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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Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension
TL;DR: In this paper, the authors extend a recent classification of three-dimensional spatially isotropic homogeneous spacetimes to Chern-Simons theories as 3D gravity theories on these spacetomes, by defining a nondegenerate bilinear form for each of the theories.
Journal ArticleDOI
Minimal electromagnetic coupling schemes. II. Relativistic and nonrelativistic Maxwell groups
J. Beckers,V. Hussin +1 more
TL;DR: In this paper, minimal electromagnetic coupling schemes entering into Klein-Gordon or Schrodinger equations are studied in connection with symmetries outside the symmetry groups of the corresponding free equations.
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Three-dimensional (higher-spin) gravities with extended Schrödinger and l-conformal Galilean symmetries
TL;DR: In this article, an extended 3D Schrodinger algebra is reformulated as a 3D Poincare algebra with an SO(2) R-symmetry generator and an SO (2) doublet of bosonic spin-1/2 generators whose commutator closes on 3D translations and a central element.
Journal ArticleDOI
Galilean free Lie algebras
TL;DR: In this article, the authors construct infinite-dimensional extensions of finite-dimensional Galilei Maxwell algebras appearing as global spacetime symmetries of extended non-relativistic objects and gravity theories, and show how various extensions of the ordinary Galilei algebra can be obtained by truncations and contractions.
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Gauge semi-simple extension of the Poincaré group
TL;DR: In this paper, an approach to the cosmological term problem is proposed, using the gauge semi-simple tensor extension of the D -dimensional Poincare group as a basis.
References
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Journal ArticleDOI
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