The galilean group in 2+1 space-times and its central extension

Bose, S. K.

doi:10.1007/bf02099478

Cited by 47 publications

(31 citation statements)

References 15 publications

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“…The first term corresponds to the so-called exotic NR gravity. The second term is the CS action for the extended Bargmann algebra [73][74][75][76][77][78], while the last term reproduces the CS action for a new NR Maxwell algebra. Let us note that, since the bilinear form does not result to acquire degeneracy in the contraction process, the equations of motion from the NR action (2.10) are given by the vanishing of all the curvatures (2.9).…”

Section: Maxwellian Extended Bargmann Gravitymentioning

confidence: 99%

Three-dimensional Maxwellian extended Bargmann supergravity

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Ravera

Rodríguez

2020

J. High Energ. Phys.

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We present a novel three-dimensional non-relativistic Chern-Simons supergravity theory invariant under a Maxwellian extended Bargmann superalgebra. We first study the nonrelativistic limits of the minimal and the N = 2 Maxwell superalgebras. We show that a well-defined Maxwellian extended Bargmann supergravity requires to construct by hand a supersymmetric extension of the Maxwellian extended Bargmann algebra by introducing additional fermionic and bosonic generators. The new non-relativistic supergravity action presented here contains the extended Bargmann supergravity as a sub-case.

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Section: Maxwellian Extended Bargmann Gravitymentioning

confidence: 99%

Three-dimensional Maxwellian extended Bargmann supergravity

Concha

Ravera

Rodríguez

2020

J. High Energ. Phys.

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“…The Galilean group is a Lie group with its associated Galilean algebra of generators. The central extension of the Galilean algebra is obtained as a semi-direct product between the Galilean algebra and the algebra generated by a central charge, which in this case denotes the mass operator M = mI , where I is the identity operator (see [13,14]). In this central extension, the symmetry generators represent the basic magnitudes of the theory: the energy H = K τ , the three momentum components P i = K r i , the three angular momentum components J i = K θ i , and the three boost components G i = K u i .…”

Section: The Galilean Groupmentioning

confidence: 99%

Quantum Mechanics: Modal Interpretation and Galilean Transformations

2009

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The aim of this paper is to consider in what sense the modal-Hamiltonian interpretation of quantum mechanics satisfies the physical constraints imposed by the Galilean group. In particular, we show that the only apparent conflict, which follows from boost-transformations, can be overcome when the definition of quantum systems and subsystems is taken into account. On this basis, we apply the interpretation to different well-known models, in order to obtain concrete examples of the previous conceptual conclusions. Finally, we consider the role played by the Casimir operators of the Galilean group in the interpretation.

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“…For a further discussion of this second central charge, see [13][14][15] . We will call the Bargmann Algebra with this second central charge the Extended Bargmann Algebra.…”

Section: Extended Bargmann Gravitymentioning

confidence: 99%