He describes Lie groups and their representations, with a focus on the quantum mechanically relevant Heisenberg group
H3 and special unitary group SU(2).
New methods for constructing a canal surface surrounding a biharmonic curve in the Lorentzian Heisenberg group
Roughly put (see the citation  for more details), if for an STGQ ([GAMMA], x, E), E is isomorphic to a general Heisenberg group
, then [GAMMA] is a flock quadrangle:
We will be interested in deformations of the discrete Heisenberg group
as a group acting properly discontinuously and cocompactly on a space X.
But many groups in physics such as the Heisenberg group
and also many applicable groups in engineering such as Motion groups are non-abelian and so that the standard STFT theory in abelian case fails.
Thanks to the magic (and obvious) relation between the 2n + 1-dimensional Heisenberg group
and its vector group [R.
In this paper we describe a method to derive a Weierstrass-type representation formula for simply connected immersed minimal surfaces in Heisenberg group
Turhan: Completeness of Lorentz Metric on 3-Dimensional Heisenberg Group
Hans-Jurgen Eisler, who heads the DFG Heisenberg group
at the Light Technology Institute.
Ten chapters discuss the skew field of quaternions; elements of the geometry of S3, Hopf bundles, and spin representations; internal variables of singularity free vector fields in a Euclidean space; isomorphism classes, Chern classes, and homotopy classes of singularity free vector fields in 3-space; Heisenberg algebras, Heisenberg groups
, Minkowski metrics, Jordan algebras, and special linear groups; the Heisenbreg group and natural C*-algebras of a vector field in 3-space; the Schrodinger representation and the metaplectic representation; the Heisenberg group
as a basic geometric background of signal analysis and geometric optics; quantization of quadratic polynomials; and field theoretic Weyl quantization of a vector field in 3-space.
This Heisenberg group
has many important applications on Sub-Riemannian geometry and has very important role in physics.
Analysis of the Hodge Laplacian on the Heisenberg Group