Kumar ◽  
Biswajit Chakraborty
Keyword(s):  
Moyal Plane

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 Lehmann-Symanzik-ZimmermannS-matrix elements on the Moyal plane

2011 ◽  
Vol 84 (6) ◽  
Author(s):  
A. P. Balachandran ◽  
Pramod Padmanabhan ◽  
Amilcar R. de Queiroz
Keyword(s):  
Matrix Elements ◽  
Moyal Plane

scholarly journals SPACETIME NONCOMMUTATIVITY WITH A BIFERMIONIC PARAMETER

2008 ◽  
Vol 23 (12) ◽  
pp. 887-893 ◽  
Author(s):  
D. M. GITMAN ◽  
D. V. VASSILEVICH
Keyword(s):  
Field Theory ◽  
Finite Number ◽  
Energy Momentum Tensor ◽  
Canonical Quantization ◽  
Momentum Tensor ◽  
Theory Model ◽  
Two Dimensional ◽  
Noncommutative Field Theory ◽  
Moyal Product ◽  
Moyal Plane

We consider a Moyal plane and propose to make the noncommutativity parameter Θμν bifermionic, i.e. composed of two fermionic (Grassmann odd) parameters. The Moyal product then contains a finite number of derivatives, which avoid the difficulties of the standard approach. As an example, we construct a two-dimensional noncommutative field theory model based on the Moyal product with a bifermionic parameter and show that it has a locally conserved energy–momentum tensor. The model has no problem with the canonical quantization and appears to be renormalizable.

scholarly journals Matrix geometries emergent from a point

2014 ◽  
Vol 26 (09) ◽  
pp. 1450017
Author(s):  
Francesco D'Andrea ◽  
Fedele Lizzi ◽  
Pierre Martinetti
Keyword(s):  
Equivalence Classes ◽  
Unitary Equivalence ◽  
Categorical Approach ◽  
Spectral Triples ◽  
Moyal Plane

We describe a categorical approach to finite noncommutative geometries. Objects in the category are spectral triples, rather than unitary equivalence classes as in other approaches. This enables us to treat fluctuations of the metric and unitary equivalences on the same footing, as representatives of particular morphisms in this category. We then show how a matrix geometry (Moyal plane) emerges as a fluctuation from one point, and discuss some geometric aspects of this space.

scholarly journals QED ON THE GROENEWOLD–MOYAL PLANE

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4789-4804 ◽  
Author(s):  
A. P. BALACHANDRAN ◽  
A. PINZUL ◽  
B. A. QURESHI ◽  
S. VAIDYA
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Center Of Mass ◽  
Pauli Principle ◽  
Mass System ◽  
Tree Approximation ◽  
Moyal Plane ◽  
Interaction Term

We investigate a version of noncommutative QED where the interaction term, although natural, breaks the spin-statistics connection. We calculate e- + e- → e- + e- and γ + e- → γ + e- cross-sections in the tree approximation and explicitly display their dependence on θμν. Remarkably the zero of the elastic e- + e- → e- + e- cross-section at 90° in the center-of-mass system, which is due to Pauli principle, is shifted away as a function of θμν and energy.

Non-commutative quantum gravity phenomenology in underground experiments

2019 ◽  
Vol 34 (29) ◽  
pp. 1950236 ◽  
Author(s):  
Andrea Addazi ◽  
Rita Bernabei
Keyword(s):  
Laboratory Experiments ◽  
Planck Scale ◽  
Pauli Exclusion Principle ◽  
Energy Scale ◽  
Exclusion Principle ◽  
Atomic Systems ◽  
Quantum Gravity Phenomenology ◽  
Nuclear Transitions ◽  
Moyal Plane ◽  
Very High

We show how non-commutative spacetime models can induce Pauli Exclusion Principle (PEP) forbidden nuclear and atomic transitions. We focalize our analysis on one of the most popular instantiations of non-commutativeness: [Formula: see text]-Poincaré model, based on the Groenewold–Moyal plane algebra. We show that PEP violating transitions induced by [Formula: see text]-Poincaré have an energy scale and angular emission dependence. PEP violating transitions in nuclear and atomic systems can be tested with very high accuracy in underground laboratory experiments such as DAMA/LIBRA and VIP(2). We derive that the Equivalence Principle assumed [Formula: see text]-Poincaré model can be already ruled-out until the Planck scale, from nuclear transitions tests by DAMA/LIBRA experiment.

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