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self-adjoint representation

См. также в других словарях:

  • Self-adjoint operator — In mathematics, on a finite dimensional inner product space, a self adjoint operator is one that is its own adjoint, or, equivalently, one whose matrix is Hermitian, where a Hermitian matrix is one which is equal to its own conjugate transpose.… …   Wikipedia

  • Representation of a Lie superalgebra — In the mathematical field of representation theory, a representation of a Lie superalgebra is an action of Lie superalgebra L on a Z2 graded vector space V , such that if A and B are any two pure elements of L and X and Y are any two pure… …   Wikipedia

  • Representation theory of the Lorentz group — The Lorentz group of theoretical physics has a variety of representations, corresponding to particles with integer and half integer spins in quantum field theory. These representations are normally constructed out of spinors.The group may also be …   Wikipedia

  • Hermitian adjoint — In mathematics, specifically in functional analysis, each linear operator on a Hilbert space has a corresponding adjoint operator. Adjoints of operators generalize conjugate transposes of square matrices to (possibly) infinite dimensional… …   Wikipedia

  • Unitary representation — In mathematics, a unitary representation of a group G is a linear representation π of G on a complex Hilbert space V such that π( g ) is a unitary operator for every g ∈ G . The general theory is well developed in case G is a locally compact… …   Wikipedia

  • Hilbert space — For the Hilbert space filling curve, see Hilbert curve. Hilbert spaces can be used to study the harmonics of vibrating strings. The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It… …   Wikipedia

  • Mathematical formulation of quantum mechanics — Quantum mechanics Uncertainty principle …   Wikipedia

  • Extensions of symmetric operators — In functional analysis, one is interested in extensions of symmetric operators acting on a Hilbert space. Of particular importance is the existence, and sometimes explicit constructions, of self adjoint extensions. This problem arises, for… …   Wikipedia

  • Stone–von Neumann theorem — In mathematics and in theoretical physics, the Stone–von Neumann theorem is any one of a number of different formulations of the uniqueness of the canonical commutation relations between position and momentum operators. The name is for Marshall… …   Wikipedia

  • Spectral theory of ordinary differential equations — In mathematics, the spectral theory of ordinary differential equations is concerned with the determination of the spectrum and eigenfunction expansion associated with a linear ordinary differential equation. In his dissertation Hermann Weyl… …   Wikipedia

  • Borel functional calculus — In functional analysis, a branch of mathematics, the Borel functional calculus is a functional calculus (that is, an assignment of operators from commutative algebras to functions defined on their spectrum), which has particularly broad… …   Wikipedia

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