# What is quantum Yang-Mills theory?

## What is quantum Yang-Mills theory?

Yang-Mills theory, in physics, a generalization of Scottish physicist James Clerk Maxwell’s unified theory of electromagnetism, also known as Maxwell’s equations, used to describe the weak force and the strong force in subatomic particles in terms of a geometric structure, or quantum field theory.

What is a gauge field theory?

A gauge field theory is a special type of quantum field theory, in which matter fields (like electrons and quarks, which make up protons and neutrons) interact with each other via forces that are mediated by the exchange of vector bosons (like photons and gluons, which bind quarks together in nucleons).

How important is Yang-Mills theory?

However, the importance of Yang-Mills theory is clear, the Standard Model has produced calculations of amazing accuracy in particle physics and, in mathematics, ideas arising from Yang-Mills theory and from quantum field theory, are increasingly important in geometry, algebra and analysis.

### Who invented gauge theory?

The classical theory of the electromagnetic field, proposed by the British physicist James Clerk Maxwell in 1864, is the prototype of gauge theories, though the concept of gauge transformation was not fully developed until the early 20th century by the German mathematician Hermann Weyl.

Why are they called gauge theories?

These theories are called gauge theories because their standard formulation contains unobservable and hence apparently redundant elements. In the philosophical community, the gauge aspects of Yang-Mills theories have received far less attention then those of general relativity.

What is gauge function?

in fractal geometry, a synonym for dimension function; in control theory and dynamical systems, a synonym for Lyapunov candidate function; in gauge theory, a synonym for gauge symmetry.

#### What is Yang Mills existence and mass gap explained?

The successful use of Yang-Mills theory to describe the strong interactions of elementary particles depends on a subtle quantum mechanical property called the “mass gap”: the quantum particles have positive masses, even though the classical waves travel at the speed of light. …

Why do we use gauge transformation?

No physics can depend on the choice of this constant, but some choices make problems more easily solvable than others. This freedom to add a constant potential is called gauge freedom and the different potentials one can obtain that lead to the same physical field are generated by means of a gauge transformation.

What is super symmetry theory?

Supersymmetry is an extension of the Standard Model that aims to fill some of the gaps. It predicts a partner particle for each particle in the Standard Model. If the theory is correct, supersymmetric particles should appear in collisions at the LHC.

## What is Yangyang–Mills theory?

Yang–Mills theory is a gauge theory based on a special unitary group SU(N), or more generally any compact, reductive Lie algebra.

What is the history of gauge theory in physics?

In early 1954, Chen Ning Yang and Robert Mills extended the concept of gauge theory for abelian groups, e.g. quantum electrodynamics, to nonabelian groups to provide an explanation for strong interactions. The idea by Yang–Mills was criticized by Pauli, as the quanta of the Yang–Mills field must be massless in order…

What is the difference between QCD and Yang-Mills theory?

This prompted a significant restart of Yang–Mills theory studies that proved successful in the formulation of both electroweak unification and quantum chromodynamics (QCD). The electroweak interaction is described by the gauge group SU(2) × U(1), while QCD is an SU(3) Yang–Mills theory.

### Can we use variational methods in Yang–Mills theory in higher dimensions?

While the scope for variational methods in Yang–Mills theory in higher dimensions is very limited, there are useful analytical results about solutions of the Yang–Mills equations. An important monotonicity result was obtained by Price (1983).

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