Search results
Results from the WOW.Com Content Network
Yang–Mills theory is a quantum field theory for nuclear binding devised by Chen Ning Yang and Robert Mills in 1953, as well as a generic term for the class of similar theories. The Yang–Mills theory is a gauge theory based on a special unitary group SU( n ) , or more generally any compact Lie group .
In theoretical physics, more specifically in quantum field theory and supersymmetry, supersymmetric Yang–Mills, also known as super Yang–Mills and abbreviated to SYM, is a supersymmetric generalization of Yang–Mills theory, which is a gauge theory that plays an important part in the mathematical formulation of forces in particle physics.
In gauge theory, topological Yang–Mills theory, also known as the theta term or -term is a gauge-invariant term which can be added to the action for four-dimensional field theories, first introduced by Edward Witten. [1]
The aim of the loop representation in the context of Yang–Mills theories is to avoid the redundancy introduced by Gauss gauge symmetries allowing to work directly in the space of physical states (Gauss gauge invariant states). The idea is well known in the context of lattice Yang–Mills theory (see lattice gauge theory). Attempts to explore ...
N = 4 super Yang–Mills can be derived from a simpler 10-dimensional theory, and yet supergravity and M-theory exist in 11 dimensions. The connection is that if the gauge group U( N ) of SYM becomes infinite as N → ∞ {\displaystyle N\rightarrow \infty } it becomes equivalent to an 11-dimensional theory known as matrix theory .
Through the process of dimensional reduction, the Yang–Mills equations may be used to derive other important equations in differential geometry and gauge theory. Dimensional reduction is the process of taking the Yang–Mills equations over a four-manifold, typically R 4 {\displaystyle \mathbb {R} ^{4}} , and imposing that the solutions be ...
The Yang–Mills existence and mass gap problem is an unsolved problem in mathematical physics and mathematics, and one of the seven Millennium Prize Problems defined by the Clay Mathematics Institute, which has offered a prize of US$1,000,000 for its solution. The problem is phrased as follows: [1] Yang–Mills Existence and Mass Gap.
In mathematical physics, two-dimensional Yang–Mills theory is the special case of Yang–Mills theory in which the dimension of spacetime is taken to be two. This special case allows for a rigorously defined Yang–Mills measure, meaning that the (Euclidean) path integral can be interpreted as a measure on the set of connections modulo gauge transformations.