Gauged Wess-Zumino terms for a general coset space

Abstract We argue that symmetry and unification can emerge as byproducts of certain physical constraints on dynamical scattering. To accomplish this we parameterize a general Lorentz invariant, four-dimensional theory of massless and massive scalar fields coupled via arbitrary local interactions. Assuming perturbative unitarity and an Adler zero condition, we prove that any finite spectrum of massless and massive modes will necessarily unify at high energies into multiplets of a linearized symmetry. Certain generators of the symmetry algebra can be derived explicitly in terms of the spectrum and three-particle interactions. Furthermore, our assumptions imply that the coset space is symmetric.

Download Full-text

Discrete symmetries and coset space dimensional reduction

Physics Letters B ◽

10.1016/0370-2693(89)90565-0 ◽

1989 ◽

Vol 232 (1) ◽

pp. 104-112 ◽

Cited By ~ 11

Author(s):

D. Kapetanakis ◽

G. Zoupanos

Keyword(s):

Dimensional Reduction ◽

Discrete Symmetries ◽

Coset Space

Download Full-text

LOCAL FRACTIONAL SUPERSYMMETRY FOR ALTERNATIVE STATISTICS

Modern Physics Letters A ◽

10.1142/s0217732396000916 ◽

1996 ◽

Vol 11 (11) ◽

pp. 899-913 ◽

Cited By ~ 26

Author(s):

N. FLEURY ◽

M. RAUSCH DE TRAUBENBERG

Keyword(s):

Group Theory ◽

Braid Group ◽

Equation Of Motion ◽

Coset Space ◽

One Dimensional ◽

The One

A group theory justification of one-dimensional fractional supersymmetry is proposed using an analog of a coset space, just like the one introduced in 1-D supersymmetry. This theory is then gauged to obtain a local fractional supersymmetry, i.e. a fractional supergravity which is then quantized à la Dirac to obtain an equation of motion for a particle which is in a representation of the braid group and should describe alternative statistics. A formulation invariant under general reparametrization is given by means of a curved fractional superline.

Download Full-text

A generalized Cartan decomposition for the double coset space $(U(n_1) \times U(n_2) \times U(n_3)) \backslash U(n) / (U(p) \times U(q))$

Journal of the Mathematical Society of Japan ◽

10.2969/jmsj/05930669 ◽

2007 ◽

Vol 59 (3) ◽

pp. 669-691 ◽

Cited By ~ 11

Author(s):

Toshiyuki KOBAYASHI

Keyword(s):

Double Coset ◽

Coset Space ◽

Cartan Decomposition

Download Full-text

Partial Characters and Signed Quotient Hypergroups

Canadian Journal of Mathematics ◽

10.4153/cjm-1999-006-6 ◽

1999 ◽

Vol 51 (1) ◽

pp. 96-116 ◽

Cited By ~ 1

Author(s):

Margit Rösler ◽

Michael Voit

Keyword(s):

Heisenberg Group ◽

Closed Subgroup ◽

Gelfand Pair ◽

Coset Space ◽

Commutative Hypergroup

AbstractIfGis a closed subgroup of a commutative hypergroupK, then the coset spaceK/Gcarries a quotient hypergroup structure. In this paper, we study related convolution structures onK/Gcoming fromdeformations of the quotient hypergroup structure by certain functions onKwhich we call partial characters with respect toG. They are usually not probability-preserving, but lead to so-called signed hypergroups onK/G. A first example is provided by the Laguerre convolution on [0, ∞[, which is interpreted as a signed quotient hypergroup convolution derived from the Heisenberg group. Moreover, signed hypergroups associated with the Gelfand pair (U(n, 1),U(n)) are discussed.

Download Full-text

A Classification of Homogeneous Surfaces

Canadian Journal of Mathematics ◽

10.4153/cjm-1981-084-x ◽

1981 ◽

Vol 33 (5) ◽

pp. 1097-1110 ◽

Cited By ~ 11

Author(s):

A. T. Huckleberry ◽

E. L. Livorni

Keyword(s):

Automorphism Group ◽

Homogeneous Space ◽

Lie Group ◽

Compact Complex Manifold ◽

Coset Space ◽

Left Coset ◽

Detailed Classification ◽

Dimensional Ball ◽

Lie Subgroup

Throughout this paper a surface is a 2-dimensional (not necessarily compact) complex manifold. A surface X is homogeneous if a complex Lie group G of holomorphic transformations acts holomorphically and transitively on it. Concisely, X is homogeneous if it can be identified with the left coset space G/H, where if is a closed complex Lie subgroup of G. We emphasize that the assumption that G is a complex Lie group is an essential part of the definition. For example, the 2-dimensional ball B2 is certainly “homogeneous” in the sense that its automorphism group acts transitively. But it is impossible to realize B2 as a homogeneous space in the above sense. The purpose of this paper is to give a detailed classification of the homogeneous surfaces. We give explicit descriptions of all possibilities.

Download Full-text

Large lepton mixing in seesaw models - Coset-space family unification -

Nuclear Physics B - Proceedings Supplements ◽

10.1016/s0920-5632(99)00431-4 ◽

1999 ◽

Vol 77 (1-3) ◽

pp. 293-298 ◽

Cited By ~ 38

Author(s):

J. Sato ◽

T. Yanagida

Keyword(s):

Coset Space

Download Full-text

Mathematical aspects of molecular replacement. III. Properties of space groups preferred by proteins in the Protein Data Bank

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s2053273314024358 ◽

2015 ◽

Vol 71 (2) ◽

pp. 186-194 ◽

Cited By ~ 2

Author(s):

G. Chirikjian ◽

S. Sajjadi ◽

D. Toptygin ◽

Y. Yan

Keyword(s):

Rigid Body ◽

Protein Data Bank ◽

Data Bank ◽

Continuous Group ◽

Molecular Replacement ◽

Macromolecular Crystallography ◽

Coset Space ◽

Space Groups ◽

The Third ◽

Rigid Body Motions

The main goal of molecular replacement in macromolecular crystallography is to find the appropriate rigid-body transformations that situate identical copies of model proteins in the crystallographic unit cell. The search for such transformations can be thought of as taking place in the coset space Γ\Gwhere Γ is the Sohncke group of the macromolecular crystal andGis the continuous group of rigid-body motions in Euclidean space. This paper, the third in a series, is concerned with viewing nonsymmorphic Γ in a new way. These space groups, rather than symmorphic ones, are the most common ones for protein crystals. Moreover, their properties impact the structure of the space Γ\G. In particular, nonsymmorphic space groups contain both Bieberbach subgroups and symmorphic subgroups. A number of new theorems focusing on these subgroups are proven, and it is shown that these concepts are related to the preferences that proteins have for crystallizing in different space groups, as observed in the Protein Data Bank.

Download Full-text