scholarly journals Affine connection representation of gauge fields

2021 ◽  
Author(s):  
Zhao-Hui Man
Keyword(s):  
Quantum Theory ◽  
Gravitational Field ◽  
Gauge Theory ◽  
Gauge Field ◽  
Affine Connection ◽  
Geometric Theory ◽  
Gravitational Theory ◽  
Coupling Constants ◽  
Gauge Fields ◽  
Coordinate Space

Abstract There are two ways to unify gravitational field and gauge field. One is to represent gravitational field as principal bundle connection, and the other is to represent gauge field as affine connection. Poincaré gauge theory and metric-affine gauge theory adopt the first approach. This paper adopts the second. In this approach: (i) Gauge field and gravitational field can both be represented by affine connection; they can be described by a unified spatial frame. (ii) Time can be regarded as the total metric with respect to all dimensions of internal coordinate space and external coordinate space. On-shell can be regarded as gradient direction. Quantum theory can be regarded as a geometric theory of distribution of gradient directions. Hence, gauge theory, gravitational theory and quantum theory obtain the same geometric foundation and a unified description of evolution. (iii) Coupling constants, chiral asymmetry, PMNS mixing and CKM mixing can appear spontaneously as geometric properties in affine connection representation. It is remarkable that PMNS mixing and CKM mixing can be interpreted as a spontaneous geometric consequence of symmetry reduction, so they are not necessary to be regarded as direct postulates in the Lagrangian anymore. (iv) The unification theory of gauge fields that are represented by affine connection can avoid the problem that a proton decays into a lepton in theories such as SU(5). (v) There exists a possible geometric interpretation to the color confinement of quarks. In the affine connection representation, we can get better interpretations of the above physical properties, therefore, to represent gauge fields by affine connection is probably a necessary step towards the ultimate theory of physics.

scholarly journals Affine connection representation of gauge fields

2021 ◽  
Author(s):  
Zhao-Hui Man
Keyword(s):  
Quantum Theory ◽  
Gravitational Field ◽  
Gauge Theory ◽  
Gauge Field ◽  
Affine Connection ◽  
Geometric Theory ◽  
Gravitational Theory ◽  
Coupling Constants ◽  
Gauge Fields ◽  
Coordinate Space

Abstract There are two ways to unify gravitational field and gauge field. One is to represent gravitational field as principal bundle connection, and the other is to represent gauge field as affine connection. Poincar{\'{e}} gauge theory and metric-affine gauge theory adopt the first approach. This paper adopts the second. In this approach:(i) Gauge field and gravitational field can both be represented by affine connection; they can be described by a unified spatial frame.(ii) Time can be regarded as the total metric with respect to all dimensions of internal coordinate space and external coordinate space. On-shell can be regarded as gradient direction. Quantum theory can be regarded as a geometric theory of distribution of gradient directions. Hence, gauge theory, gravitational theory and quantum theory obtain the same geometric foundation and a unified description of evolution.(iii) Coupling constants, chiral asymmetry, PMNS mixing and CKM mixing arise spontaneously as geometric properties in affine connection representation, so they are not necessary to be regarded as direct postulates in the Lagrangian anymore.(iv) The unification theory of gauge fields that are represented by affine connection can avoid the problem that a proton decays into a lepton in theories such as $SU(5)$.(v) There exists a geometric interpretation to the color confinement of quarks.In the affine connection representation, we can get better interpretations to the above physical properties, therefore, to represent gauge fields by affine connection is probably a necessary step towards the ultimate theory of physics.

scholarly journals A generalization of intrinsic geometry and an affine connection representation of gauge fields

2021 ◽  
Author(s):  
Zhao-Hui Man
Keyword(s):  
Quantum Theory ◽  
Gravitational Field ◽  
Gauge Theory ◽  
Gauge Field ◽  
Principal Bundle ◽  
Affine Connection ◽  
Geometric Theory ◽  
Coupling Constants ◽  
Gauge Fields ◽  
Coordinate Space

Abstract There are two ways to unify gravitational field and gauge field. One is to represent gravitational field as principal bundle connection, and the other is to represent gauge field as affine connection. Poincare gauge theory and metric-affine gauge theory adopt the first approach. This paper adopts the second. We show a generalization of Riemannian geometry and a new affine connection, and apply them to establishing a unified coordinate description of gauge field and gravitational field. It has the following advantages. (i) Gauge field and gravitational field have the same affine connection representation, and can be described by a unified spatial frame. (ii) Time can be regarded as the total metric with respect to all dimensions of internal coordinate space and external coordinate space. On-shell can be regarded as gradient direction. Quantum theory can be regarded as a geometric theory of distribution of gradient directions. Hence, gravitational theory and quantum theory obtain the same view of time and space and a unified description of evolution in affine connection representation of gauge fields. (iii) Chiral asymmetry, coupling constants, MNS mixing and CKM mixing can appear spontaneously in affine connection representation, while in $U(1) \times SU(2)\times SU(3)$ principal bundle connection representation they can just only be artificially set up. Some principles and postulates of the conventional theories that are based on principal bundle connection representation can be turned into theorems in affine connection representation, so they are not necessary to be regarded as principles or postulates anymore.

