nLab state-field correspondence

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

The following needs clarification.

A field operator ϕ\phi in a quantum field theory with a distinguished vacuum vector |0|0\rangle defines its incoming state as the |ϕ inU(0,)ϕ|0|\phi_{in}\rangle \coloneqq U(0,-\infty)\phi |0\rangle i.e. as the limit when time goes to infinity of the state ϕ|0\phi|0\rangle, here U(t 1,t 2)U(t_1,t_2) is the evolution operator from t 1t_1 to t 2t_2 (which may be written as U(t 2t 1)U(t_2-t_1) when the Hamiltonian is time-independent), which is by definition the inverse of U(t 2,t 1)U(t_2,t_1) for t 2>t 1t_2\gt t_1. The assignment ϕ|ϕ in\phi\mapsto |\phi_{in}\rangle is a bijection for conformal field theories.

References

Discussion in conformal field theory:

Last revised on December 25, 2021 at 10:42:28. See the history of this page for a list of all contributions to it.