In mathematics, the Heisenberg group H {\displaystyle H} , named after Werner Heisenberg, is the group of 3×3 upper triangular matrices of the form ( 1...

Werner Karl Heisenberg (pronounced [ˈvɛʁnɐ kaʁl ˈhaɪzn̩bɛʁk] ; 5 December 1901 – 1 February 1976) was a German theoretical physicist, one of the main pioneers...

Exercise 5  namely Sylvester's clock and shift matrices in the finite Heisenberg group, discussed below.) One would like to classify representations of the...

is Lagrangian. A Heisenberg group can be defined for any symplectic vector space, and this is the typical way that Heisenberg groups arise. A vector space...

Karl Heisenberg: Euler–Heisenberg Lagrangian Heisenberg commutation relation Heisenberg cut Heisenberg ferromagnet Heisenberg group Heisenberg algebra...

The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is a...

of the Heisenberg group (fixing its center) form the symplectic group, so at first sight this seems to give an action of the symplectic group on H {\displaystyle...

U(1) (the circle group of unit modulus complex numbers). As an abstract group, the Heisenberg group is the three-dimensional Lie group of triples (x, ξ...

asserting the uniqueness of the Schrödinger representation of the Heisenberg group. The fields of probability and statistics frequently use the normal...

translations on the Heisenberg group of the reals, identified with 3-dimensional Euclidean space. This is a discrete cocompact group of affine transformations...

S^{3}} ; as a group, it may be identified with the group of unit quaternions. The Heisenberg group is a connected nilpotent Lie group of dimension 3...

The quantum Heisenberg model, developed by Werner Heisenberg, is a statistical mechanical model used in the study of critical points and phase transitions...

mathematics, the theta representation is a particular representation of the Heisenberg group of quantum mechanics. It gains its name from the fact that the Jacobi...

abelian normal subgroup of the group, and the corresponding quotient is the circle group. The finite Heisenberg group H3,p of order p3 is metabelian....

In group theory, a branch of abstract algebra, extraspecial groups are analogues of the Heisenberg group over finite fields whose size is a prime. For...

In particular, taking n = 3 yields the Heisenberg group H, an example of a non-abelian infinite nilpotent group. It has nilpotency class 2 with central...

discrete subgroup of the Heisenberg group. This invariance is presented in the article on the theta representation of the Heisenberg group. If F is a quadratic...

Aut(G) ⟶ Out(G) ⟶ 1. The center of an abelian group, G, is all of G. The center of the Heisenberg group, H, is the set of matrices of the form: ( 1 0...

on the Heisenberg group have been also studied, like minimal surfaces in the Heisenberg group, the Bernstein problem in the Heisenberg group and curvature...

quantum Heisenberg chain. The recipe can be applied for every translationally invariant one-dimensional lattice. DMRG is a renormalization-group technique...

representations of a certain group. In several joint papers, Deninger and Wilhelm Singhof studied quotients of the n-dimensional Heisenberg group H by the standard...

to the generators of the Heisenberg group, and the Hilbert space appears as a group representation of the Heisenberg group. In 1946, H. J. Groenewold...

Heisenberg algebra, the Lie algebra of the Heisenberg group, by setting the central element of the Heisenberg algebra (namely [X,Y]) equal to the unit of...

the Heisenberg group. The point stabilizer is O(2, R). The group G has 2 components, and is a semidirect product of the 3-dimensional Heisenberg group by...

Benjamin Heisenberg (born 9 June 1974) is a German film director and screenwriter. He has directed sixteen films since 1995. His film Schläfer was screened...

rate Heisenberg group, discrete Heisenberg group Molecular symmetry Nielsen transformation Reflection group Tarski monster group Thompson groups Tietze...

method of specifying a group. A presentation of a group G comprises a set S of generators—so that every element of the group can be written as a product...

Lorentz group Spinor group Symplectic group Exceptional groups G2 F4 E6 E7 E8 Affine group Euclidean group Poincaré group Heisenberg group Commutator...

relations lead naturally to an uncertainty relation—in physics called the Heisenberg uncertainty principle—between them. In mathematical terms, conjugate variables...

instance for the action of the Lorentz group on the character space of R4. The Heisenberg group is the group of 3 × 3 real matrices of the form: [ 1...