Gauge theories on the kappa-Minkowski spacetime

Abstract

This study of gauge field theories on kappa-deformed Minkowski spacetime extends previous work on field theories on this example of a noncommutative spacetime. We construct deformed gauge theories for arbitrary compact Lie groups using the concept of enveloping algebra-valued gauge transformations and the Seiberg-Witten formalism. Derivative-valued gauge fields lead to field strength tensors as the sum of curvature- and torsion-like terms. We construct the Lagrangians explicitly to first order in the deformation parameter. This is the first example of a gauge theory that possesses a deformed Lorentz covariance.

arXiv comment17 pages, few minor revisions

References in corpus (14)

• String Theory and Noncommutative Geometry
• Deformation quantization of Poisson manifolds, I
• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Gauge Theory on Noncommutative Spaces
• The Standard Model on Non-Commutative Space-Time
• Construction of non-Abelian gauge theories on noncommutative spaces
• Enveloping algebra valued gauge transformations for non-abelian gauge groups on non-commutative spaces
• Deformed Field Theory on kappa-spacetime
• Non-Commutative GUTs, Standard Model and C,P,T
• A Cohomological Approach to the Non-Abelian Seiberg-Witten Map
• Local BRST cohomology and Seiberg-Witten maps in noncommutative Yang-Mills theory
• Chern-Simons in the Seiberg-Witten map for non-commutative Abelian gauge theories in 4D

Cited by in corpus (71)

• A Gravity Theory on Noncommutative Spaces
• Kappa-Minkowski space-time and the star product realizations
• New realizations of Lie algebra kappa-deformed Euclidean space
• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
• Twisted Statistics in kappa-Minkowski Spacetime
• Covariant realizations of kappa-deformed space
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
• The Standard Model on Non-Commutative Space-Time: Electroweak Currents and Higgs Sector
• From noncommutative kappa-Minkowski to Minkowski space-time
• Electrodynamics on $\kappa$-Minkowski space-time
• Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
• Generalized kappa-deformed spaces, star-products, and their realizations
• Scalar field theory on $\kappa$-Minkowski space-time and Doubly Special Relativity
• Construction of Gauge Theories on Curved Noncommutative Spacetime
• Derivatives, forms and vector fields on the kappa-deformed Euclidean space
• Geodesic equation in $k$-Minkowski spacetime
• 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
• Newton's Equation on the kappa space-time and the Kepler problem
• A twisted look on kappa-Minkowski: U(1) gauge theory
• $\kappa$-deformed Dirac Equation
• $\kappa$-Poincaré invariant quantum field theories with KMS weight
• Gauge theories on quantum spaces
• kappa-Minkowski representations on Hilbert spaces
• U(1) gauge field theory on kappa-Minkowski space
• Second order expansions of action functionals of noncommutative gauge theories
• Maxwell's equations on the $\kappa$-Minkowski spacetime and Electric-Magnetic duality
• Field theory on kappa-spacetime
• A symmetry invariant integral on kappa-deformed spacetime
• $\kappa$-Poincaré invariant orientable field theories at 1-loop
• Gauge theories on $\kappa$-Minkowski spaces: Twist and modular operators
• Non-commutative deformation of Chern-Simons theory
• Uniformly accelerating observer in $\kappa$-deformed space-time
• $k$-Minkowski-deformation of $U(1)$ gauge theory
• Gauge Theories on Deformed Spaces
• Poisson gauge theory
• Jordanian Quantum Deformations of D=4 Anti-de-Sitter and Poincare Superalgebras
• Star product and interacting fields on $\kappa$-Minkowski space
• Low-energy constraints on kappa-Minkowski extension of the Standard Model
• $\kappa$-Minkowski star product in any dimension from symplectic realization
• Gauge Theory on Twisted $\kappa$-Minkowski: Old Problems and Possible Solutions
• Light-like $\kappa$-deformations and scalar field theory via Drinfeld twist
• Gauge Theory of the Star Product
• Hermitian realizations of kappa-Minkowski spacetime
• Uniformly accelerated detector in the $\kappa$-deformed Dirac vacuum
• $L_{\infty }$-Bootstrap Approach to Non-Commutative Gauge Theories
• Star Product and Invariant Integration for Lie type Noncommutative Spacetimes
• Dirac equation on coordinate dependent noncommutative space-time
• Twisted BRST symmetry in gauge theories on $\kappa$-Minkowski
• Vacuum energy and the cosmological constant problem in $\kappa$-Poincaré invariant field theories
• Exponential Formulas and Lie Algebra Type Star Products
• Quantisation of Klein-Gordon field in $\kappa$ space-time: deformed oscillators and Unruh effect
• Lie-Poisson gauge theories and $\kappa$-Minkowski electrodynamics
• Leibniz rules for enveloping algebras in symmetric ordering
• Heisenberg double versus deformed derivatives
• q-Quaternions and q-deformed su(2) instantons
• Maximal acceleration in non-commutative space-time and its implications
• Twisted Fermionic Oscillator Algebra in $\kappa$-Minkowski space-time
• A Field Theory Model With a New Lorentz-Invariant Energy Scale
• q-Deformed su(2) instantons by q-quaternions
• $\kappa$-deformed power spectrum and modified Unruh temperature
• Quantisation of $\kappa$-deformed Dirac equation
• A universal formula for representing Lie algebra generators as formal power series with coefficients in the Weyl algebra
• Some considerations on duality concerning kappa-Minkowski spacetime theories
• Twist deformations leading to kappa-Poincare Hopf algebra and their application to physics
• Gauge theory on kappa-Minkowski revisited: the twist approach
• Non-Commutative GUTs, Standard Model and C,P,T properties from Seiberg-Witten map
• Gauge theory models on $\kappa$-Minkowski space: Results and prospects