scholarly journals DISCRETE SYMMETRY, NONCOMMUTATIVE GEOMETRY AND GRAVITY

1994 ◽  
Vol 09 (10) ◽  
pp. 875-883 ◽  
Author(s):  
NOUREDDINE MOHAMMEDI
Keyword(s):  
Noncommutative Geometry ◽  
Vector Fields ◽  
Differential Forms ◽  
Scalar Fields ◽  
Discrete Symmetry ◽  
Space Time ◽  
Orthonormal Frame ◽  
Graded Algebra ◽  
Scalar And Vector Fields ◽  
Torsion Free

We consider gravity using the formalism of a differential Z2-graded algebra of 2 × 2 matrices whose elements are differential forms on space-time. The connection and the orthonormal frame are extended to incorporate additional scalar and vector fields. The extended torsion-free constraints are solved for a simple case. The resulting action describes a set of scalar fields minimally coupled to Einstein-Hilbert gravity.

scholarly journals A DISCRETIZED VERSION OF KALUZA–KLEIN THEORY WITH TORSION AND MASSIVE FIELDS

1996 ◽  
Vol 11 (13) ◽  
pp. 2403-2418 ◽  
Author(s):  
NGUYEN AI VIET ◽  
KAMESHWAR C. WALI
Keyword(s):  
Noncommutative Geometry ◽  
Vector Fields ◽  
Complex Structure ◽  
Scalar Fields ◽  
Type Model ◽  
Internal Space ◽  
Tensor Fields ◽  
Fifth Dimension ◽  
Klein Theory ◽  
Kaluza Klein

We consider an internal space of two discrete points in the fifth dimension of the Kaluza–Klein theory by using the formalism of noncommutative geometry — developed in a previous paper1 — of a spacetime supplemented by two discrete points. With the non-vanishing internal torsion two-form there are no constraints implied on the vielbeins. The theory contains a pair of tensor fields, a pair of vector fields and a pair of scalar fields. Using the generalized Cartan structure equation we are able to uniquely determine not only the Hermitian and metric-compatible connection one-forms, but also the nonvanishing internal torsion two-form in terms of vielbeins. The resulting action has a rich and complex structure, a particular feature being the existence of massive modes. Thus the nonvanishing internal torsion generates a Kaluza–Klein type model with zero and massive modes.

scholarly journals KALUZA–KLEIN THEORY WITH TORSION CONFINED TO THE EXTRA DIMENSION

2010 ◽  
Vol 25 (25) ◽  
pp. 2121-2130 ◽  
Author(s):  
KARTHIK H. SHANKAR ◽  
KAMESHWAR C. WALI
Keyword(s):  
Ricci Tensor ◽  
Vector Fields ◽  
Dynamical Variable ◽  
Einstein Equations ◽  
Cosmic Acceleration ◽  
Scalar And Vector Fields ◽  
Klein Theory ◽  
Cartan Theory ◽  
Torsion Free ◽  
Kaluza Klein

Here we consider a variant of the five-dimensional Kaluza–Klein (KK) theory within the framework of Einstein–Cartan formalism that includes torsion. By imposing a set of constraints on torsion and Ricci rotation coefficients, we show that the torsion components are completely expressed in terms of the metric. Moreover, the Ricci tensor in 5D corresponds exactly to what one would obtain from torsion-free general relativity on a 4D hypersurface. The contributions of the scalar and vector fields of the standard KK theory to the Ricci tensor and the affine connections are completely nullified by the contributions from torsion. As a consequence, geodesic motions do not distinguish the torsion free 4D spacetime from a hypersurface of 5D spacetime with torsion satisfying the constraints. Since torsion is not an independent dynamical variable in this formalism, the modified Einstein equations are different from those in the general Einstein–Cartan theory. This leads to important cosmological consequences such as the emergence of cosmic acceleration.

scholarly journals THE FINITE VACUUM ENERGY FOR SPINOR, SCALAR AND VECTOR FIELDS

1995 ◽  
Vol 10 (16) ◽  
pp. 2333-2347
Author(s):  
N.N. SHTYKOV
Keyword(s):  
Physical Model ◽  
Vector Fields ◽  
Vacuum Energy ◽  
Scalar Fields ◽  
Casimir Energy ◽  
Divergent Part ◽  
Scalar And Vector Fields ◽  
Massive Spinor ◽  
The One

