scholarly journals The Bargmann-Wigner equations in spherical space

2006 ◽  
Vol 84 (1) ◽  
pp. 37-52
Author(s):  
D.G.C. McKeon ◽  
T N Sherry
Keyword(s):  
Gauge Invariance ◽  
Wave Equations ◽  
Antisymmetric Tensor ◽  
Spherical Space ◽  
Point Function ◽  
Tensor Fields ◽  
Abelian Gauge ◽  
Five Dimensions ◽  
Spherical Surfaces ◽  
The One

The Bargmann–Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations are gauge invariant for particular values of the parameters characterizing them. For spheres embedded in three, four, and five dimensions, this gauge invariance can be generalized so as to become non-Abelian. This non-Abelian gauge invariance is shown to be a property of second-order models for two index antisymmetric tensor fields in any number of dimensions. The O(3) model is quantized and the two-point function is shown to vanish at the one-loop order.PACS No.: 11.30–j

scholarly journals Antisymmetric tensor gauge fields on S4

2004 ◽  
Vol 82 (7) ◽  
pp. 541-548
Author(s):  
D.G.C. McKeon
Keyword(s):  
Field Model ◽  
Free Field ◽  
Flat Space ◽  
Antisymmetric Tensor ◽  
Gauge Fields ◽  
Scalar Model ◽  
Abelian Gauge ◽  
Five Dimensions ◽  
Higher Dimensional

Antisymmetric tensor gauge fields ϕab(η) are formulated on the surface of a sphere S4(η2 = a2) embedded in five dimensions. Such compact manifolds occur in the dimensional reduction of higher dimensional spaces that naturally occur in string theories. The free field model is equivalent to a scalar model on this sphere. Interactions with gauge fields are discussed. It is feasable to formulate models for interactions with U(1) gauge fields Aa(η) that are akin to those of Freedman and Townsend in flat space. In addition, it proves possible to have a novel interaction of ϕab with Aa and a spinor field Ψ(η) on S4 with both Abelian and non-Abelian gauge invariance. In these models, Aa plays the role of a Stueckelberg field.PACS No.: 11.30.Ly

scholarly journals Non-Abelian gauge antisymmetric tensor fields

1993 ◽  
Vol 108 (11) ◽  
pp. 1275-1291 ◽  
Author(s):  
S. N. Solodukhin
Keyword(s):  
Antisymmetric Tensor ◽  
Tensor Fields ◽  
Abelian Gauge

ABELIAN GAUGE THEORY IN TOPOLOGICALLY NON-TRIVIAL SPACE

1989 ◽  
Vol 04 (26) ◽  
pp. 2539-2547 ◽  
Author(s):  
AKIO HOSOYA ◽  
JIRO SODA
Keyword(s):  
Gauge Theory ◽  
Higher Dimensions ◽  
Antisymmetric Tensor ◽  
Wilson Loops ◽  
Tensor Fields ◽  
Maxwell Theory ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Global Modes

We quantize the (1+1)-dimensional Abelian gauge theory on cylinder to illustrate our idea how to extract global modes of topological origin. A new analysis is made for the (2+1)-dimensional Maxwell theory on T2(torus)×R(time). The dynamics is explicitly given for the Wilson loops around cycles of the torus with arbitrary moduli parameters. We also discuss an extension to antisymmetric tensor fields in higher dimensions.

Stueckelberg mechanism for antisymmetric tensor fields

2002 ◽  
Vol 80 (7) ◽  
pp. 767-779 ◽  
Author(s):  
S V Kuzmin ◽  
D.G.C. McKeon
Keyword(s):  
Gauge Invariance ◽  
Tensor Field ◽  
Vector Fields ◽  
Antisymmetric Tensor ◽  
Tensor Fields ◽  
Antisymmetric Tensor Field ◽  
Mass Terms

It is shown how vector Stueckelberg fields can be introduced to ensure gauge invariance for mass terms for an antisymmetric tensor field. Scalar Stueckelberg fields allow one to have gauge invariance for these vector fields. Both the Abelian and non-Abelian cases are considered. Fully antisymmetric rank-three tensor fields and symmetric rank-two tensor fields are also discussed. PACS No.: 11.15-1

scholarly journals CHIRAL TENSOR FIELDS AND SPONTANEOUS BREAKING OF LORENTZ SYMMETRY

2008 ◽  
Vol 23 (26) ◽  
pp. 4345-4359 ◽  
Author(s):  
JAN-MARKUS SCHWINDT ◽  
CHRISTOF WETTERICH
Keyword(s):  
Top Quark ◽  
Lorentz Invariance ◽  
Beta Function ◽  
Antisymmetric Tensor ◽  
Spontaneous Breaking ◽  
Tensor Fields ◽  
Hierarchy Problem ◽  
Running Coupling ◽  
Gauge Hierarchy ◽  
The One

Antisymmetric tensor fields interacting with quarks and leptons have been proposed as a possible solution to the gauge hierarchy problem. We compute the one-loop beta function for a quartic self-interaction of the chiral antisymmetric tensor fields. Fluctuations of the top quark drive the corresponding running coupling to a negative value as the renormalization scale is lowered. This may indicate a nonvanishing expectation value of the tensor field, and thus a spontaneous breaking of Lorentz invariance. Settling this issue will need the inclusion of tensor loops.

scholarly journals FIELD STRENGTH FORMULATION OF SU(2) YANG–MILLS THEORY IN THE MAXIMAL ABELIAN GAUGE: PERTURBATION THEORY

1998 ◽  
Vol 13 (23) ◽  
pp. 4049-4076 ◽  
Author(s):  
M. QUANDT ◽  
H. REINHARDT
Keyword(s):  
Perturbation Theory ◽  
Gauge Field ◽  
Trivial Solution ◽  
Semiclassical Approximation ◽  
Tensor Fields ◽  
Abelian Gauge ◽  
Standard Result ◽  
Yang Mills ◽  
Β Function ◽  
The One

We present a reformulation of SU(2) Yang–Mills theory in the maximal Abelian gauge, where the non-Abelian gauge field components are exactly integrated out at the expense of a new Abelian tensor field. The latter can be treated in a semiclassical approximation and the corresponding saddle point equation is derived. Besides the nontrivial solutions, which are presumably related to nonperturbative interactions for the Abelian gauge field, the equation of motion for the tensor fields allows for a trivial solution as well. We show that the semiclassical expansion around this trivial solution is equivalent to the standard perturbation theory. In particular, we calculate the one-loop β-function for the running coupling constant in this approach and reproduce the standard result.

scholarly journals Covariant phase space and soft factorization in non-Abelian gauge theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Temple He ◽  
Prahar Mitra
Keyword(s):  
Phase Space ◽  
Ward Identity ◽  
Gauge Theories ◽  
Minkowski Spacetime ◽  
Soft Gluon ◽  
Careful Study ◽  
Abelian Gauge ◽  
Gauge Sector ◽  
Vacuum States ◽  
The One

Abstract We perform a careful study of the infrared sector of massless non-abelian gauge theories in four-dimensional Minkowski spacetime using the covariant phase space formalism, taking into account the boundary contributions arising from the gauge sector of the theory. Upon quantization, we show that the boundary contributions lead to an infinite degeneracy of the vacua. The Hilbert space of the vacuum sector is not only shown to be remarkably simple, but also universal. We derive a Ward identity that relates the n-point amplitude between two generic in- and out-vacuum states to the one computed in standard QFT. In addition, we demonstrate that the familiar single soft gluon theorem and multiple consecutive soft gluon theorem are consequences of the Ward identity.

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