Gauge theory is a physical theory based on the idea that symmetric transformation can be realized locally or locally by full gauge field theory formula. Gauge field theory of noncommutative symmetric groups is sometimes called Yang-Mills theory. Physical systems are often represented by Lagrangian quantities that are invariant under certain transformations. When transformations are performed simultaneously in every time and space, they have global symmetry. Gauge field theory promotes this idea, which requires that Lagrangian quantities must also have local symmetry-it should be possible to realize these symmetric transformations in a specific region of time and space without affecting another region. This requirement is a generalization of the equivalence principle of general relativity.
The symmetry of specification reflects the redundancy of system expression.
The importance of gauge field theory in physics is that it successfully provides a unified mathematical formal framework-standard model for quantum electrodynamics, weak interaction and strong interaction. This theory accurately describes the experimental prediction of three basic forces in nature. It is a gauge field theory with gauge group SU(3) × SU(2) × U( 1). Modern theories such as string theory and some expressions of general relativity are gauge field theory in a sense.
Sometimes, the term gauge symmetry is used in a broader sense, including any local symmetry, such as differential homeomorphism. This meaning of the term is not used in this entry.
Maxwell electrodynamics is the earliest physical theory that contains gauge symmetry. However, the importance of this symmetry was not noticed in the early expression. After Einstein developed the general theory of relativity, Herman Weil tried to unify the general theory of relativity and electromagnetism, and speculated that the invariance under the transformation of Eichvarianz or scale ("gauge") may also be the local symmetry of the general theory of relativity. Later, it was found that this conjecture would lead to some non-physical results. However, after the development of quantum mechanics, Weil, Vladimir Fogg and Fritz London realized this idea, but made some modifications (the scale factor was replaced by a complex number, and the scale change became a phase change-a U( 1) gauge symmetry), which gave a beautiful explanation to a charged quantum particle whose wave function was affected by electromagnetic field. This is the first gauge field theory. Pauli promoted the spread of this theory in 1940. See R.M.P.13,203.
In the 1950' s, in order to solve some great confusion in elementary particle physics, Yang Zhenning and robert mills introduced the noncommutative gauge field theory as a model to understand the strong interaction of bound nucleons in the nucleus. Ronald Shaw, who worked with abdul sallam, independently put forward the same concept in his doctoral thesis. By extending gauge invariance in electromagnetism, they tried to construct a theory based on the effect of (noncommutative) SU(2) symmetric group on isospin proton and neutron pairs, similar to the effect of U( 1) group on quantum electrodynamics spinor field. In particle physics, the emphasis is on the use of quantized gauge field theory.
This idea was later found to be applicable to the quantum field theory of weak interaction and its unity with electromagnetism in weak current theory. When people realize that the noncommutative gauge field theory can derive a characteristic called asymptotic freedom, the gauge field theory becomes more attractive, because asymptotic freedom is considered as an important characteristic of strong interaction-thus promoting the research on finding the gauge field theory of strong interaction. This theory, called quantum chromodynamics, is the gauge field theory of SU(3) group acting on quark color charge. The standard model unifies the expressions of electromagnetic force, weak interaction and strong interaction in the language of gauge field theory.
In the1970s, Sir Michael attiya put forward a plan to study the mathematical solution of the classical Young-Mills equation. On the basis of this work, Simon Donaldson, a student of Atiyah, proved that the differentiable classification of smooth 4- manifolds is very different from their classification with only one homeomorphism. Michael Freedman used Donaldson's work to prove the existence of pseudo R4, that is, the singular differential structure in Euclidean four-dimensional space. This leads to the interest in gauge field theory itself, which is independent of its success in basic physics. 1994, edward witten and Nathan Seiberg invented gauge field technology based on supersymmetry, which made it possible to calculate specific topological invariants. These contributions of gauge field theory to mathematics have led to the emergence of this field. Fun.