We compute the one-loop potential (the Casimir energy) for scalar fields with coupling ξR and massive spinor and vector fields on the spaces Rm+1×Y with Y=SN, CP2. We find that in most of the models a divergent part of the Casimir energy on even-dimensional spaces is canceled by means of the appropriate values of ξ, msp, mv. As a physical model we consider spinor electrodynamics on four-dimensional product manifolds and show that the Casimir energy is finite on R1×S3, R3×S1 and R2×S2 for msp=0, msp=0 and [Formula: see text] respectively.

scholarly journals INFLATIONARY COSMOLOGY FROM NONCOMMUTATIVE GEOMETRY

1996 ◽  
Vol 11 (16) ◽  
pp. 2907-2929 ◽  
Author(s):  
F. LIZZI ◽  
G. MIELE ◽  
G. SPARANO ◽  
G. MANGANO
Keyword(s):  
Noncommutative Geometry ◽  
Gauge Theories ◽  
Scalar Fields ◽  
Field Configuration ◽  
Space Time ◽  
Inflationary Cosmology ◽  
Basic Features ◽  
The Universe ◽  
Universe Evolution ◽  
Fermion Generation

In the framework of the Connes-Lott model based on noncommutative geometry, the basic features of a gauge theory in the presence of gravity are reviewed, in order to show the possible physical relevance of this scheme for inflationary cosmology. These models naturally contain at least two scalar fields, interacting with each other whenever more than one fermion generation is assumed. In this paper we propose to investigate the behavior of these two fields (one of which represents the distance between the copies of a two-sheeted space-time) in the early stages of the universe evolution. In particular the simplest Abelian model, which preserves the main characteristics of more complicate gauge theories, is considered and the corresponding inflationary dynamics is studied. We find that a chaotic inflation is naturally favored, leading to a field configuration in which no symmetry breaking occurs and the final distance between the two sheets of space-time is smaller the greater the number of e fold in each sheet.

GAUGED SU(2)L×SU(2)R/SU(2)L+Rσ MODEL IN THE FRAMEWORK OF NONCOMMUTATIVE GEOMETRY

1994 ◽  
Vol 09 (31) ◽  
pp. 5531-5539 ◽  
Author(s):  
DAE SUNG HWANG ◽  
TAEHOON LEE
Keyword(s):  
Noncommutative Geometry ◽  
Vector Fields ◽  
Axial Vector ◽  
Scalar Fields ◽  
Gauge Fields ◽  
The Matrix ◽  
Vector Gauge ◽  
The Masses ◽  
Higgs Fields ◽  
Matrix Derivative

We study the gauged SU(2) L× SU(2) Rσ model in the SU(2|2) superalgebra formalism. The superconnection is taken to have one-form vector fields as its even part and zero-form scalar fields as its odd part. Incorporating the matrix derivative of noncommutative geometry proposed by Connes and Coquereaux et al., we naturally obtain the spontaneously symmetry broken SU(2) L× SU(2) Rσ model. The masses of the axial vector gauge fields and the Higgs fields are obtained.

The representation of microscopic charge and current densities in terms of polarization and magnetization fields

1978 ◽  
Vol 358 (1694) ◽  
pp. 367-383 ◽  
Keyword(s):  
Reference Point ◽  
Vector Fields ◽  
Scalar Fields ◽  
Transformation Rules ◽  
Scalar And Vector Fields ◽  
Fixed Reference ◽  
Current Densities ◽  
Delta Functions ◽  
Magnetization Field ◽  
Charged Point

The microscopic charge and current densities due to an aggregate of charged point particles are shown to be derivable from polarization and magnetization fields defined as sums of line integrals of delta functions along curves joining an arbitrary reference point, which may be moving, to the positions of the particles. The analysis given generalizes previous treatm ents th at deal with a fixed reference point and includes the description of ionic, free electronic and Rontgen currents. The class of ‘admissible’ polarization and magnetization fields, which give rise to a specified charge and current distribution, is shown to be generated by two arbitrary differentiable fields, one scalar and one vector. The class of these latter fields that effect the transformation connecting two given pairs of admissible polarization and magnetization fields is shown in turn to be generated by two arbitrary scalar fields, one a function of position and time and the other a function of time only. The transformation rules are verified for polarization and magnetization fields that are representable as sums of line integrals of delta functions, and the scalar and vector fields that appear in the transformations are identified with integrals over certain moving surfaces and volumes. By means of these identifications it is demonstrated that the class of polarization and magnetization fields that are representable as sums of line integrals of delta functions forms a proper subset of the total class of admissible fields, so that not every admissible polarization or magnetization field is so representable.

