Kappa-Deformations: Historical Developments and Recent Results

Abstract

I shall recall in historical perspective some results from nineties and show further how $\kappa$-deformed symmetries and $\kappa$-Minkowski space inspired DSR (Doubly of Deformed Special Relativity) approach proposed after 2000. As very recent development I shall show how to describe quantum-covariant $\kappa$-deformed phase spaces by passing from Hopf algebras to Hopf algebroids (arXiv:1507.02612) and I will briefly describe the $\kappa$-deformations of $Ad{S}_5\times S^5$ superstring target spaces (arXiv:1510.030.83).

19 pages; presented at ISQS24 Conference on Integrable Systems and Quantum Symmetries, Prague (Czech Republik), 14.06-18.06.2016, 3-rd POTOR (Polish Society on Relativity) Conference, Cracov (Poland), 25-29.09.2016 and 5-th Conference "New Trends in Field Theories", Varanasi (India), 06.11-10.11.2016. To be published in JPhysA, Conf.Series

References in corpus (4)

• On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
• Quantum Gravity, Dynamical Phase Space and String Theory
• Lie algebraic Noncommutative Gravity
• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems

Cited by in corpus (15)

• $\kappa$-Poincaré invariant quantum field theories with KMS weight
• Gauge theories on quantum spaces
• $\kappa$-Poincaré invariant orientable field theories at 1-loop
• Gauge theories on $\kappa$-Minkowski spaces: Twist and modular operators
• $\kappa$-Poincaré-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• Twisted BRST symmetry in gauge theories on $\kappa$-Minkowski
• Observables and Dynamics, Quantum to Classical, from a Relativity Symmetry and Noncommutative Geometric Perspective
• Quantum instability of gauge theories on $\kappa$-Minkowski space
• Field theories on $\rho$-deformed Minkowski space-time
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• Fuzzy de Sitter Space from kappa-Minkowski Space in Matrix Basis
• Quantum causality in $\kappa$-Minkowski and related constraints
• On the UV/IR mixing of Lie algebra-type noncommutatitive ${\varphi }^4$-theories
• Star-products for Lie-algebraic noncommutative Minkowski space-times