The Maxwell Group and the Quantum Theory of Particles in Classical Homogeneous Electromagnetic Fields

Schrader, Robert

doi:10.1002/prop.19720201202

Cited by 163 publications

(268 citation statements)

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“…Nowadays one might think of magnetars. However it is Schrader [28] who seems to have been the first to study it systematically. Other earlier work applying group theoretic methods to uniform electromagnetic fields is in [29,30].…”

Section: The Maxwell Algebramentioning

confidence: 99%

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Deforming the Maxwell-Sim algebra

2010

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The Maxwell algebra is a non-central extension of the Poincaré algebra, in which the momentum generators no longer commute, but satisfy [P µ , P ν ] = Z µν . The charges Z µν commute with the momenta, and transform tensorially under the action of the angular momentum generators. If one constructs an action for a massive particle, invariant under these symmetries, one finds that it satisfies the equations of motion of a charged particle interacting with a constant electromagnetic field via the Lorentz force. In this paper, we explore the analogous constructions where one starts instead with the ISim subalgebra of Poincaré, this being the symmetry algebra of Very Special Relativity. It admits an analogous non-central extension, and we find that a particle action invariant under this Maxwell-Sim algebra again describes a particle subject to the ordinary Lorentz force. One can also deform the ISim algebra to DISim b , where b is a non-trivial dimensionless parameter. We find that the motion described by an action invariant under the corresponding MaxwellDISim algebra is that of a particle interacting via a Finslerian modification of the Lorentz force. In an appendix is it shown that the DISim b algebra is isomorphic to the extended Schrödinger algebra with b = 1 1−z .

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Section: The Maxwell Algebramentioning

confidence: 99%

“…The Maxwell group acts on these wave functions by pull-back, and in this way one obtains a projective representation of the Maxwell group. For details of the procedure, including the calculation of the relevant co-cycles, the reader is referred to Schrader's paper [28].…”

Section: Quantisationmentioning

confidence: 99%

Deforming the Maxwell-Sim algebra

2010

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“…Maxwell symmetry was introduced around 40 years ago [1,2], but it is only recently that has attracted more attention. The D = 4 Maxwell algebra, with sixteen generators (P a , M ab , Z ab ), is obtained from Poincaré algebra if we replace its commuting fourmomenta by noncommuting ones [P a , P b ] = ΛZ ab , [P a , Z bc ] = 0 , a, b = 0, 1, 2, 3 ,…”

Section: Introductionmentioning

confidence: 99%

“…The global Maxwell symmetries have been introduced in order to describe Minkowski space with constant e.m. background [1][2][3][4] in models of relativistic particles interacting with a constant e.m. field 1 . In this paper, following [6], we present the construction of a local D = 4 gauge theory based on the Maxwell algebra (eqs.…”

Section: Introductionmentioning

confidence: 99%

Maxwell Symmetries and Some Applications

Azcárraga

Kamimura

Lukierski

2013

Int. J. Mod. Phys. Conf. Ser.

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The Maxwell algebra is the result of enlarging the Poincaré algebra by six additional tensorial Abelian generators that make the fourmomenta non-commutative. We present a local gauge theory based on the Maxwell algebra with vierbein, spin connection and six additional geometric Abelian gauge fields. We apply this geometric framework to the construction of Maxwell gravity, which is described by the Einstein action plus a generalized cosmological term. We mention a FriedmanRobertson-Walker cosmological approximation to the Maxwell gravity field equations, with two scalar fields obtained from the additional gauge fields. Finally, we outline further developments of the Maxwell symmetries framework.

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“…Recently the approach to the cosmological constant problem based on the tensor extension of the Poincaré algebra with the generators of the rotations M ab and translations P a [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] […”

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confidence: 99%