scholarly journals TOPOLOGICALLY MASSIVE GAUGE THEORY: A LORENTZIAN SOLUTION

2007 ◽  
Vol 22 (16n17) ◽  
pp. 2961-2976 ◽  
Author(s):  
K. SAYGILI
Keyword(s):  
Field Equation ◽  
Gauge Theory ◽  
Field Strength ◽  
Gauge Transformation ◽  
Global Section ◽  
Gauge Potential ◽  
Abelian Gauge ◽  
Abelian Field ◽  
Hopf Map ◽  
Topological Mass

We obtain a Lorentzian solution for the topologically massive non-Abelian gauge theory on AdS space [Formula: see text] by means of an SU (1, 1) gauge transformation of the previously found Abelian solution. There exists a natural scale of length which is determined by the inverse topological mass ν ~ ng2. In the topologically massive electrodynamics the field strength locally determines the gauge potential up to a closed 1-form via the (anti-)self-duality equation. We introduce a transformation of the gauge potential using the dual field strength which can be identified with an Abelian gauge transformation. Then we present map [Formula: see text] including the topological mass which is the Lorentzian analog of the Hopf map. This map yields a global decomposition of [Formula: see text] as a trivial [Formula: see text] bundle over the upper portion of the pseudosphere [Formula: see text] which is the Hyperboloid model for the Lobachevski geometry. This leads to a reduction of the Abelian field equation onto [Formula: see text] using a global section of the solution on [Formula: see text]. Then we discuss the integration of the field equation using the Archimedes map [Formula: see text]. We also present a brief discussion of the holonomy of the gauge potential and the dual field strength on [Formula: see text].

Gauge theories

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Gauge Theory ◽  
Field Strength ◽  
Gauge Theories ◽  
Local Symmetry ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Abelian Field ◽  
Feynman Rules ◽  
Popov Method ◽  
Special Case

After reviewing electrodynamics as the special case of an abelian gauge theory, this local symmetry is generalised to non-abelian gauge theories. The curvature of space-time is introduced as analogue of the non-abelian field-strength. Non-abelian gauge theories are quantised using the Fadeev–Popov method and the resulting Feynman rules are derived.

scholarly journals On Spinor Representations in the Weyl Gauge Theory

1997 ◽  
Vol 12 (26) ◽  
pp. 1957-1968 ◽  
Author(s):  
B. M. Barbashov ◽  
A. B. Pestov
Keyword(s):  
Gauge Theory ◽  
Differential Forms ◽  
Current Source ◽  
Gauge Potential ◽  
Spinor Representation ◽  
Abelian Gauge ◽  
Cartan Torsion ◽  
Gauge Space ◽  
Spinor Current ◽  
Spinor Representations

A spinor current-source is found in the Weyl non-Abelian gauge theory which does not contain the abstract gauge space. It is shown that the searched spinor representation can be constructed in the space of external differential forms and it is a 16-component quantity for which a gauge-invariant Lagrangian is determined. The connection between the Weyl non-Abelian gauge potential and the Cartan torsion field, and the problem of a possible manifestation of the considered interactions are considered.

scholarly journals TOPOLOGICALLY MASSIVE ABELIAN GAUGE THEORY

2008 ◽  
Vol 23 (13) ◽  
pp. 2015-2035 ◽  
Author(s):  
K. SAYGILI
Keyword(s):  
Gauge Theory ◽  
Bianchi Type ◽  
Dual Solutions ◽  
Contact Structures ◽  
Type I ◽  
Three Solutions ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Complex Solutions ◽  
Topological Mass

We discuss three mathematical structures which arise in topologically massive Abelian gauge theory. First, the Euclidean topologically massive Abelian gauge theory defines a contact structure on a manifold. We briefly discuss three solutions and the related contact structures on the flat 3-torus, the AdS space, the 3-sphere which respectively correspond to Bianchi type I, VIII, IX spaces. We also present solutions on Bianchi type II, VI and VII spaces. Secondly, we discuss a family of complex (anti-)self-dual solutions of the Euclidean theory in Cartesian coordinates on [Formula: see text] which are given by (anti)holomorpic functions. The orthogonality relation of contact structures which are determined by the real parts of these complex solutions separates them into two classes: the self-dual and the anti-self-dual solutions. Thirdly, we apply the curl transformation to this theory. An arbitrary solution is given by a vector tangent to a sphere whose radius is determined by the topological mass in transform space. Meanwhile a gauge transformation corresponds to a vector normal to this sphere. We discuss the quantization of topological mass in an example.

CHIRALITY IN ELECTRODYNAMICS

1999 ◽  
Vol 14 (32) ◽  
pp. 5121-5135 ◽  
Author(s):  
G. C. MARQUES ◽  
D. SPEHLER
Keyword(s):  
Gauge Theory ◽  
Gauge Transformation ◽  
Gauge Invariance ◽  
Spinor Field ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Left Right Asymmetry

We show that a not necessarily totally symmetric Bargman–Wigner second rank spinor field is able to accommodate a left–right symmetric U (1)L⊗ U (1)R Abelian gauge theory. We show that some features of the standard QED, such as vectorial gauge invariance, invariance under gauge transformation of the second kind, and the nonexistence of monopoles, follow from imposing left–right asymmetry on the level of self-interaction of the spinorial constituents.

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