The Principle of Stationary Variance in Quantum Field Theory

TL;DR

This paper advocates the principle of stationary variance as a variational method in quantum field theory, demonstrating its effectiveness across diverse areas such as magnetism, QED, and gauge theories.

Contribution

It introduces and validates the stationary variance principle as a novel variational approach in quantum field theory, expanding its application beyond quantum mechanics.

Findings

Effective in quantum field theory applications

Applicable to models like Heisenberg antiferromagnetism

Useful in gauge theories and QED

Abstract

The principle of stationary variance is advocated as a viable variational approach to quantum field theory. The method is based on the principle that the variance of energy should be at its minimum when the state of a quantum system reaches its best approximation for an eigenstate. While not too much popular in quantum mechanics, the method is shown to be valuable in quantum field theory, and three special examples are given in very different areas ranging from Heisenberg model of antiferromagnetism to quantum electrodynamics and gauge theories.