scholarly journals Affine connection representation of gauge fields

2021 ◽  
Author(s):  
Zhao-Hui Man
Keyword(s):  
Gravitational Field ◽  
Gauge Theory ◽  
Gauge Field ◽  
Affine Connection ◽  
Gravitational Theory ◽  
Geometric Interpretation ◽  
Coupling Constants ◽  
Gauge Fields ◽  
Coordinate Space ◽  
Color Confinement

Abstract There are two ways to unify gravitational field and gauge field. One is to represent gravitational field asprincipal bundle connection, and the other is to represent gauge field as affine connection. Poincaré gauge theoryand metric-affine gauge theory adopt the first approach. This paper adopts the second. In this approach:(i) Gauge field and gravitational field can both be represented by affine connection; they can be described by aunified spatial frame.(ii) Time can be regarded as the total metric with respect to all dimensions of internal coordinate space andexternal coordinate space. On-shell can be regarded as gradient direction. Quantum theory can be regarded as ageometric theory of distribution of gradient directions. Hence, gauge theory, gravitational theory, and quantumtheory all reflect intrinsic geometric properties of manifold.(iii) Coupling constants, chiral asymmetry, PMNS mixing and CKM mixing arise spontaneously as geometricproperties in affine connection representation, so they are not necessary to be regarded as direct postulates in theLagrangian anymore.(iv) The unification theory of gauge fields that are represented by affine connection can avoid the problem thata proton decays into a lepton in theories such as SU(5).(v) There exists a geometric interpretation to the color confinement of quarks.In the affine connection representation, we can get better interpretations to the above physical properties,therefore, to represent gauge fields by affine connection is probably a necessary step towards the ultimate theory ofphysics.

scholarly journals Affine connection representation of gauge fields

2021 ◽  
Author(s):  
Zhao-Hui Man
Keyword(s):  
Quantum Theory ◽  
Gravitational Field ◽  
Gauge Theory ◽  
Standard Model ◽  
Gauge Field ◽  
Principal Bundle ◽  
Affine Connection ◽  
Coupling Constants ◽  
Gauge Fields ◽  
Coordinate Space

Abstract There are two ways to unify gravitational field and gauge field. One is to represent gravitational field as principal bundle connection, and the other is to represent gauge field as affine connection. Poincaré gauge theory and metric affine gauge theory adopt the first approach. This paper adopts the second.An affine connection is used to establish a unified coordinate description of gauge field and gravitational field. This theory has the following advantages.(i) Gauge field and gravitational field can both be represented by affine connection; they can be described by a unified spatial frame.(ii) Time can be regarded as the total metric with respect to all dimensions of internal coordinate space and external coordinate space. On-shell can be regarded as gradient direction. Quantum theory can be regarded as a geometric theory of distribution of gradient directions. Hence, gravitational theory and quantum theory obtain the same view of time and space and a unified description of evolution in affine connection representation of gauge fields.(iii) Chiral asymmetry, coupling constants, MNS mixing and CKM mixing can appear spontaneously as geometric properties in affine connection representation, whereas in U(1) x SU(2) x SU(3) principal bundle connection representation they can just only be artificially set up. Some postulates of the Standard Model can be turned into theorems in affine connection representation, so they are not necessary to be regarded as postulates anymore.(iv) The unification theory of gauge fields that are represented by affine connection can avoid the problem that a proton decays into a lepton.(v) Since the concept of point particle is thoroughly abandoned, this theory is not required to be renormalized.(iv) There exists a possible geometric interpretation to the color confinement of quarks.The Standard Model is not possessed of the above advantages. In the affine connection representation, we can get better interpretations of these physical properties. This is probably a necessary step towards the ultimate theory ofphysics.

