Deformed Field Theory on kappa-spacetime

Abstract

A general formalism is developed that allows the construction of a field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime (Poincar\' e group) is replaced by a quantum group. This formalism is demonstrated for the kappa-deformed Poincaré algebra and its quantum space. The algebraic setting is mapped to the algebra of functions of commuting variables with a suitable star-product. Fields are elements of this function algebra. The Dirac and Klein-Gordon equation are defined and an action is found from which they can be derived.

19 pages; changes made in section 4 concerning the definition of field transformations

References in corpus (15)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Gauge Theory on Noncommutative Spaces
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• Doubly Special Relativity theories as different bases of $\kappa$--Poincaré algebra
• Quantum $\kappa$-Poincare in Any Dimensions
• Coproduct and star product in field theories on Lie-algebra non-commutative space-times
• Local D=4 Field Theory on $\kappa$--Deformed Minkowski Space
• Noncommutative Differential Calculus on the Kappa-Minkowski Space
• A New Null-Plane Quantum Poincare Algebra
• The Quantum Deformed Dirac Equation from the k-Poincare` Algebra
• $\kappa$--deformed Wigner construction of relativistic wave functions and free fields on $\kappa$-Minkowski space
• The classical basis for $\kappa$-deformed Poincaré (super)algebra and the second $\kappa$-deformed supersymmetric Casimir
• Solutions of Klein--Gordon and Dirac equations on quantum Minkowski spaces

Cited by in corpus (122)

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• 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
• Topics in Noncommutative Geometry Inspired Physics
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• Fock space, quantum fields and kappa-Poincaré symmetries
• Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
• kappa-Minkowski spacetime as the result of Jordanian twist deformation
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• The Standard Model on Non-Commutative Space-Time: Electroweak Currents and Higgs Sector
• Scalar Field Theory on Non-commutative Snyder Space-Time
• Quantum Black Hole in the Generalized Uncertainty Principle Framework
• From noncommutative kappa-Minkowski to Minkowski space-time
• Hopf-algebra description of noncommutative-spacetime symmetries
• Construction of $\theta$-Poincaré Algebras and their Invariants on ${\mathcal{M}}_{\theta }$
• Classical basis for kappa-Poincare algebra and doubly special relativity theories
• On $\kappa$-Deformation and UV/IR Mixing
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• 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
• $\kappa$-Minkowski Spacetime Through Exotic "Oscillator"
• On the $\kappa$-Dirac Oscillator revisited
• Lorentz invariant field theory on kappa-Minkowski space
• Scalar field propagation in the phi^4 kappa-Minkowski model
• Scalar field theory on $\kappa$-Minkowski space-time and Doubly Special Relativity
• Derivatives, forms and vector fields on the kappa-deformed Euclidean space
• Noncommutative field theory from angular twist
• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• Noncommutative Differential Forms on the kappa-deformed Space
• Pauli-Jordan Function and Scalar Field Quantization in $\kappa$-Minkowski Noncommutative Spacetime
• Localization and Reference Frames in $\kappa$-Minkowski Spacetime
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• Newton's Equation on the kappa space-time and the Kepler problem
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• A twisted look on kappa-Minkowski: U(1) gauge theory
• $\kappa$-deformed Dirac Equation
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• On kappa-deformation and triangular quasibialgebra structure
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• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
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• Effects of Noncommutativity on the Black Hole Entropy
• U(1) gauge field theory on kappa-Minkowski space
• Maxwell's equations on the $\kappa$-Minkowski spacetime and Electric-Magnetic duality
• Unified description for kappa-deformations of orthogonal groups
• A symmetry invariant integral on kappa-deformed spacetime
• Kappa-deformed oscillators, the choice of star product and free kappa-deformed quantum fields
• $\kappa$-Poincaré invariant orientable field theories at 1-loop
• Gauge theories on $\kappa$-Minkowski spaces: Twist and modular operators
• The 2D $\kappa$-Dirac oscillator
• Spectral geometry of $\kappa$-Minkowski space
• The $AdS$ particle
• $k$-Minkowski-deformation of $U(1)$ gauge theory
• Uniformly accelerating observer in $\kappa$-deformed space-time
• Gauge Theories on Deformed Spaces
• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
• Jordanian Quantum Deformations of D=4 Anti-de-Sitter and Poincare Superalgebras
• $\kappa$-Deformations and Extended $\kappa$-Minkowski Spacetimes
• Star product and interacting fields on $\kappa$-Minkowski space
• Noncommutative Field Theory on Homogeneous Gravitational Waves
• Entanglement dynamics in $\kappa$-deformed spacetime
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• $\kappa$-Minkowski star product in any dimension from symplectic realization
• Low-energy constraints on kappa-Minkowski extension of the Standard Model
• Gauge Theory on Twisted $\kappa$-Minkowski: Old Problems and Possible Solutions
• Poisson gauge models and Seiberg-Witten map
• Differential forms and k-Minkowski spacetime from extended twist
• Light-like $\kappa$-deformations and scalar field theory via Drinfeld twist
• Particle and Antiparticle sectors in DSR1 and kappa-Minkowski space-time
• Lorentz Covariant k-Minkowski Spacetime
• Uniformly accelerated detector in the $\kappa$-deformed Dirac vacuum
• Effects of quantum deformation on the integer quantum Hall effect
• Star Product and Invariant Integration for Lie type Noncommutative Spacetimes
• Twisted BRST symmetry in gauge theories on $\kappa$-Minkowski
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• A Dynamical 2-dimensional Fuzzy Space
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• Deformed conformal and super-Poincaré symmetries in the non-(anti)commutative spaces
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• Photonic realization of the kappa-deformed Dirac equation
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• Heisenberg Evolution in a Quantum Theory of Noncommutative Fields
• Twisted Fermionic Oscillator Algebra in $\kappa$-Minkowski space-time
• Doubly special relativity as a non-local quantum field theory
• A Field Theory Model With a New Lorentz-Invariant Energy Scale
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• Poisson electrodynamics on $\kappa$-Minkowski space-time
• Newtonian cosmology and Evolution of kappa-deformed universe
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• From quantum deformations of relativistic symmetries to modified kinematics and dynamics
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