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.

ADVANCES IN TERNARY AND OCTONIONIC GAUGE FIELD THEORIES

2011 ◽  
Vol 26 (18) ◽  
pp. 2997-3012 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Lie Algebra ◽  
Space Time ◽  
Time Dependent ◽  
Gauge Field Theory ◽  
Gauge Fields ◽  
Gauge Transformations ◽  
Quadratic Action ◽  
Rigid Transformations

A ternary gauge field theory is explicitly constructed based on a totally antisymmetric ternary-bracket structure associated with a 3-Lie algebra. It is shown that the ternary infinitesimal gauge transformations do obey the key closure relations [δ1, δ2] = δ3. Invariant actions for the 3-Lie algebra-valued gauge fields and scalar fields are displayed. We analyze and point out the difficulties in formulating a nonassociative octonionic ternary gauge field theory based on a ternary-bracket associated with the octonion algebra and defined earlier by Yamazaki. It is shown that a Yang–Mills-like quadratic action is invariant under global (rigid) transformations involving the Yamazaki ternary octonionic bracket, and that there is closure of these global (rigid) transformations based on constant antisymmetric parameters Λab = - Λba. Promoting the latter parameters to space–time dependent ones Λab(xμ) allows one to build an octonionic ternary gauge field theory when one imposes gauge covariant constraints on the latter gauge parameters leading to field-dependent gauge parameters and nonlinear gauge transformations. In this fashion one does not spoil the gauge invariance of the quadratic action under this restricted set of gauge transformations and which are tantamount to space–time dependent scalings (homothecy) of the gauge fields.

Conformal transformations in spinor space–time

1979 ◽  
Vol 57 (2) ◽  
pp. 298-299
Author(s):  
Nguyen Thi Hong
Keyword(s):  
Space Time ◽  
Spinor Representation ◽  
Conformal Transformations ◽  
Poincaré Group ◽  
Poincare Group ◽  
Time Symmetry ◽  
Spinor Space ◽  
Representation Of Space

In our previous works a method of realizing the bilinear spinor representation of space–time has been suggested, in which the usual translation transformation can be established and therefore the space–time symmetry Poincaré group can remain. In this note we are extending the formalism to involve the conformal transformations.

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.

scholarly journals ON THE UNIQUENESS OF D = 11 INTERACTIONS AMONG A GRAVITON, A MASSLESS GRAVITINO AND A THREE-FORM II: THREE-FORM AND GRAVITINI

2008 ◽  
Vol 23 (30) ◽  
pp. 4841-4859 ◽  
Author(s):  
EUGEN-MIHĂIŢĂ CIOROIANU ◽  
EUGEN DIACONU ◽  
SILVIU CONSTANTIN SĂRARU
Keyword(s):  
Master Equation ◽  
Gauge Field ◽  
Space Time ◽  
Free Solution ◽  
Coupling Constant ◽  
Abelian Gauge ◽  
Gauge Transformations ◽  
Lorentz Covariance ◽  
Brst Cohomology ◽  
Chern Simons

The interactions that can be introduced between a massless Rarita–Schwinger field and an Abelian three-form gauge field in 11 space–time dimensions are analyzed in the context of the deformation of the "free" solution of the master equation combined with local BRST cohomology. Under the hypotheses of smoothness of the interactions in the coupling constant, locality, Poincaré invariance, Lorentz covariance, and the presence of at most two derivatives in the Lagrangian of the interacting theory (the same number of derivatives as in the free Lagrangian), we prove that there are neither cross-couplings nor self-interactions for the gravitino in D = 11. The only possible term that can be added to the deformed solution to the master equation is nothing but a generalized Chern–Simons term for the three-form gauge field, which brings contributions to the deformed Lagrangian, but does not modify the original, Abelian gauge transformations.

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.

scholarly journals NEW GEOMETRIC FORMALISM FOR GRAVITY EQUATION IN EMPTY SPACE

2005 ◽  
Vol 14 (06) ◽  
pp. 1009-1022 ◽  
Author(s):  
XIN-BING HUANG
Keyword(s):  
Differential Equations ◽  
Gauge Field ◽  
Empty Space ◽  
Space Time ◽  
Gravity Theory ◽  
Spin Connection ◽  
Square Root ◽  
Field Equations ◽  
Complex Spin ◽  
Set Up

In this paper, a complex daor field which can be regarded as the square root of space–time metric is proposed to represent gravity. The locally complexified geometry is set up, and the complex spin connection constructs a bridge between gravity and SU(1, 3) gauge field. Daor field equations in empty space are acquired, which are one-order differential equations and do not conflict with Einstein's gravity theory.

U(2) GAUGE THEORY ON NONCOMMUTATIVE GEOMETRY

2009 ◽  
Vol 24 (15) ◽  
pp. 2889-2897
Author(s):  
G. ZET
Keyword(s):  
Gauge Theory ◽  
Equations Of Motion ◽  
Local Symmetry ◽  
Noncommutative Space ◽  
Gauge Fields ◽  
Zeroth Order ◽  
Field Equations ◽  
Relativistic Analog ◽  
Analog Form ◽  
General Relativistic

We develop a model of gauge theory with U (2) as local symmetry group over a noncommutative space-time. The integral of the action is written considering a gauge field coupled with a Higgs multiplet. The gauge fields are calculated up to the second order in the noncommutativity parameter using the equations of motion and Seiberg-Witten map. The solutions are determined order by order supposing that in zeroth-order they have a general relativistic analog form. The Wu-Yang ansatz for the gauge fields is used to solve the field equations. Some comments on the quantization of the electrical and magnetical charges are also given, with a comparison between commutative and noncommutative cases.

scholarly journals PARTICLE SPECTRUM OF NON-ABELIAN TENSOR GAUGE FIELDS

2010 ◽  
Vol 25 (14) ◽  
pp. 1137-1161 ◽  
Author(s):  
GEORGE SAVVIDY
Keyword(s):  
Gauge Field ◽  
Free Field ◽  
Gauge Fields ◽  
Particle Spectrum ◽  
Field Equations ◽  
Abelian Gauge ◽  
Dimensional Spacetime ◽  
Higher Dimensional ◽  
Extended Field ◽  
Rank 2

We review the non-Abelian tensor gauge field theory and analyze its free field equations for lower rank gauge fields when the interaction coupling constant tends to zero. The free field equations are written in terms of the first-order derivatives of extended field strength tensors similar to the electrodynamics and non-Abelian gauge theories. We determine the particle content of the free field equations and count the propagating modes which they describe. In four-dimensional spacetime the rank-2 gauge field describes propagating modes of helicity two and zero. We show that the rank-3 gauge field describes propagating modes of helicity-three and a doublet of helicity-one gauge bosons. Only four-dimensional spacetime is physically acceptable, because in five- and higher-dimensional spacetime the equation has solutions with negative norm states. We discuss the structure of the particle spectrum for higher rank gauge fields.

Higher spin theories in flat space–time

2018 ◽  
Vol 33 (34) ◽  
pp. 1845007
Author(s):  
Loriano Bonora
Keyword(s):  
Equations Of Motion ◽  
Flat Space ◽  
Space Time ◽  
Local Fields ◽  
Field Theories ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Higher Spin ◽  
Chern Simons

It is shown that, contrary to a widespread prejudice, massless higher spin (HS) field theories can be defined in flat space–time. Examples of Yang–Mills-like theories with infinite many local fields of any spin are constructed explicitly in any dimension, along with Chern–Simons-like models in any odd dimension. These theories are defined via actions invariant under HS gauge transformations and their equations of motion are derived. It is also briefly explained why these theories circumvent well-known no-go theorems.

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