In this paper we investigate the form of induced gauge fields that arises in two types of quantum systems. In the first we consider quantum mechanics on coset spaces G/H, and argue that G-invariance is central to the emergence of the H-connection as induced gauge fields in the different quantum sectors. We then demonstrate why the same connection, now giving rise to the non-abelian generalizati...

An explicit parameterization for the state space of an n-level density matrix is given. The parameterization is based on the canonical coset decomposition of unitary matrices. We also compute, explicitly, the Bures metric tensor over the state space of twoand three-level quantum systems.

We prove that for every homogeneous and strongly locally homogeneous separable metrizable space X there is a metrizable compactification γX of X such that, among other things, for all x, y ∈ X there is a homeomorphism f : γX → γX such that f(x) = y. This implies that X is a coset space of some separable metrizable topological group G.

A formal “small tension” expansion of D=11 supergravity near a spacelike singularity is shown to be equivalent, at least up to 30th order in height, to a null geodesic motion in the infinite dimensional coset space E10/K(E10), where K(E10) is the maximal compact subgroup of the hyperbolic KacMoody group E10(R). For the proof we make use of a novel decomposition of E10 into irreducible represent...

We find a two-parameter family of solutions the Yang–Mills equations for gauge group SO(1,3) on Minkowski space by foliating different parts it with non-compact coset spaces isometry. The interior lightcone is foliated hyperbolic H3≅SO(1,3)/SO(3), while exterior employs de Sitter dS≅3SO(1,3)/SO(1,2). itself parametrized SO(1,3)/ISO(2) in nilpotent fashion. Equivariant reduction system first two...

Conformal field theories corresponding to two–dimensional electrically charged black holes and to two–dimensional anti–de Sitter space with a covariantly constant electric field are simply constructed as SL(2, IR)/ZZ WZW coset models. The two–dimensional electrically charged black holes are related by Kaluza–Klein reduction to the 2+1–dimensional rotating black hole of Bañados, Teitelboim and Z...

A Lagrangian treatment of the quantization of first class Hamiltonian systems with constraints and Hamiltonian linear and quadratic in the momenta respectively is performed. The " first reduce and then quantize " and the " first quantize and then reduce " (Dirac's) methods are compared. A new source of ambiguities in this latter approach is revealed and its relevance on issues concerning self-c...

Let G be a linear algebraic group defined over an algebraically closed field. The double coset question addressed in this paper is the following: Given closed subgroups X and P , is X\G/P finite or infinite? We limit ourselves to the case where X is maximal rank and reductive and P parabolic. This paper presents a criterion for infiniteness which involves only dimensions of centralizers of semi...

In this paper we introduce new techniques for the eecient computation of a Fourier transform on a nite group. We use the decomposition of a group into double cosets and a graph theoretic indexing scheme to derive algorithms that generalize the Cooley-Tukey FFT to arbitrary nite groups. We apply our general results to special linear groups and low rank symmetric groups, and obtain new eecient al...