Local Field Theory ON $\kappa$-Minkowski Space, Star Products and Noncommutative Translations

Abstract

We consider local field theory on $\kappa$-deformed Minkowski space which is an example of solvable Lie-algebraic noncommutative structure. Using integration formula over $\kappa$-Minkowski space and $\kappa$-deformed Fourier transform we consider for deformed local fields the reality conditions as well as deformation of action functionals in standard Minkowski space. We present explicite formulas for two equivalent star products describing CBH quantization of field theory on $\kappa$-Minkowski space. We express also via star product technique the noncommutative translations in $\kappa$-Minkowski space by commutative translations in standard Minkowski space.

LateX2e, 8 pages, Talk by J. Lukierski at Colloqium on Quantum Groups and Integrable Systems, Prague, June 2000, (Czech. J. Phys. 50, 2000 in press)

References in corpus (1)

• String Theory and Noncommutative Geometry

Cited by in corpus (45)

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• New realizations of Lie algebra kappa-deformed Euclidean space
• Twisted Statistics in kappa-Minkowski Spacetime
• Deformed Special Relativity and Deformed Symmetries in a Canonical Framework
• Improved limit on quantum-spacetime modifications of Lorentz symmetry from observations of gamma-ray blazars
• Covariant realizations of kappa-deformed space
• Phenomenology of Doubly Special Relativity
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• Fractional and noncommutative spacetimes
• Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
• Generalized kappa-deformed spaces, star-products, and their realizations
• Scalar field propagation in the phi^4 kappa-Minkowski model
• Derivatives, forms and vector fields on the kappa-deformed Euclidean space
• Space-time symmetry of noncommutative field theory
• Anatomy of a deformed symmetry: field quantization on curved momentum space
• $\kappa$--deformed Wigner construction of relativistic wave functions and free fields on $\kappa$-Minkowski space
• Noncommutative Differential Forms on the kappa-deformed Space
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• Newton's Equation on the kappa space-time and the Kepler problem
• $\kappa$-deformed Dirac Equation
• kappa-Minkowski representations on Hilbert spaces
• Interplay between curvature and Planck-scale effects in astrophysics and cosmology
• Gravitational Collapse of a Homogeneous Scalar Field in Deformed Phase Space
• Introduction to Quantum-Gravity Phenomenology
• Kappa-deformed oscillators, the choice of star product and free kappa-deformed quantum fields
• Kappa-Deformations: Historical Developments and Recent Results
• The Momentum Spaces of $\kappa$-Minkowski noncommutative spacetime
• Uniformly accelerating observer in $\kappa$-deformed space-time
• Lorentz Covariant k-Minkowski Spacetime
• Uniformly accelerated detector in the $\kappa$-deformed Dirac vacuum
• Star Product and Invariant Integration for Lie type Noncommutative Spacetimes
• Canonical and Lie-algebraic twist deformations of $\kappa$-Poincare and contractions to $\kappa$-Galilei algebras
• A short introduction to $\kappa$-deformation
• $\kappa$--Rindler space
• Twisted Fermionic Oscillator Algebra in $\kappa$-Minkowski space-time
• Heisenberg Evolution in a Quantum Theory of Noncommutative Fields
• Poincaré Covariant k-Minkowski Spacetime
• Covariant formulation of Noether's Theorem for translations on kappa-Minkowski spacetime
• Global Space-Time Symmetries of Quantized Euclidean and Minkowski Superspaces
• Braided Tensor Products and the Covariance of Quantum Noncommutative Free Fields
• Total momentum and other Noether charges for particles interacting in a quantum spacetime
• Two ${\theta }_{\mu \nu }$ -deformed covariant relativistic quantum phase spaces as Poincare-Hopf algebroids
• Braided algebras and the kappa-deformed oscillators