THE DISLOCATION TREATMENT OF GAUGE FIELDS OF SPACE-TIME TRANSLATIONS

1987 ◽  
Vol 02 (08) ◽  
pp. 609-616 ◽  
Author(s):  
G. SARDANASHVILY ◽  
M. GOGBERSHVILY
Keyword(s):  
Dislocation Structure ◽  
Space Time ◽  
Gauge Fields

A particular "dislocation" structure of a space-time due to Poincaré translation gauge fields which results in modifications of standard gravitation effects is predicted.

MANIFOLD-SPLITTING REGULARIZATION, SELF-LINKING, TWISTING, WRITHING NUMBERS OF SPACE-TIME RIBBONS and POLYAKOV’S PROOF OF FERMI-BOSE TRANSMUTATIONS

1988 ◽  
Vol 03 (08) ◽  
pp. 1959-1979 ◽  
Author(s):  
CHIA-HSIUNG TZE
Keyword(s):  
Integral Formula ◽  
Space Time ◽  
Gauge Fields ◽  
Alternative Formulation ◽  
Complex Numbers ◽  
Closed Space ◽  
Feynman Path ◽  
Higher Dimensional ◽  
Linking Coefficient ◽  
In Memoriam

We present an alternative formulation of Polyakov’s regularization of Gauss’ integral formula for a single closed Feynman path. A key element in his proof of the D=3 fermi-bose transmutations induced by topological gauge fields, this regularization is linked here with the existence and properties of a nontrivial topological invariant for a closed space ribbon. This self-linking coefficient, an integer, is the sum of two differential characteristics of the ribbon, its twisting and writhing numbers. These invariants form the basis for a physical interpretation of our regularization. Their connection to Polyakov’s spinorization is discussed. We further generalize our construction to the self-linking, twisting and writhing of higher dimensional d=n (odd) submanifolds in D=(2n+1) space-time. Our comprehensive analysis intends to supplement Polyakov’s work as it identifies a natural path to its higher dimensional mathematical and physical generalizations. Combining the theorems of White on self-linking of manifolds and of Adams on nontrivial Hopf fibre bundles and the four composition-division algebras, we argue that besides Polyakov’s case where (d, D)=(1, 3) tied to complex numbers, the potentially interesting extensions are two chiral models with (d, D)=(3, 7) and (7, 15) uniquely linked to quaternions and octonions. In Memoriam Richard P. Feynman

scholarly journals EXTENSION OF THE POINCARÉ GROUP AND NON-ABELIAN TENSOR GAUGE FIELDS

2010 ◽  
Vol 25 (31) ◽  
pp. 5765-5785 ◽  
Author(s):  
GEORGE SAVVIDY
Keyword(s):  
Gauge Group ◽  
Gauge Transformation ◽  
Space Time ◽  
Gauge Fields ◽  
Poincaré Group ◽  
Matrix Representations ◽  
Poincare Group ◽  
Yang Mills ◽  
The Matrix ◽  
Transversal Plane

In the recently proposed generalization of the Yang–Mills theory, the group of gauge transformation gets essentially enlarged. This enlargement involves a mixture of the internal and space–time symmetries. The resulting group is an extension of the Poincaré group with infinitely many generators which carry internal and space–time indices. The matrix representations of the extended Poincaré generators are expressible in terms of Pauli–Lubanski vector in one case and in terms of its invariant derivative in another. In the later case the generators of the gauge group are transversal to the momentum and are projecting the non-Abelian tensor gauge fields into the transversal plane, keeping only their positively definite spacelike components.

scholarly journals Worldlines and worldsheets for non-abelian lattice field theories: Abelian color fluxes and Abelian color cycles

2018 ◽  
Vol 175 ◽  
pp. 11007 ◽  
Author(s):  
Christof Gattringer ◽  
Daniel Göschl ◽  
Carlotta Marchis
Keyword(s):  
Degrees Of Freedom ◽  
Chemical Potential ◽  
Space Time ◽  
Field Theories ◽  
Gauge Fields ◽  
Chiral Model ◽  
Staggered Fermions ◽  
Lattice Field ◽  
Principal Chiral Model ◽  
Matter Fields

We discuss recent developments for exact reformulations of lattice field theories in terms of worldlines and worldsheets. In particular we focus on a strategy which is applicable also to non-abelian theories: traces and matrix/vector products are written as explicit sums over color indices and a dual variable is introduced for each individual term. These dual variables correspond to fluxes in both, space-time and color for matter fields (Abelian color fluxes), or to fluxes in color space around space-time plaquettes for gauge fields (Abelian color cycles). Subsequently all original degrees of freedom, i.e., matter fields and gauge links, can be integrated out. Integrating over complex phases of matter fields gives rise to constraints that enforce conservation of matter flux on all sites. Integrating out phases of gauge fields enforces vanishing combined flux of matter-and gauge degrees of freedom. The constraints give rise to a system of worldlines and worldsheets. Integrating over the factors that are not phases (e.g., radial degrees of freedom or contributions from the Haar measure) generates additional weight factors that together with the constraints implement the full symmetry of the conventional formulation, now in the language of worldlines and worldsheets. We discuss the Abelian color flux and Abelian color cycle strategies for three examples: the SU(2) principal chiral model with chemical potential coupled to two of the Noether charges, SU(2) lattice gauge theory coupled to staggered fermions, as well as full lattice QCD with staggered fermions. For the principal chiral model we present some simulation results that illustrate properties of the worldline dynamics at finite chemical potentials.