scholarly journals Canonical transformation path to gauge theories of gravity-II: Space-time coupling of spin-0 and spin-1 particle fields

2019 ◽  
Vol 28 (01n02) ◽  
pp. 1950007 ◽  
Author(s):  
J. Struckmeier ◽  
J. Muench ◽  
P. Liebrich ◽  
M. Hanauske ◽  
J. Kirsch ◽  
...  
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Vector Field ◽  
Vector Fields ◽  
Energy Momentum Tensor ◽  
Scalar Fields ◽  
Momentum Tensor ◽  
Space Time ◽  
Complex Scalar ◽  
Time Dynamics

The generic form of space-time dynamics as a classical gauge field theory has recently been derived, based on only the action principle and on the principle of general relativity. It was thus shown that Einstein’s general relativity is the special case where (i) the Hilbert Lagrangian (essentially the Ricci scalar) is supposed to describe the dynamics of the “free” (uncoupled) gravitational field, and (ii) the energy–momentum tensor is that of scalar fields representing real or complex structureless (spin-[Formula: see text]) particles. It followed that all other source fields — such as vector fields representing massive and nonmassive spin-[Formula: see text] particles — need careful scrutiny of the appropriate source tensor. This is the subject of our actual paper: we discuss in detail the coupling of the gravitational field with (i) a massive complex scalar field, (ii) a massive real vector field, and (iii) a massless vector field. We show that different couplings emerge for massive and nonmassive vector fields. The massive vector field has the canonical energy–momentum tensor as the appropriate source term — which embraces also the energy density furnished by the internal spin. In this case, the vector fields are shown to generate a torsion of space-time. In contrast, the system of a massless and charged vector field is associated with the metric (Hilbert) energy–momentum tensor due to its additional [Formula: see text] symmetry. Moreover, such vector fields do not generate a torsion of space-time. The respective sources of gravitation apply for all models of the dynamics of the “free” (uncoupled) gravitational field — which do not follow from the gauge formalism but must be specified based on separate physical reasoning.

A Multi-Parameter Integrated Magnetometer Based on Combination of Scalar and Vector fields

2021 ◽  
pp. 1-1
Author(s):  
Jian Ge ◽  
Rui Wang ◽  
Haobin Dong ◽  
Huan Liu ◽  
Qianwei Zheng ◽  
...  
Keyword(s):  
Vector Fields ◽  
Scalar And Vector Fields

scholarly journals Higgs Scalar Fields and Discrete Symmetry

1995 ◽  
Vol 93 (6) ◽  
pp. 1093-1104 ◽  
Author(s):  
G. Konisi ◽  
T. Saito
Keyword(s):  
Scalar Fields ◽  
Discrete Symmetry ◽  
Higgs Scalar

scholarly journals ON THE QUANTUM CHROMODYNAMICS OF A MASSIVE VECTOR FIELD IN THE ADJOINT REPRESENTATION

2013 ◽  
Vol 28 (14) ◽  
pp. 1350054 ◽  
Author(s):  
ALFONSO R. ZERWEKH
Keyword(s):  
Vector Field ◽  
Quantum Chromodynamics ◽  
Extra Dimensions ◽  
Scalar Fields ◽  
Discrete Symmetry ◽  
Adjoint Representation ◽  
Coupling Constants ◽  
Gauge Symmetries ◽  
Gauge Fixing ◽  
Definition Of

In this paper, we explore the possibility of constructing the quantum chromodynamics of a massive color-octet vector field without introducing higher structures like extended gauge symmetries, extra dimensions or scalar fields. We show that gauge invariance is not enough to constraint the couplings. Nevertheless, the requirement of unitarity fixes the values of the coupling constants, which otherwise would be arbitrary. Additionally, it opens a new discrete symmetry which makes the coloron stable and avoid its resonant production at a collider. On the other hand, a judicious definition of the gauge fixing terms modifies the propagator of the massive field making it well-behaved in the ultraviolet limit. The relation between our model and the more general approach based on extended gauge symmetries is also discussed.

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