Semiclassical Quantization of Classical Field Theories

Abstract

These lectures are an introduction to formal semiclassical quantization of classical field theory. First we develop the Hamiltonian formalism for classical field theories on space time with boundary. It does not have to be a cylinder as in the usual Hamiltonian framework. Then we outline formal semiclassical quantization in the finite dimensional case. Towards the end we give an example of such a quantization in the case of Abelian Chern-Simons theory.


Keywords » Chern-Simons Theory - Factorization Algebras - Factorization Homology - Frobenius Algebras - Grupoids - Perturbative Quantum Field Theories - Quantum Teichmueller Theory - Supersymmetric Gauge Theories - Topological Field Theories - Witten-Reshetikhin-Turaev Invariants

Related subjects » History & Philosophical Foundations of Physics - Theoretical, Mathematical & Computational Physics