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

Palese, Marcella; Winterroth, Ekkehart Hans Konrad

doi:10.1142/s021988781950049x

Cited by 3 publications

(1 citation statement)

References 36 publications

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“…Note that we have fixed an orthonormal basis for the Cartan-Killing metric; working with a specific group G of course the equation can be further specialized writing down the structure constants. The corresponding gauge-natural version of the Jacobi equation obtained here could be of interest for a canonical variational characterization [58] of confinement phases in non-abelian gauge theories [63].…”

Section: Working Out This Expression In Local Coordinates We Getmentioning

confidence: 86%

The Jacobi morphism and the Hessian in higher order field theory; with applications to a Yang-Mills theory on a Minkowskian background

Accornero,

Palese

2017

Preprint

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We investigate higher variations of Lagrangians in the framework of finite order variational sequences. In particular we obtain explicit expressions for second variations that are naturally related to the geometric structure of the problem. We recover the definition of the Jacobi morphism and of the Hessian at an arbitrary order, and show the relation between them. We investigate the relation between Jacobi fields, symmetries of higher variations and conserved currents; we show that a pair given by a symmetry of the l-th variation of a Lagrangian and by a Jacobi field of the s-th variation of the same Lagrangian (with s < l) is associated with a (strongly) conserved current. Furthermore we prove that a pair of Jacobi fields always generates a (weakly) conserved current. The example of the Jacobi equation for a Yang-Mills theory on a Minkowskian background is worked out and the current associated with two Jacobi fields is obtained in this case.

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Section: Working Out This Expression In Local Coordinates We Getmentioning

confidence: 86%

The Jacobi morphism and the Hessian in higher order field theory; with applications to a Yang-Mills theory on a Minkowskian background

Accornero,

Palese

2017

Preprint

Self Cite

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Symmetry transformations of extremals and higher conserved quantities: Invariant Yang–Mills connections

Accornero

Palese²

2021

Journal of Mathematical Physics

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We characterize symmetry transformations of Lagrangian extremals generating “on shell” conservation laws. We relate symmetry transformations of extremals to Jacobi fields and study symmetries of higher variations by proving that a pair given by a symmetry of the lth variation of a Lagrangian and by a Jacobi field of the sth variation of the same Lagrangian (with s < l) is associated with an “off shell” conserved current. The conserved current associated with two symmetry transformations is constructed, and as a case of study, its expression for invariant sets of Yang–Mills connections on Minkowski space-times is obtained.

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The Jacobi morphism and the Hessian in higher order field theory; with applications to a Yang–Mills theory on a Minkowskian background

Accornero

Palese²

2020

Int. J. Geom. Methods Mod. Phys.

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We characterize the second variation of an higher order Lagrangian by a Jacobi morphism and by currents strictly related to the geometric structure of the variational problem. We discuss the relation between the Jacobi morphism and the Hessian at an arbitrary order. Furthermore, we prove that a pair of Jacobi fields always generates a (weakly) conserved current. An explicit example is provided for a Yang–Mills theory on a Minkowskian background.

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

Cited by 3 publications

References 36 publications

The Jacobi morphism and the Hessian in higher order field theory; with applications to a Yang-Mills theory on a Minkowskian background

The Jacobi morphism and the Hessian in higher order field theory; with applications to a Yang-Mills theory on a Minkowskian background

Symmetry transformations of extremals and higher conserved quantities: Invariant Yang–Mills connections

The Jacobi morphism and the Hessian in higher order field theory; with applications to a Yang–Mills theory on a Minkowskian background

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