Gauge theory is usually discussed in the language of differential geometry. Mathematically, a specification is the selection of (partial) parts of a main package. Normative transformation is the transformation between two parts …
Mathematicians have noticed that the gauge potential in Young-Mills field is the connection on fiber bundles that mathematicians have been studying deeply since 1930s-1940s. Since 1975, mathematicians have done a lot of in-depth research on Young-Mills equation, which has also promoted the development of pure mathematics.
Young-Mills equation is an important differential equation, which refers to the Euler-Lagrange equation determined by Yang Yi Mills. Young-Mills equation is also called Young-Mills theory.
Young's theory is a canonical theory based on SU(N) group, or more generally, it is a compact semi-simple Lie group. Yang Zhenning's Mills theory aims to describe the behavior of elementary particles by using the strength of these non-Abelian lie groups and unified core electromagnetic and weak forces (that is, U( 1)×SU(2)) and quantum chromodynamics theory (based on SU(3)). Therefore, it forms the basis for us to understand the standard model of particle physics.
Modern gauge field theory with Yang-Mills theory as the core forms the so-called standard model of particle physics, so modern quantum field theory takes gauge field theory as the core. As the most successful physical framework to describe the subatomic world, quantum field theory is unparalleled in both computing power and conceptual coverage, and its prediction of the interaction between electrons and photons is accurate to 10.
Einstein's unified field theory, which he pondered hard in the latter half of his life, was not realized until his death, while Yang Zhenning's gauge field theory directly unified the weak interaction force and the strong interaction force. The description of gravity by Yang Mills' equation is comparable to that of general relativity, which actually unified three of the four basic forces of the universe in one fell swoop and completed three quarters of the unified field theory. In fact, China has never lacked a master, but the master can no longer shine for the whole era.
If the whole thing is done by one person, then his achievements are as great as Einstein's, even surpassing Einstein's! Only Einstein established the theory of relativity. Other physical theories, such as quantum mechanics, especially the later quantum field theory, were established by many people, sometimes after years of continuous efforts by generations.
Therefore, some physicists list Yang Zhenning as the third great scientist after Newton and Einstein …