nLab Fredholm index

Contents

Context

Index theory

Operator algebra

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

A Fredholm operator F:F \,\colon\, \mathcal{H} \longrightarrow \mathcal{H} by definition has finite-dimensional kernel ker(F)ker(F) and cokernel coker(F)coker(F). Its index is the difference between these dimensions:

ind(F)dim(ker(F))dim(coker(F)). ind(F) \;\coloneqq\; dim\big(ker(F)\big) \,-\, dim\big(coker(F)\big) \,.

Examples

References

Textbook account:

Created on May 9, 2022 at 02:57:02. See the history of this page for a list of all contributions to it.