Dynamical origin of the ${\star }_{\theta }$-noncommutativity in field theory from quantum mechanics

Abstract

We show that introducing an extended Heisenberg algebra in the context of the Weyl-Wigner-Groenewold-Moyal formalism leads to a deformed product of the classical dynamical variables that is inherited to the level of quantum field theory, and that allows us to relate the operator space noncommutativity in quantum mechanics to the quantum group inspired algebra deformation noncommutativity in field theory.

arXiv comment17 pages, to be published in Phys. Lett. A

References in corpus (13)

• String Theory and Noncommutative Geometry
• Quantum Field Theory on Noncommutative Spaces
• The quantum structure of spacetime at the Planck scale and quantum fields
• Noncommutative Open String and D-brane
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• New concept of relativistic invariance in NC space-time: twisted Poincaré symmetry and its implications
• Untwisting Noncommutative R^d and the Equivalence of Quantum Field Theories
• New Lie-Algebraic and Quadratic Deformations of Minkowski Space from Twisted Poincare Symmetries
• Deformed Coordinate Spaces; Derivatives
• Gauge Theory on a Quantum Phase Space
• Path Integral Formulation of Noncommutative Quantum Mechanics
• Space-Time Noncommutativity from Particle Mechanics
• Noncommutativity and Reparametrisation symmetry

Cited by in corpus (7)

• Weyl-Wigner Formulation of Noncommutative Quantum Mechanics
• Noncommutative Field Theory from Quantum Mechanical Space-Space Noncommutativity
• Deformation quantization of noncommutative quantum mechanics and dissipation
• Canonical Quantization, Space-Time Noncommutativity and Deformed Symmetries in Field Theory
• Space-Time Diffeomorphisms in Noncommutative Gauge Theories
• Deformation of Noncommutative Quantum Mechanics
• On deformed quantum mechanical schemes and $\star$-value equations based on the space-space noncommutative Heisenberg-Weyl group