Systems of vector valued forms on a fibred manifold and applications to gauge theories

2006 ◽  
pp. 238-264 ◽  
Author(s):  
Marco Modugno
Keyword(s):  
Gauge Theories ◽  
Fibred Manifold ◽  
Vector Valued

scholarly journals On duality between Cosserat elasticity and fractons

2020 ◽  
Vol 8 (4) ◽  
Author(s):  
Andrey Gromov ◽  
Piotr Surowka
Keyword(s):  
Gauge Field ◽  
Degrees Of Freedom ◽  
Gauge Theories ◽  
Symmetric Tensor ◽  
Theory Of Elasticity ◽  
Cosserat Theory ◽  
Curved Space ◽  
Local Element ◽  
Vector Valued ◽  
Coupled Theory

We present a dual formulation of the Cosserat theory of elasticity. In this theory a local element of an elastic body is described in terms of local displacement and local orientation. Upon the duality transformation these degrees of freedom map onto a coupled theory of a U(1) vector-valued one-form gauge field and an ordinary U(1) gauge field. We discuss the degrees of freedom in the corresponding gauge theories, relation to symmetric tensor gauge theories, the defect matter and coupling to the curved space.

scholarly journals Symmetry breaking via internal geometry

2005 ◽  
Vol 2005 (13) ◽  
pp. 2023-2030 ◽  
Author(s):  
Andrew Talmadge
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Principal Bundle ◽  
Gauge Theories ◽  
Higgs Mechanism ◽  
Internal Space ◽  
Hermitian Metric ◽  
Unitary Transformations ◽  
Vector Valued ◽  
Higgs Scalar

Gauge theories commonly employ complex vector-valued fields to reduce symmetry groups through the Higgs mechanism of spontaneous symmetry breaking. The geometry of the internal spaceVis tacitly assumed to be the metric geometry of some static, nondynamical hermitian metrick. In this paper, we considerG-principal bundle gauge theories, whereGis a subgroup ofU(V,k)(the unitary transformations on the internal vector spaceVwith hermitian metrick) and we consider allowing the hermitian metric on the internal spaceVto become an additional dynamical element of the theory. We find a mechanism for interpreting the Higgs scalar field as a feature of the geometry of the internal space while retaining the successful aspects of the Higgs mechanism and spontaneous symmetry breaking

The range of block Hankel operators

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3237-3243
Author(s):  
In Hwang ◽  
In Kim ◽  
Sumin Kim
Keyword(s):  
Hardy Space ◽  
Invariant Subspace ◽  
Hankel Operators ◽  
Coprime Factorization ◽  
Backward Shift ◽  
Vector Valued

In this note we give a connection between the closure of the range of block Hankel operators acting on the vector-valued Hardy space H2Cn and the left coprime factorization of its symbol. Given a subset F ? H2Cn, we also consider the smallest invariant subspace S*F of the backward shift S* that contains F.

Geometry and Quantum Dynamics

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
General Relativity ◽  
Quantum Dynamics ◽  
Gauge Theories ◽  
Brst Symmetry ◽  
Abelian Gauge ◽  
Yang Mills ◽  
History Of ◽  
Brst Invariance

A geometrical derivation of Abelian and non- Abelian gauge theories. The Faddeev–Popov quantisation. BRST invariance and ghost fields. General discussion of BRST symmetry. Application to Yang–Mills theories and general relativity. A brief history of gauge theories.

Path integral for gauge theories with fermions

1980 ◽  
Vol 21 (10) ◽  
pp. 2848-2858 ◽  
Author(s):  
Kazuo Fujikawa
Keyword(s):  
Path Integral ◽  
Gauge Theories
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