Search results
Results from the WOW.Com Content Network
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 it becomes equivalent to an 11-dimensional theory known as matrix theory. [citation needed]
The Sciences of the Artificial (1969) [1] is a book by Herbert A. Simon in the domain of the learning sciences and artificial intelligence; it is especially influential in design theory. [2] The book is themed around how artificial phenomena ought to be categorized, discussing as to whether such phenomena belong within the domain of 'science'. [3]
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 ...
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.
Floer also developed a closely related theory for Lagrangian submanifolds of a symplectic manifold. A third construction, also due to Floer, associates homology groups to closed three-dimensional manifolds using the Yang–Mills functional. These constructions and their descendants play a fundamental role in current investigations into the ...
In mathematics, and especially differential topology and gauge theory, Donaldson's theorem states that a definite intersection form of a compact, oriented, smooth manifold of dimension 4 is diagonalizable. If the intersection form is positive (negative) definite, it can be diagonalized to the identity matrix (negative identity matrix) over the ...
In 1978, Albert Schwarz formulated Chern–Simons theory, early topological quantum field theory, using Chern-Simons forms. [ 5 ] In the gauge theory , the integral of Chern-Simons form is a global geometric invariant, and is typically gauge invariant modulo addition of an integer.
Simon & Griffiths (1973) extended the Lee–Yang theorem to certain continuous probability distributions by approximating them by a superposition of Ising models. Newman (1974) gave a general theorem stating roughly that the Lee–Yang theorem holds for a ferromagnetic interaction provided it holds for zero interaction.