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.

Based on the Les Houches lectures given by authors in February 2012

References in corpus (5)

• Classical and quantum Lagrangian field theories with boundary
• Chern-Simons Theory with Wilson Lines and Boundary in the BV-BFV Formalism
• Feynman-diagrammatic description of the asymptotics of the time evolution operator in quantum mechanics
• Cohomology of Harmonic Forms on Riemannian Manifolds With Boundary
• Lie groups and Chern-Simons Theory

Cited by in corpus (7)

• BV-BFV approach to General Relativity, Einstein-Hilbert action
• Quantum Chern-Simons theories on cylinders: BV-BFV partition functions
• Quantum Abelian Yang-Mills Theory on Riemannian Manifolds with Boundary
• Dirichlet to Neumann operator for abelian Yang-Mills gauge fields
• General Boundary Formulation for $n$-Dimensional Classical Abelian Theory with Corners
• Theta Invariants of lens spaces via the BV-BFV formalism
• Harmonic Maps and the Symplectic Category