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.

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 MAXWELL SYMMETRIES AND SOME APPLICATIONS

2013 ◽  
Vol 23 ◽  
pp. 350-356 ◽  
Author(s):  
JOSÉ A. DE AZCÁRRAGA ◽  
KIYOSHI KAMIMURA ◽  
JERZY LUKIERSKI
Keyword(s):  
Gauge Theory ◽  
Gravity Field ◽  
Scalar Fields ◽  
Cosmological Term ◽  
Gauge Fields ◽  
Spin Connection ◽  
Field Equations ◽  
Geometric Framework ◽  
Abelian Gauge ◽  
Poincaré Algebra

The Maxwell algebra is the result of enlarging the Poincaré algebra by six additional tensorial Abelian generators that make the fourmomenta non-commutative. We present a local gauge theory based on the Maxwell algebra with vierbein, spin connection and six additional geometric Abelian gauge fields. We apply this geometric framework to the construction of Maxwell gravity, which is described by the Einstein action plus a generalized cosmological term. We mention a Friedman-Robertson-Walker cosmological approximation to the Maxwell gravity field equations, with two scalar fields obtained from the additional gauge fields. Finally, we outline further developments of the Maxwell symmetries framework.

scholarly journals CANONICAL QUANTIZATION OF NONLOCAL FIELD EQUATIONS

1996 ◽  
Vol 11 (12) ◽  
pp. 2111-2126 ◽  
Author(s):  
D.G. BARCI ◽  
L.E. OXMAN ◽  
M. ROCCA
Keyword(s):  
Gauge Theory ◽  
Equations Of Motion ◽  
Canonical Quantization ◽  
Field Operator ◽  
Kinetic Term ◽  
Field Equations ◽  
Commutator Algebra ◽  
Reducible Representation ◽  
Nonlocal Equations ◽  
Nonlocal Field

We consistently quantize a class of relativistic nonlocal field equations characterized by a nonlocal kinetic term in the Lagrangian. We solve the classical nonlocal equations of motion for a scalar field and evaluate the on-shell Hamiltonian. The quantization is realized by imposing Heisenberg’s equation, which leads to the commutator algebra obeyed by the Fourier components of the field. We show that the field operator carries, in general, a reducible representation of the Poincaré group. We also consider the Gupta-Bleuler quantization of a nonlocal gauge theory and analyze the propagators and the physical modes of the gauge field.

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.

REFORMULATION OF EINSTEIN GRAVITY AS A FLAT SPACE GAUGE THEORY

1988 ◽  
Vol 03 (05) ◽  
pp. 497-509 ◽  
Author(s):  
K. BABU JOSEPH ◽  
M. SABIR
Keyword(s):  
Gauge Theory ◽  
Flat Space ◽  
Gravitational Theory ◽  
Einstein Gravity ◽  
Gauge Fields ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Linearized Equations ◽  
Yang Mills ◽  
Rank Tensor

Based on an algebraic decomposition of a fourth rank tensor in terms of second rank tensors we suggest a reformulation of Einstein’s gravitational theory as a flat space gauge theory. This has been done by associating a curved manifold with a flat space U(2)×U(2) gauge theory. It is shown that while, in order to reproduce Einstein field equations one has to use a non-Yang-Mills action, the linearized equations follow from a Yang-Mills action. A relation between the metric and gauge fields is obtained. The consistency of the postulates is also verified.

SELF-DUAL POINCARÉ GAUGE THEORY OF GRAVITATION

2002 ◽  
Vol 13 (04) ◽  
pp. 509-516 ◽  
Author(s):  
G. ZET ◽  
V. MANTA
Keyword(s):  
Gauge Theory ◽  
Torsion Tensor ◽  
The Self ◽  
Gauge Fields ◽  
Field Equations ◽  
Yang Mills ◽  
Self Duality ◽  
Minkowski Space Time ◽  
Theory Of Gravitation ◽  
Generally True

A model of Poincaré gauge self-dual theory over the Minkowski space–time, endowed with spherical symmetry, is considered. The self-duality (S-D) conditions are imposed and two sets of the self-duality equations for the gauge fields are obtained: one for the torsion tensor and another for the curvature tensor. An analytical solution of the gauge field equations is also obtained. The Yang–Mills (Y–M) equations of the gauge fields are also derived. It is shown that these Y–M equations can be obtained from the S-D equations, a result which is generally true for any S-D gauge theory. Most of all calculations are performed using the GRTensorII package, running on the MapleV platform.

scholarly journals Nilpotent symmetries as a mechanism for Grand Unification

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Lars Andersson ◽  
András László ◽  
Błażej Ruba
Keyword(s):  
Gauge Field ◽  
Scalar Product ◽  
Local Symmetry ◽  
Matter Field ◽  
Gauge Fields ◽  
Spacetime Symmetries ◽  
Invariant Scalar ◽  
Spacetime Manifold ◽  
Local Symmetries ◽  
Dilatation Group

