Quantum Field Theory and Functional Integrals

Described here is Feynman's path integral approach to quantum mechanics and quantum field theory from a functional integral point of view. Therein lies the main focus of Euclidean field theory. The notion of Gaussian measure and the construction of the Wiener measure are covered. As well, the notion of classical mechanics and the Schrödinger picture of quantum mechanics are recalled. There, the equivalence to the path integral formalism is shown by deriving the quantum mechanical propagator from it. Additionally, an introduction to elements of constructive quantum field theory is provided for readers.

Gives a compact guide to the mathematical structure of quantum field theory Explains concisely the relation of the Schrödinger picture of quantum mechanics with Feynman's path integral approach Includes a rigorous mathematical treatment of measure theoretic and probability aspects of the relevant object

Autorentext

Nima Moshayedi's research is in mathematical physics where he is interested in geometric and algebraic methods of quantum field theory. In particular, his focus lies on topological quantum field theories, local gauge theories, algebraic topology, symplectic geometry, quantization procedures and higher structures in quantum field theory.

Inhalt
A Brief Recap of Classical Mechanics.- The Schrödinger Picture of Quantum Mechanics.- The Path Integral Approach to Quantum Mechanics.- Construction of Quantum Field Theories.