nLab
field history

Contents

Context

Algebraic Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Contents

Idea

Given a Lagrangian field theory with field bundle EfbΣE \overset{fb}{\to} \Sigma over spacetime Σ\Sigma, then a field history is a smooth section of this field bundle ΦΓ Σ(E)\Phi \in \Gamma_\Sigma(E).

For every Cauchy surface Σ pΣ\Sigma_p \hookrightarrow \Sigma the restriction Φ| Σ p\Phi\vert_{\Sigma_p} of Φ\Phi to Σ p\Sigma_p may be thought of as the field configuration “at that time” and hence the change of Φ| Σ p\Phi\vert_{\Sigma_p} as the choice of Cauchy surface changes reflects the “history” of these configurations, whence the name.

For a sigma model field theory a field history may be thought of as a trajectory.

For more see at geometry of physics – perturbative quantum field theory the chapter Fields.

Last revised on August 1, 2018 at 08:23:32. See the history of this page for a list of all contributions to it.