Supermetrics on Supermanifolds

Sardanashvily, G.

doi:10.1142/s021988780800276x

Cited by 9 publications

(7 citation statements)

References 30 publications

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“…Nonetheless, already at this simple level they provide physically important consequences; indeed the relation with confinement phases in non-abelian gauge theories [39] deserves further study. As for the interest in Physics, it is also worth to mention the possibility to extend the concept of a Higgs field defined here to principal superbundles in the category of G-supermanifolds; see in particular [36].…”

Section: An Application To Yang-mills Type Lagrangians On a Minkowski...mentioning

confidence: 99%

Higgs fields induced by Yang–Mills type Lagrangians on gauge-natural prolongations of principal bundles

Palese¹,

Winterroth²

2019

Int. J. Geom. Methods Mod. Phys.

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We address some new issues concerning spontaneous symmetry breaking. We define classical Higgs fields for gauge-natural invariant Yang-Mills type Lagrangian field theories through the requirement of the existence of canonical covariant gauge-natural conserved quantities. As an illustrative example we consider the 'gluon Lagrangian', i.e. a Yang-Mills Lagrangian on the (1, 1)-order gauge-natural bundle of SU (3)-principal connections, and canonically define a 'gluon' classical Higgs field through the split reductive structure induced by the kernel of the associated gauge-natural Jacobi morphism.

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Section: An Application To Yang-mills Type Lagrangians On a Minkowski...mentioning

confidence: 99%

Higgs fields induced by Yang–Mills type Lagrangians on gauge-natural prolongations of principal bundles

Palese¹,

Winterroth²

2019

Int. J. Geom. Methods Mod. Phys.

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“…As noted in [19], it is well known that a structure Lie group of a principal bundle is reducible to a closed subgroup if and only if there exists a global section of the quotient bundle and it is also well known that in physical gauge theory, such sections play the role of Higgs fields. It should be noted that in the field of Cartan connection which we associated here with invariant variational problems, is related with such a kind of field.…”

Section: Lemmamentioning

confidence: 99%

Gauge-Natural Noether Currents and Connection Fields

Ferraris¹,

Francaviglia²,

Palese³

et al. 2011

Int. J. Geom. Methods Mod. Phys.

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We study geometric aspects concerned with symmetries and conserved quantities in gauge-natural invariant variational problems and investigate implications of the existence of a reductive split structure associated with canonical Lagrangian conserved quantities on gauge-natural bundles. In particular, we characterize the existence of covariant conserved quantities in terms of principal Cartan connections on gauge-natural prolongations. Supported by the University of Torino through the research project 2008 Teorie di campo classiche: calcolo delle variazioni, struttura Lagrangiana e Hamiltoniana, etc.; and (E.W.) through the research contract Sequenze variazionali e teoremi di Noether su fibrati gauge-naturali: quantità conservate canoniche in teoria dei campi 2009-2010. 177 Int. J. Geom. Methods Mod. Phys. 2011.08:177-185. Downloaded from www.worldscientific.com by YALE UNIVERSITY on 07/11/15. For personal use only.

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“…19,20 It is metric-affine gravitation theory whose Lagrangian L MA is invariant under general covariant transformations. Infinitesimal generators of local one-parameter groups of these transformations are the functorial lift ͑i.e., the Lie algebra monomorphism͒ of vector fields on X onto a natural bundle.…”

Section: Gauge Gravitation Theorymentioning

confidence: 99%

On the notion of gauge symmetries of generic Lagrangian field theory

Giachetta

Mangiarotti

Sardanashvily

2009

Journal of Mathematical Physics

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General Lagrangian theory of even and odd fields on an arbitrary smooth manifold is considered. Its non-trivial reducible gauge symmetries and their algebra are defined in this very general setting by means of the inverse second Noether theorem. In contrast with gauge symmetries, non-trivial Noether and higher-stage Noether identities of Lagrangian theory can be intrinsically defined by constructing the exact Koszul-Tate complex. The inverse second Noether theorem that we prove associates to this complex the cochain sequence with the ascent operator whose components define non-trivial gauge and higher-stage gauge symmetries. These gauge symmetries are said to be algebraically closed if the ascent operator can be extended to a nilpotent operator. The necessary conditions for this extension are stated. The characteristic examples of Yang-Mills supergauge theory, topological Chern-Simons theory, gauge gravitation theory and topological BF theory are presented.Comment: 27 pages, accepted for publication in J. Math. Phy

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Supermetrics on Supermanifolds

Cited by 9 publications

References 30 publications

Higgs fields induced by Yang–Mills type Lagrangians on gauge-natural prolongations of principal bundles

Higgs fields induced by Yang–Mills type Lagrangians on gauge-natural prolongations of principal bundles

Gauge-Natural Noether Currents and Connection Fields

On the notion of gauge symmetries of generic Lagrangian field theory

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