nLab Seiberg-Witten flow

Contents

Context

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

Differential cohomology

Contents

Idea

For a scalar function, a curve whose derivative is opposite to its gradient is called a gradient flow. It always points down the way of steepest descent and hence is monotonically descreasing with respect to the scalar function. It is then possible to study its convergence to critical points, especially those that are local minima.

If the scalar function is the Seiberg-Witten action functional, then the gradient flow is called Seiberg-Witten flow. It is described by the Seiberg-Witten equation and can be used to find solutions of the Seiberg-Witten equations, which are the critical points.

The Seiberg-Witten flow is named after Nathan Seiberg und Edward Witten, who introduced Seiberg-Witten theory in 1994.

References

See also:

Created on August 8, 2025 at 23:58:59. See the history of this page for a list of all contributions to it.