scholarly journals Deformed symmetries in noncommutative and multifractional spacetimes

2017 ◽  
Vol 95 (4) ◽  
Author(s):  
Gianluca Calcagni ◽  
Michele Ronco
Keyword(s):  
Deformed Symmetries

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.

Deformed symmetries on canonical noncommutative spaces

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

scholarly journals From infinitesimal symmetries to deformed symmetries of Lax-type equations

2015 ◽  
Vol 633 ◽  
pp. 012013
Author(s):  
Jean-Pierre Magnot
Keyword(s):  
Deformed Symmetries

scholarly journals GUP-BASED AND SNYDER NONCOMMUTATIVE ALGEBRAS, RELATIVISTIC PARTICLE MODELS, DEFORMED SYMMETRIES AND INTERACTION: A UNIFIED APPROACH

2013 ◽  
Vol 28 (27) ◽  
pp. 1350131 ◽  
Author(s):  
SOUVIK PRAMANIK ◽  
SUBIR GHOSH
Keyword(s):  
Relativistic Particle ◽  
Generalized Uncertainty Principle ◽  
External Electromagnetic Field ◽  
Point Particle ◽  
Dynamical Analysis ◽  
Lagrangian Model ◽  
Nonlinear Constraints ◽  
Unified Approach ◽  
Deformed Symmetries ◽  
Noncommutative Algebras

We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincaré generators for the systems that keep space–time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.

scholarly journals Canonical quantization, spacetime noncommutativity and deformed symmetries in field theory

2007 ◽  
Vol 40 (33) ◽  
pp. 10367-10382 ◽  
Author(s):  
Marcos Rosenbaum ◽  
J David Vergara ◽  
L Roman Juarez
Keyword(s):  
Field Theory ◽  
Canonical Quantization ◽  
Deformed Symmetries

scholarly journals QUANTUM SPACE-TIME: DEFORMED SYMMETRIES VERSUS BROKEN SYMMETRIES

2002 ◽  
Author(s):  
GIOVANNI AMELINO-CAMELIA
Keyword(s):  
Space Time ◽  
Quantum Space ◽  
Broken Symmetries ◽  
Deformed Symmetries

scholarly journals Onq-deformed symmetries as Poisson–Lie symmetries and application to Yang–Baxter type models

2016 ◽  
Vol 49 (41) ◽  
pp. 415402 ◽  
Author(s):  
F Delduc ◽  
S Lacroix ◽  
M Magro ◽  
B Vicedo
Keyword(s):  
Lie Symmetries ◽  
Deformed Symmetries

scholarly journals An Introduction to κ-Deformed Symmetries, Phase Spaces and Field Theory

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 946
Author(s):  
Michele Arzano ◽  
Jerzy Kowalski-Glikman
Keyword(s):  
Field Theory ◽  
Phase Space ◽  
Scalar Field ◽  
Lie Groups ◽  
Relativistic Particle ◽  
Deformed Symmetries ◽  
Poincaré Algebra ◽  
Free Scalar ◽  
Poisson Lie Groups ◽  
Relativistic Phase

In this review, we give a basic introduction to the κ-deformed relativistic phase space and free quantum fields. After a review of the κ-Poincaré algebra, we illustrate the construction of the κ-deformed phase space of a classical relativistic particle using the tools of Lie bi-algebras and Poisson–Lie groups. We then discuss how to construct a free scalar field theory on the non-commutative κ-Minkowski space associated to the κ-Poincaré and illustrate how the group valued nature of momenta affects the field propagation.

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