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The projective general orthogonal group PGO_n(q) is the group obtained from the general orthogonal group GO_n(q) on factoring the scalar matrices contained in that group.

The study of the implications of chaos for a system in the semiclassical (i.e., between classical and quantum mechanical) regime. In quantum chaos, trajectories do not ...

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. ...

Let A be a C^*-algebra, then two element a,b of A are called unitarily equivalent if there exists a unitary u in A such that b=uau^*.

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 ...

A positive integer n is kth powerfree if there is no number d such that d^k|n (d^k divides n), i.e., there are no kth powers or higher in the prime factorization of n. A ...

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 ...

If alpha is any number and m and n are integers, then there is a rational number m/n for which |alpha-m/n|<=1/n. (1) If alpha is irrational and k is any whole number, there ...

A number D that possesses no common divisor with a prime number p is either a quadratic residue or nonresidue of p, depending whether D^((p-1)/2) is congruent mod p to +/-1.