Chennai Mathematical Institute


2.00 pm, Seminar Hall
Localization in Quantum field theory

A.P. Balachandran
Chennai Mathematical Institute.


A covariant position operator does not exist for interacting relativistic quantum systems. Thus wave functions localised in spacetime regions cannot be defined and Born's probability interpretation fails for these systems.

Instead, an algebraic notion of localisation exists which is local, causal and covariant. It emerges already from Wigner's theory of unitary irreducible representations and is called modular localisation. This talk reviews this concept developed by Brunetti,Guido and Longo, Schroer and others. The basic ingredient in such localisation is the Rindler wedge. For the Rindler wedge, it shows in an elegant way how the well-known mixed state emerges. This wedge and associated mixed state are of fundamental importance in black hole physics.

Modular localisation also works for the intersection of an arbitrary number of wedges. Any causally complete region can be generated in this manner.

This talk will also suggest applications of modular theory to entanglement entropy, edge states and emergent spacetimes.