Young-Mills field theory is the basis of modern gauge field theory and an important physical breakthrough in the second half of the 20th century, aiming at describing the behavior of elementary particles with non-Abelian Lie groups. It was first proposed by physicists Yang Zhenning and Mills in 1954.

This theory, which was not valued by the physics community at that time, developed into the standard model today through the concepts of spontaneous symmetry breaking and asymptotic freedom introduced by many scholars from 1960 to 1970. The Young-Mills equation in this theory is a set of nonlinear partial differential equations that have never been considered in mathematics.

Extended data:

Young-Mills theory is a normative theory based on SU(N) group. 1953, Wolfgang Pauli wrote this kind of normative theory for the first time, and summarized the five-dimensional Kaluza-Klein theory. However, he found it impossible to make the gauge boson have mass, so he chose not to publish his results.

Although this achievement was not officially published in the paper, he talked about this theory in his later speech.

1954 and robert mills wrote the present Yang -Mills theory, which extended the gauge theory of commutative groups (applying quantum electrodynamics) to non-commutative groups to explain the strong interaction, so it is also called non-Abelian gauge field theory.

At first, the idea was not successful. The reason is that the quantum of Young-Mills theory must have zero mass to keep gauge invariance. If its particle mass is zero, its function is long-range force. However, the influence of long-range force was not observed in the experiment. So this theory was not taken seriously at that time.

It was not until 1960s and others began to use symmetry breaking's mechanism to get the particles with mass from the zero-mass particle theory that the importance of Yang-Mills theory emerged.

Baidu Encyclopedia-Young Mills Theory