Journal ArticleDOI
Group-theoretical analysis of elementary particles in an external electromagnetic field@@@Теоретико-групповой анализ элементарных частиц во внешнем электромагнитном поле.: I. The relativistic particle in a constant and uniform field@@@I. Релятивистская частица в постоянном и однородном поле
H. Bacry,Ph. Combe,J. L. Richard +2 more
- Vol. 67, Iss: 2, pp 267-299
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The article was published on 1970-05-01. It has received 161 citations till now. The article focuses on the topics: Relativistic particle & Electromagnetic field.read more
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On the supersymmetry invariance of flat supergravity with boundary
TL;DR: In this paper, the supersymmetry invariance of the Lagrangian in four dimensions on a manifold with non-trivial boundary is explored using a geometric approach, which is achieved by adding additional gauge fields to the boundary without modifying the bulk Lagrangians.
Journal ArticleDOI
Non-Relativistic Maxwell Chern-Simons Gravity
Luis Avilés,Luis Avilés,Ernesto Frodden,Joaquim Gomis,Joaquim Gomis,Joaquim Gomis,Diego Hidalgo,Diego Hidalgo,Jorge Zanelli +8 more
TL;DR: In this paper, a non-relativistic (NR) limit of the Chern-Simons (CS) gravity with gauge algebra was considered and a degenerate invariant bilinear form was obtained.
Journal ArticleDOI
(In)finite extensions of algebras from their İnönü–Wigner contractions
TL;DR: In this article, Houart et al. showed that the central extension of the Poincare algebra can be encoded in the non-relativistic contraction of the SO(3) algebra.
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Supersymmetrization schemes of D=4 Maxwell algebra
Kiyoshi Kamimura,Jerzy Lukierski +1 more
TL;DR: In this article, the authors studied various D = 4 N-extended Maxwell superalgebras obtained by the contractions of real superalgesbras OSp R ( 2 N − k ; 2 | C ) ⊕ OSp ( k ; 4 ) ( k = 0, 1, 2, …, 2 N ); (extended Lorentz superalgebra ⊆ extended AdS superal algebra).
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Generalized cosmological term in D=4 supergravity from a new AdS-Lorentz superalgebra
TL;DR: In this article, a supersymmetrization of the so-called AdS-Lorentz algebra is presented, which involves two fermionic generators and is obtained by performing an abelian semigroup expansion of the superalgebra.
References
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On Unitary Representations of the Inhomogeneous Lorentz Group
TL;DR: The superposition principle of the wave function is defined in this article, which is the fundamental principle of quantum mechanics that the system of states forms a linear manifold, in which a unitary scalar product is defined.
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On Unitary ray representations of continuous groups
TL;DR: In this article, the inner product of two rays is introduced, and the transition probability from a state f to a state g is (f, I)'2 where f, g are representatives of the rays f and g respectively.
Journal ArticleDOI
Galilei Group and Nonrelativistic Quantum Mechanics
TL;DR: In this article, the authors studied the Galilei group and its representations and showed that the behavior of an elementary system with respect to rotations is very similar to the relativistic case, and that the number of polarization states reduces to two for the zero mass case.
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The Representations of the Oscillator Group
TL;DR: In this paper, all the unitary continuous irreducible representations of the 4-dimensional Lie group generated by the canonical variables and a positive definite quadratic "hamiltonian" are found.
Journal ArticleDOI
Space--time and degrees of freedom of the elementary particle.
TL;DR: In this article, a general property of Lie groups is used in the case of the Poincare group in order to define the one particle phase space, which is eight-dimensional in the general case and six-dimensional for a spinless or massless particle.
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The Maxwell Group and the Quantum Theory of Particles in Classical Homogeneous Electromagnetic Fields
Group-theoretical analysis of elementary particles in an external electromagnetic field II.—The nonrelativistic particle in a constant and uniform field
H. Bacry,Ph. Combe,J. L. Richard +2 more