FRACTIONAL STATISTICS INDUCED BY GAUGE FIELDS

1991 ◽  
Vol 06 (05) ◽  
pp. 391-398 ◽  
Author(s):  
ASHOK CHATTERJEE ◽  
V.V. SREEDHAR
Keyword(s):  
Gauge Theory ◽  
Gauge Field ◽  
Path Integral ◽  
Simple Proof ◽  
Scalar Particle ◽  
Gauge Fields ◽  
Fractional Statistics ◽  
Chern Simons

An explicit extension of Polyakov’s analysis of a scalar particle coupled to an Abelian Chern-Simons gauge theory to the case of two particles and arbitrary values of the coupling is given. A simple proof of the emergence of fractional statistics induced by the gauge field follows within the path-integral framework.

scholarly journals PARALLEL TRANSPORT ON NON-ABELIAN FLUX TUBES

2005 ◽  
Vol 20 (22) ◽  
pp. 1695-1702
Author(s):  
AMITABHA LAHIRI
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Gauge Field ◽  
Integrability Condition ◽  
Parallel Transport ◽  
The Other ◽  
Gauge Fields ◽  
Flux Tubes ◽  
Gauge Transformations ◽  
Arbitrary Gauge

We propose a way of unambiguously parallel transporting fields on non-Abelian flux tubes, or strings, by means of two gauge fields. One gauge field transports along the tube, while the other transports normal to the tube. Ambiguity is removed by imposing an integrability condition on the pair of fields. The construction leads to a gauge theory of mathematical objects known as Lie 2-groups, which are known to result also from the parallel transport of the flux tubes themselves. The integrability condition is also shown to be equivalent to the assumption that parallel transport along nearby string configurations are equal up to arbitrary gauge transformations. Attempts to implement this condition in a field theory leads to effective actions for two-form fields.

scholarly journals Bosonization based on Clifford algebras and its gauge theoretic interpretation

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
A. Bochniak ◽  
B. Ruba
Keyword(s):  
Gauge Theory ◽  
Clifford Algebra ◽  
Gauge Field ◽  
Degrees Of Freedom ◽  
Clifford Algebras ◽  
Gauge Fields ◽  
Field Solution ◽  
Chern Simons

Abstract We study the properties of a bosonization procedure based on Clifford algebra valued degrees of freedom, valid for spaces of any dimension. We present its interpretation in terms of fermions in presence of ℤ2 gauge fields satisfying a modified Gauss’ law, resembling Chern-Simons-like theories. Our bosonization prescription involves constraints, which are interpreted as a flatness condition for the gauge field. Solution of the constraints is presented for toroidal geometries of dimension two. Duality between our model and (d − 1)- form ℤ2 gauge theory is derived, which elucidates the relation between the approach taken here with another bosonization map proposed recently.

TWO-POINT GREEN FUNCTION OF CHERN–SIMONS GAUGE FIELD IN ANYON GAS

1992 ◽  
Vol 06 (02) ◽  
pp. 261-279
Author(s):  
NGUYEN VAN HIEU ◽  
NGUYEN HUNG SON
Keyword(s):  
Magnetic Field ◽  
Quantum Theory ◽  
Green Function ◽  
Fermi Level ◽  
Gauge Field ◽  
Effective Magnetic Field ◽  
Gauge Fields ◽  
Green Functions ◽  
Chern Simons ◽  
Classical Background

The quantum theory of the anyon gas was developed in the framework of the field theoretical formalism. The existence of the classical background CS gauge field created by the quasiparticles below the Fermi level and acting as some effective magnetic field was taken into account. The expressions of the two-point Green functions of the free and interacting CS gauge fields were derived. It was shown that they determine the conductivity tensor of the anyon gas. The relevance to the FQHE was discussed.

scholarly journals Confining boundary conditions from dynamical coupling constants for Abelian and non-Abelian symmetries

2014 ◽  
Vol 29 (29) ◽  
pp. 1450165 ◽  
Author(s):  
Roee Steiner ◽  
Eduardo Guendelman
Keyword(s):  
Scalar Field ◽  
Boundary Conditions ◽  
Gauge Field ◽  
Coupling Constants ◽  
Gauge Fields ◽  
Abelian Case ◽  
Dynamical Coupling ◽  
Dirac Current ◽  
Local Value ◽  
Confinement Condition

The present work represents among other things a generalization to the non-Abelian case of our previous result where the Abelian case was studied. In the U(1) case the coupling to the gauge field contains a term of the form g(ϕ)jμ(Aμ +∂μB), where B is an auxiliary field and jμ is the Dirac current. The scalar field ϕ determines the local value of the coupling of the gauge field to the Dirac particle. The consistency of the equations determines the condition ∂μϕjμ = 0 which implies that the Dirac current cannot have a component in the direction of the gradient of the scalar field. As a consequence, if ϕ has a soliton behavior, we obtain that jμ cannot have a flux through the wall of the bubble, defining a confinement mechanism where the fermions are kept inside those bags. In this paper, we present more models in Abelian case which produce constraint on the Dirac or scalar current and also spin. Furthermore a model that gives the MIT confinement condition for gauge fields is obtained. We generalize this procedure for the non-Abelian case and we find a constraint that can be used to build a bag model. In the non-Abelian case, the confining boundary conditions hold at a specific surface of a domain wall.

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.

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