A gauge theory of the Weyl group

1974 ◽  
Vol 340 (1622) ◽  
pp. 249-262 ◽  
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Conservation Laws ◽  
Weyl Group ◽  
Lorentz Group ◽  
Space Time ◽  
Gauge Fields ◽  
Field Equations ◽  
Covariant Derivatives ◽  
The World

The construction of field theory which exhibits invariance under the Weyl group with parameters dependent on space–time is discussed. The method is that used by Utiyama for the Lorentz group and by Kibble for the Poincaré group. The need to construct world-covariant derivatives necessitates the introduction of three sets of gauge fields which provide a local affine connexion and a vierbein system. The geometrical implications are explored; the world geometry has an affine connexion which is not symmetric but is semi-metric. A possible choice of Lagrangian for the gauge fields is presented, and the resulting field equations and conservation laws discussed.

PROPERTY VALUES

2007 ◽  
Vol 22 (27) ◽  
pp. 4911-4922 ◽  
Author(s):  
R. DELBOURGO
Keyword(s):  
Basic Property ◽  
Property Values ◽  
Space Time ◽  
Gauge Fields ◽  
Fundamental Particles ◽  
Anticommuting Variable ◽  
Higgs Fields

By ascribing a complex anticommuting variable ζ to each basic property of a field it is possible to describe all the fundamental particles as combinations of only five ζ and understand the occurrence of particle generations. An extension of space-time x to include property then specifies the 'where, when and what' of an event and allows for a generalized relativity where the gauge fields lie in the x - ζ sector and the Higgs fields in the ζ - ζ sector.

scholarly journals SUPERSYMMETRIC STRING WAVES

1994 ◽  
Vol 03 (01) ◽  
pp. 149-152
Author(s):  
ERIC BERGSHOEFF
Keyword(s):  
Plane Wave ◽  
Effective Action ◽  
Space Time ◽  
Gauge Fields ◽  
Wave Type ◽  
Axion Field ◽  
String Corrections ◽  
Crucial Property

We present plane-wave-type solutions to the superstring effective action which have unbroken space-time supersymmetries. They describe dilaton, axion and gauge fields in a generalization of the Brinkmann metric. A crucial property of the solutions is a conspiracy between the metric and the axion field. Furthermore, due to a relation between the geometry and the gauge fields, the α′ string corrections to the effective on-shell action and to the solutions themselves vanish. We call these solutions supersymmetric string waves.

scholarly journals INTERACTING OPEN p-BRANES

1995 ◽  
Vol 10 (32) ◽  
pp. 4671-4679 ◽  
Author(s):  
SUMIO ISHIKAWA ◽  
YASUHIRO IWAMA ◽  
TADASHI MIYAZAKI ◽  
MOTOWO YAMANOBE
Keyword(s):  
Dimensional Space ◽  
Boundary Surface ◽  
Space Time ◽  
Gauge Fields ◽  
Dimensional Space Time ◽  
Action At A Distance

The Kalb-Ramond action, derived for interacting strings through an action-at-a-distance force, is generalized to the case of interacting p-dimensional objects (p-branes) in D- dimensional space-time. The openp-brane version of the theory is especially taken up. On account of the existence of their boundary surface, the fields mediating interactions between open p-branes are obtained as massive gauge fields, quite in contrast to massless gauge ones for closedp-branes.

EXACT SOLUTIONS OF THE SELF-DUALITY EQUATIONS ON THE MINKOWSKI SPACE-TIME

2001 ◽  
Vol 12 (06) ◽  
pp. 801-806 ◽  
Author(s):  
V. MANTA ◽  
G. ZET
Keyword(s):  
Gauge Theory ◽  
Exact Solutions ◽  
Minkowski Space ◽  
Space Time ◽  
The Self ◽  
Gauge Fields ◽  
Self Duality ◽  
Minkowski Space Time ◽  
Dynamical Type ◽  
Analytical Program

A SU(2) Gauge Theory with spherical symmetry over the Minkowski space-time is considered. The self-duality equation of the gauge fields are written and their solutions are obtained. Two exact solutions, one of which is statical and another of dynamical type are given. All the calculations are performed using an analytical program written in GRTensor computer algebra package, which runs on the MapleV platform.

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