What is non Abelian gauge theory?
In theoretical physics, a non-abelian gauge transformation means a gauge transformation taking values in some group G, the elements of which do not obey the commutative law when they are multiplied. By contrast, the original choice of gauge group in the physics of electromagnetism had been U(1), which is commutative.
What is a gauge gauge theory?
The term gauge refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian of a physical system. The transformations between possible gauges, called gauge transformations, form a Lie group—referred to as the symmetry group or the gauge group of the theory.
What are gauge fields?
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).
Is Yang Mills theory correct?
The current state of Yang-Mills theory has been compared to the early days of the calculus, when undeniably accurate and useful results were being obtained but before the formal development of analysis added rigorous definitions that eliminated logical fallacies.
What is local gauge invariance?
An important phenomenon discussed especially in the context of quantum field theories is local gauge invariance (e.g. [134]). The basic idea is that these symmetries allow different local configurations of rule applications—that can be thought of as different local “gauge” coordinate systems.
Is quantum electrodynamics a Yang Mills theory?
By the 1950s, when Yang–Mills theory was discovered, it was already known that the quantum version of Maxwell theory—known as Quantum Electrodynamics or QED—gives an extremely accurate account of electromagnetic fields and forces.
Is QCD a Yang Mills theory?
QCD is a theory that uses the Yang-Mills framework, specifically when we restrict attention to the gauge group SU(3).
Why it is called gauge theory?
The term gauge theory was coined by Weyl in analogy to a marking gauge , which a carpenter or machinist uses to precisely mark off fixed distances. The marking gauge is continuously adjustable, however, so that one can change the distance fixed by the gauge.
What do you understand by gauge invariance?
The term gauge invariance refers to the property that a whole class of scalar and vector potentials, related by so-called gauge transformations, describe the same electric and magnetic fields.
What is the difference between Lie group and gauge field?
The transformations between possible gauges, called gauge transformations, form a Lie group—referred to as the symmetry group or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field (usually a vector field) called the gauge field.
What is gauge theory?
(September 2016) ( Learn how and when to remove this template message) In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations ( Lie groups ).
What is a gauge field configuration?
A configuration in which the gauge field can be eliminated by a gauge transformation has the property that its field strength (in mathematical language, its curvature) is zero everywhere; a gauge theory is not limited to these configurations.
Why is the gauge field important in physics?
The gauge field becomes an essential part of the description of a mathematical configuration. A configuration in which the gauge field can be eliminated by a gauge transformation has the property that its field strength (in mathematical language, its curvature) is zero everywhere; a gauge theory is not limited to these configurations.