On invariance groups and Lagrangian theories

Houard, J. C.

doi:10.1063/1.523294

Cited by 16 publications

(2 citation statements)

References 6 publications

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“…where w : G x G+ U(1) is a factor system that is differentiable due to the assumed differentiability of 2 (see HOUARD [19]). It will always be used the convention L(e) = I, where e is the identity element of G. Henceforth the term "lift" will be referred to a map satisfying all the above conditions a), b) and c).…”

Section: The Lift Of the G-action On M To A ''Global Action" On Pmentioning

confidence: 99%

Relativistic Gauge Invariant Potentials

1995

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A global method characterizing the invariant connections on an abelian principal bundle under a group of transformations is applied in order to get gauge invariant electromagnetic (elm.) potentials in a systematic way. So, we have classified all the elm. gauge invariant potentials under the Poincaré subgroups of dimensions 4, 5, and 6, up to conjugation. It is paid attention in particular to the situation where these subgroups do not act transitively on the space‐time manifold. We have used the same procedure for some galilean subgroups to get nonrelativistic potentials and study the way they are related to their relativistic partners by means of contractions. Some conformal gauge invariant potentials have also been derived and considered when they are seen as consequence of an enlargement of the Poincaré symmetries.

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Section: The Lift Of the G-action On M To A ''Global Action" On Pmentioning

confidence: 99%

Relativistic Gauge Invariant Potentials

1995

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“…There are two existing standard methods of finding continuous (normalized) cocycles in the quantum theory context. One method uses the cohomology theory of Lie groups and Lie algebras (see [2], [9]); the other uses the powerful coordinateindependent techniques of modern differential geometry (see [7]). Krause [8] introduced a simpler, coordinate-dependent version of the latter method.…”

Section: Introductionmentioning

confidence: 99%