scholarly journals A confining quark model and new gauge symmetry

2014 ◽  
Vol 29 (22) ◽  
pp. 1450120 ◽  
Author(s):  
Jong-Ping Hsu
Keyword(s):  
Gauge Symmetry ◽  
Quark Model ◽  
Power Counting ◽  
Gauge Fields ◽  
Linear Potential ◽  
Field Equations ◽  
Color Charge ◽  
Gauge Bosons ◽  
Gauge Transformations ◽  
Empirical Potentials

We discuss a confining model for quark–antiquark system with a new color SU3 gauge symmetry. New gauge transformations involve non-integrable phase factors and lead to the fourth-order gauge field equations and a linear potential. The massless gauge bosons have non-definite energies, which are not observable because they are permanently confined in quark systems by the linear potential. We use the empirical potentials of charmonium to determine the coupling strength of the color charge gs and find [Formula: see text]. The rules for Feynman diagrams involve propagators with poles of order 2 associated with new gauge fields. The confining quark model may be renormalizable by power counting and compatible with perturbation theory.

QUANTUM FIELD THEORY TOOLS: A MECHANISM OF MASS GENERATION OF GAUGE FIELDS

2006 ◽  
Vol 21 (06) ◽  
pp. 1307-1324
Author(s):  
F. V. FLORES-BAEZ ◽  
J. J. GODINA-NAVA ◽  
G. ORDAZ-HERNANDEZ
Keyword(s):  
Gauge Symmetry ◽  
Mass Term ◽  
Higgs Bosons ◽  
Gauge Fields ◽  
Quantum Model ◽  
Mass Generation ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Local Gauge ◽  
Local Gauge Symmetry

We present a simple mechanism for mass generation of gauge fields for the Yang–Mills theory, where two gauge SU (N)-connections are introduced to incorporate the mass term. Variations of these two sets of gauge fields compensate each other under local gauge transformations with the local gauge transformations of the matter fields, preserving gauge invariance. In this way the mass term of gauge fields is introduced without violating the local gauge symmetry of the Lagrangian. Because the Lagrangian has strict local gauge symmetry, the model is a renormalizable quantum model. This model, in the appropriate limit, comes from a class of universal Lagrangians which define a new massive Yang–Mills theories without Higgs bosons.

Spinor gauge field in the spinor space–time formalism

1978 ◽  
Vol 56 (3) ◽  
pp. 395-398
Author(s):  
Nguyen Thi Hong
Keyword(s):  
Gauge Field ◽  
Equations Of Motion ◽  
Space Time ◽  
Gauge Fields ◽  
Spinor Representation ◽  
Field Equations ◽  
Gauge Transformations ◽  
Spinor Space ◽  
Time Formalism ◽  
Representation Of Space

In our previous work a method of realizing the bilinear spinor representation of space–time has been suggested, in the language of the spinor coordinates the field equations of motion have been considered. In this work, proceeding from these equations of motion, we consider the spinor gauge fields appearing in the local gauge transformations in the spinor space–time.

scholarly journals Gauge × gauge = gravity on homogeneous spaces using tensor convolutions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
L. Borsten ◽  
I. Jubb ◽  
V. Makwana ◽  
S. Nagy
Keyword(s):  
Homogeneous Spaces ◽  
Gauge Fields ◽  
Convolution Product ◽  
Tensor Fields ◽  
Einstein Universe ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Static Einstein Universe ◽  
Definition Of ◽  
Gauge Gravity

Abstract A definition of a convolution of tensor fields on group manifolds is given, which is then generalised to generic homogeneous spaces. This is applied to the product of gauge fields in the context of ‘gravity = gauge × gauge’. In particular, it is shown that the linear Becchi-Rouet-Stora-Tyutin (BRST) gauge transformations of two Yang-Mills gauge fields generate the linear BRST diffeomorphism transformations of the graviton. This facilitates the definition of the ‘gauge × gauge’ convolution product on, for example, the static Einstein universe, and more generally for ultrastatic spacetimes with compact spatial slices.

scholarly journals On the Mathematics of Coframe Formalism and Einstein–Cartan Theory—A Brief Review

Universe ◽  
2019 ◽  
Vol 5 (10) ◽  
pp. 206 ◽  
Author(s):  
Manuel Tecchiolli
Keyword(s):  
Conservation Laws ◽  
Gauge Fields ◽  
Field Equations ◽  
Principal Bundles ◽  
Bianchi Identities ◽  
Cartan Theory

This article is a review of what could be considered the basic mathematics of Einstein–Cartan theory. We discuss the formalism of principal bundles, principal connections, curvature forms, gauge fields, torsion form, and Bianchi identities, and eventually, we will end up with Einstein–Cartan–Sciama–Kibble field equations and conservation laws in their implicit formulation.

scholarly journals Generalization of the Yang–Mills theory

2016 ◽  
Vol 31 (01) ◽  
pp. 1630003 ◽  
Author(s):  
G. Savvidy
Keyword(s):  
Beta Function ◽  
Coupling Constants ◽  
Standard Theory ◽  
Large Integer ◽  
Tree Level ◽  
Gauge Fields ◽  
Gauge Bosons ◽  
Yang Mills ◽  
Conformally Invariant ◽  
Vector Gauge