Abstract In the classic Coleman-Mandula no-go theorem which prohibits the unification of internal and spacetime symmetries, the assumption of the existence of a positive definite invariant scalar product on the Lie algebra of the internal group is essential. If one instead allows the scalar product to be positive semi-definite, this opens new possibilities for unification of gauge and spacetime symmetries. It follows from theorems on the structure of Lie algebras, that in the case of unified symmetries, the degenerate directions of the positive semi-definite invariant scalar product have to correspond to local symmetries with nilpotent generators. In this paper we construct a workable minimal toy model making use of this mechanism: it admits unified local symmetries having a compact (U(1)) component, a Lorentz (SL(2, ℂ)) component, and a nilpotent component gluing these together. The construction is such that the full unified symmetry group acts locally and faithfully on the matter field sector, whereas the gauge fields which would correspond to the nilpotent generators can be transformed out from the theory, leaving gauge fields only with compact charges. It is shown that already the ordinary Dirac equation admits an extremely simple prototype example for the above gauge field elimination mechanism: it has a local symmetry with corresponding eliminable gauge field, related to the dilatation group. The outlined symmetry unification mechanism can be used to by-pass the Coleman-Mandula and related no-go theorems in a way that is fundamentally different from supersymmetry. In particular, the mechanism avoids invocation of super-coordinates or extra dimensions for the underlying spacetime manifold.

scholarly journals Does general relativity highlight necessary connections in nature?

Synthese ◽  
2021 ◽  
Author(s):  
Antonio Vassallo
Keyword(s):  
General Relativity ◽  
Laws Of Nature ◽  
Coupling Mechanism ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Bianchi Identities ◽  
Physical Role ◽  
General Relativistic ◽  
Differential Relations ◽  
Necessary Connections

AbstractThe dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein’s equations represent a physical law describing the coupling of spacetime with material fields. However, just six of these equations actually describe the coupling mechanism: the remaining four represent a set of differential relations known as Bianchi identities. The paper discusses the physical role that the Bianchi identities play in general relativity, and investigates whether these identities—qua part of a physical law—highlight some kind of a posteriori necessity in a Kripkean sense. The inquiry shows that general relativistic physics has an interesting bearing on the debate about the metaphysics of the laws of nature.

scholarly journals ON THE KALUZA–KLEIN GEOMETRIZATION OF THE ELECTROWEAK MODEL WITHIN A GAUGE THEORY OF THE FIVE-DIMENSIONAL LORENTZ GROUP

2006 ◽  
Vol 15 (05) ◽  
pp. 717-736
Author(s):  
ORCHIDEA MARIA LECIAN ◽  
GIOVANNI MONTANI
Keyword(s):  
Gauge Theory ◽  
Lorentz Group ◽  
Lagrangian Density ◽  
Gauge Fields ◽  
Normalization Factor ◽  
Current Term ◽  
Electroweak Model ◽  
Kaluza Klein

The geometrization of the Electroweak Model is achieved in a five-dimensional Riemann–Cartan framework. Matter spinorial fields are extended to 5 dimensions by the choice of a proper dependence on the extracoordinate and of a normalization factor. U (1) weak hypercharge gauge fields are obtained from a Kaluza–Klein scheme, while the tetradic projections of the extradimensional contortion fields are interpreted as SU (2) weak isospin gauge fields. SU (2) generators are derived by the identification of the weak isospin current to the extradimensional current term in the Lagrangian density of the local Lorentz group. The geometrized U (1) and SU (2) groups will provide the proper transformation laws for bosonic and spinorial fields. Spin connections will be found to be purely Riemannian.

On a non-symmetric theory of the pure gravitational field

1958 ◽  
Vol 54 (1) ◽  
pp. 72-80 ◽  
Author(s):  
D. W. Sciama
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Symmetric Tensor ◽  
Momentum Tensor ◽  
Unified Field Theory ◽  
Field Equations ◽  
Metric Tensor ◽  
Unified Field

ABSTRACTIt is suggested, on heuristic grounds, that the energy-momentum tensor of a material field with non-zero spin and non-zero rest-mass should be non-symmetric. The usual relationship between energy-momentum tensor and gravitational potential then implies that the latter should also be a non-symmetric tensor. This suggestion has nothing to do with unified field theory; it is concerned with the pure gravitational field.A theory of gravitation based on a non-symmetric potential is developed. Field equations are derived, and a study is made of Rosenfeld identities, Bianchi identities, angular momentum and the equations of motion of test particles. These latter equations represent the geodesics of a Riemannian space whose contravariant metric tensor is gij–, in agreement with a result of Lichnerowicz(9) on the bicharacteristics of the Einstein–Schrödinger field equations.

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