Quantum Symmetries and K-Theory
نویسنده
چکیده
Modified from Vienna Lectures August 2014 for PiTP, July 2015. VERY ROUGH VERSION: UNDER CONSTRUCTION. Version: July 23, 2015
منابع مشابه
Quantum double and κ-Poincaré symmetries in (2+1)-gravity and Chern-Simons theory
We review the role of Drinfeld doubles and κ-Poincaré symmetries in quantised (2+1)gravity and Chern-Simons theory. We discuss the conditions under which a given Hopf algebra symmetry is compatible with a Chern-Simons theory and determine this compatibility explicitly for the Drinfeld doubles and κ-Poincaré symmetries associated with the isometry groups of (2+1)-gravity. In particular, we expla...
متن کاملGENERALIZED JOINT HIGHER-RANK NUMERICAL RANGE
The rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. For noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. In this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, Generaliz...
متن کاملReduction of Differential Equations by Lie Algebra of Symmetries
The paper is devoted to an application of Lie group theory to differential equations. The basic infinitesimal method for calculating symmetry group is presented, and used to determine general symmetry group of some differential equations. We include a number of important applications including integration of ordinary differential equations and finding some solutions of partial differential equa...
متن کامل’t Hooft Anomaly Matching Conditions for Generalized Symmetries in 2D
The ’t Hooft anomaly matching conditions are a standard tool to study and test nonperturbative issues in quantum field theory. We give a new, simple proof of the anomaly matching conditions in 2D Poincarè invariant theories. We consider the case of invariance under a large class of generalized symmetries, which include abelian and non-abelian internal symmetries, space-time symmetries generated...
متن کاملA Note on the Symmetries and Renormalisability of (Quantum) Gravity
We make some remarks on the group of symmetries in gravity; we believe that K-theory and noncommutative geometry inescepably have to play an important role. Furthermore we make some comments and questions on the recent work of Connes and Kreimer on renormalisation, the Riemann-Hilbert correspondence and their relevance to quantum gravity. PACS classification: 11.10.-z; 11.15.-q; 11.30.-Ly
متن کامل