We suggest an extension of the gauge principle which includes tensor gauge fields. In this extension of the Yang–Mills theory the vector gauge boson becomes a member of a bigger family of gauge bosons of arbitrary large integer spins. The proposed extension is essentially based on the extension of the Poincaré algebra and the existence of an appropriate transversal representations. The invariant Lagrangian is expressed in terms of new higher-rank field strength tensors. It does not contain higher derivatives of tensor gauge fields and all interactions take place through three- and four-particle exchanges with a dimensionless coupling constant. We calculated the scattering amplitudes of non-Abelian tensor gauge bosons at tree level, as well as their one-loop contribution into the Callan–Symanzik beta function. This contribution is negative and corresponds to the asymptotically free theory. Considering the contribution of tensorgluons of all spins into the beta function we found that it is leading to the theory which is conformally invariant at very high energies. The proposed extension may lead to a natural inclusion of the standard theory of fundamental forces into a larger theory in which vector gauge bosons, leptons and quarks represent a low-spin subgroup. We consider a possibility that inside the proton and, more generally, inside hadrons there are additional partons — tensorgluons, which can carry a part of the proton momentum. The extension of QCD influences the unification scale at which the coupling constants of the Standard Model merge, shifting its value to lower energies.

scholarly journals ON THE HAMILTONIAN FORMULATION OF THE EINSTEIN–HILBERT ACTION IN TWO DIMENSIONS

2006 ◽  
Vol 21 (11) ◽  
pp. 899-905 ◽  
Author(s):  
N. KIRIUSHCHEVA ◽  
S. V. KUZMIN
Keyword(s):  
Hamiltonian Formulation ◽  
Two Dimensions ◽  
General Covariance ◽  
Sufficient Condition ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Metric Tensor ◽  
Gauge Transformations ◽  
Total Divergence ◽  
Hilbert Action

It is shown that if general covariance is to be preserved (i.e. a coordinate system is not fixed) the well-known triviality of the Einstein field equations in two dimensions is not a sufficient condition for the Einstein–Hilbert action to be a total divergence. Consequently, a Hamiltonian formulation is possible without any modification of the two-dimensional Einstein–Hilbert action. We find the resulting constraints and the corresponding gauge transformations of the metric tensor.

scholarly journals SCALE TRANSFORMATIONS ON THE NONCOMMUTATIVE PLANE AND THE SEIBERG–WITTEN MAP

2005 ◽  
Vol 20 (25) ◽  
pp. 5871-5890 ◽  
Author(s):  
A. PINZUL ◽  
A. STERN
Keyword(s):  
Star Product ◽  
Field Theories ◽  
Gauge Fields ◽  
Gauge Transformations ◽  
Commutation Relations ◽  
Defining Relations ◽  
Scale Transformations ◽  
Noncommutative Plane ◽  
Noncommutative Parameter

We write down three kinds of scale transformations (i)–(iii) on the noncommutative plane. Transformation (i) is the analogue of standard dilations on the plane, transformation (ii) is a rescaling of the noncommutative parameter θ, and transformation (iii) is a combination of the previous two, whereby the defining relations for the noncommutative plane are preserved. The action of the three transformations is defined on gauge fields evaluated at fixed coordinates and θ. The transformations are obtained only up to terms which transform covariantly under gauge transformations. We give possible constraints on these terms. We show how the transformations (i) and (ii) depend on the choice of star product, and show the relation of (ii) to Seiberg–Witten transformations. Because transformation (iii) preserves the fundamental commutation relations it is a symmetry of the algebra. One has the possibility of implementing it as a symmetry of the dynamics, as well, in noncommutative field theories where θ is not fixed.

scholarly journals LHC Probes of TeV-Scale Scalars in SO(10) Grand Unification

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Ufuk Aydemir ◽  
Tanumoy Mandal
Keyword(s):  
Scalar Field ◽  
Gauge Symmetry ◽  
Symmetry Breaking ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Gluon Fusion ◽  
Grand Unification ◽  
Gauge Bosons ◽  
The Standard Model ◽  
Last Stage

We investigate the possibility of TeV-scale scalars as low energy remnants arising in the nonsupersymmetric SO(10) grand unification framework where the field content is minimal. We consider a scenario where the SO(10) gauge symmetry is broken into the gauge symmetry of the Standard Model (SM) through multiple stages of symmetry breaking, and a colored and hypercharged scalar χ picks a TeV-scale mass in the process. The last stage of the symmetry breaking occurs at the TeV-scale where the left-right symmetry, that is, SU(2)L⊗SU(2)R⊗U(1)B-L⊗SU(3)C, is broken into that of the SM by a singlet scalar field S of mass MS~1 TeV, which is a component of an SU(2)R-triplet scalar field, acquiring a TeV-scale vacuum expectation value. For the LHC phenomenology, we consider a scenario where S is produced via gluon-gluon fusion through loop interactions with χ and also decays to a pair of SM gauge bosons through χ in the loop. We find that the parameter space is heavily constrained from the latest LHC data. We use a multivariate analysis to estimate the LHC discovery reach of S into the diphoton channel.

scholarly journals COUPLINGS BETWEEN A COLLECTION OF BF MODELS AND A SET OF THREE-FORM GAUGE FIELDS

2006 ◽  
Vol 21 (31) ◽  
pp. 6477-6490 ◽  
Author(s):  
CONSTANTIN BIZDADEA ◽  
EUGEN-MIHĂIŢĂ CIOROIANU ◽  
SILVIU CONSTANTIN SĂRARU
Keyword(s):  
Gauge Theory ◽  
Master Equation ◽  
Gauge Fields ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Gauge Transformations ◽  
Free Theory ◽  
Lagrangian Action ◽  
Deformation Procedure

Consistent interactions that can be added to a free, Abelian gauge theory comprising a collection of BF models and a set of three-form gauge fields are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. Under the hypotheses of smooth, local, PT invariant, Lorentz covariant, and Poincaré invariant interactions, supplemented with the requirement on the preservation of the number of derivatives on each field with respect to the free theory, we obtain that the deformation procedure modifies the Lagrangian action, the gauge transformations as well as the accompanying algebra.

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.

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