Quantum kappa-deformed differential geometry and field theory

Abstract

I introduce in kappa-Minkowski noncommutative spacetime the basic tools of quantum differential geometry, namely bicovariant differential calculus, Lie and inner derivatives, the integral, the Hodge-star and the metric. I show the relevance of these tools for field theory with an application to complex scalar field, for which I am able to identify a vector-valued four-form which generalizes the energy-momentum tensor. Its closedness is proved, expressing in a covariant form the conservation of energy-momentum.

23 pages, latex

References in corpus (4)

• The principle of relative locality
• Relative locality: A deepening of the relativity principle
• Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
• A no-pure-boost uncertainty principle from spacetime noncommutativity

Cited by in corpus (13)

• Localization and Reference Frames in $\kappa$-Minkowski Spacetime
• Gauge theories on $\kappa$-Minkowski spaces: Twist and modular operators
• The Momentum Spaces of $\kappa$-Minkowski noncommutative spacetime
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• $\kappa$-Poincaré-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Central tetrads and quantum spacetimes
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces
• Generalization of Weyl realization to a class of Lie superalgebras
• T-Minkowski noncommutative spacetimes II: classical field theory
• The Weyl-Mellin quantization map for $\kappa$-Minkowski Noncommutative Spacetime
• Asymmetry in momentum space: restoring $\mathcal{C}\mathcal{P}\mathcal{T}$ invariance of $\kappa$-field theory