Hopf algebra, thermodynamics and entanglement in quantum field theory

Abstract

The quantum deformation of the Hopf algebra describes the skeleton of quantum field theory, namely its characterizing feature consisting in the existence of infinitely many unitarily inequivalent representations of the canonical commutation relations. From this we derive the thermal properties of quantum field theory, with the entropy playing the role of the generator of the non-unitary time evolution. The entanglement of the quantum vacuum appears to be robust against interaction with the environment: on cannot ``unknot the knots" in the infinite volume limit.

6 pages, to appear in Proceedings of the First International Conference on Quantum Limits to the Second Law, July 29-31, 2002, University of San Diego, San Diego, California, USA