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A theorem which specifies the structure of the generic unitary representation of the Weyl relations and thus establishes the equivalence of Heisenberg's matrix mechanics and ...

Informally, a symplectic map is a map which preserves the sum of areas projected onto the set of (p_i,q_i) planes. It is the generalization of an area-preserving map. ...

In the Wolfram Language, WignerD[{j, m ,n}, psi, theta, phi] gives the m×n matrix element of a (2j+1)-dimensional unitary representation of SU(2) parametrized by three Euler ...

Gauge theory studies principal bundle connections, called gauge fields, on a principal bundle. These connections correspond to fields, in physics, such as an electromagnetic ...

The eight Gell-Mann matrices lambda_i, i=1,...,8, are an example of the set of generators of the Lie algebra associated to the special unitary group SU(3). Explicitly, these ...

The generalized Gell-Mann matrices are the n^2-1 matrices generating the Lie algebra associated to the special unitary group SU(n), n>=2. As their name suggests, these ...

There are two types of singular values, one in the context of elliptic integrals, and the other in linear algebra. For a square matrix A, the square roots of the eigenvalues ...

Let X and Y be Banach spaces and let f:X->Y be a function between them. f is said to be Gâteaux differentiable if there exists an operator T_x:X->Y such that, for all v in X, ...

The tilde is the mark "~" placed on top of a symbol to indicate some special property. x^~ is voiced "x-tilde." The tilde symbol is commonly used to denote an operator. In ...

The notion of a Hilbert C^*-module is a generalization of the notion of a Hilbert space. The first use of such objects was made by Kaplansky (1953). The research on Hilbert ...