A topological way of finding solutions to the Yang–Mills equation

doi:10.1088/1572-9494/ab8a22

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Communications in Theoretical Physics ›› 2020, Vol. 72 ›› Issue (8): 085202. doi: 10.1088/1572-9494/ab8a22

• Particle Physics and Quantum Field Theory • Previous Articles Next Articles

A topological way of finding solutions to the Yang–Mills equation

Jun Nian^1,(),Yachao Qian²

¹Leinweber Center for Theoretical Physics, University of Michigan, Ann Arbor, MI 48109, United States of America
²Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, United States of America

Received: 2020-02-14 Revised: 2020-03-27 Accepted: 2020-03-27 Published: 2020-08-01

Abstract

Abstract:

We propose a systematic way of finding solutions to the classical Yang–Mills equation with nontrivial topology. This approach is based on one of the Wightman axioms for quantum field theory, which is referred to as the form invariance condition in this paper. For a given gauge group and a spacetime with certain isometries, thanks to this axiom that imposes strong constraints on the general ansatz, a systematic way of solving the Yang–Mills equation can be obtained in both flat and curved spacetimes. In order to demonstrate this method, we recover various known solutions as special cases, as well as producing new solutions not previously reported in the literature.

Key words: Yang–Mills theory, form invariance, curved space, exact solutions, Wu-Yang monopole, instanton

Jun Nian,Yachao Qian, Commun. Theor. Phys. 72 (2020) 085202.

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A topological way of finding solutions to the Yang–Mills equation

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