scispace - formally typeset
Search or ask a question
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

01 May 1970-Vol. 67, Iss: 2, pp 267-299
About: 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.
Citations
More filters
Journal ArticleDOI
TL;DR: In this article, two subgroups of the Galilei group are shown to play a particular role in the case of charged systems in an external electro-magnetic field which is constant and uniform.
Abstract: Two subgroups of the Galilei group are shown to play a particular role in the case of charged systems in an external electro-magnetic field which is constant and uniform. Projective representations of these subgroups involve the electric charge and mass as generators of phase factors. Additivity and superselection rules for charge and mass appear as direct consequences. A comparison is made with the relativistic case investigated in the first part of this article.

147 citations

Journal ArticleDOI
TL;DR: In this paper, a unified treatment of the quantum-mechanical operators and wave functions for a molecular system (composed of N moving charged particles) in static uniform electric and magnetic fields E and B.
Abstract: A thorough unified treatment is given of the quantum-mechanical operators and wave functions for a molecular system (composed of N moving charged particles) in static uniform electric and magnetic fields E and B. The treatment is rigorous within the nonrelativistic approximation. The system may either be neutral or charged. The fields may have arbitrary intensities and orientations. Close correspondence is maintained between the classical and quantum-mechanical treatments. The wave functions are expressed both in time-independent energy representation and in time-dependent wave packets. Three types of momentum play important roles. For single-particle systems they are the canonical momentum P; the mechanical momentum Pi = P(e/c) A = MR; and the pseudomomentum K = Pi-(e/c)R x B-eEt.B. For neutral molecules, the Schroedinger equation is ''pseudoseparated'' and the internal degrees of freedom are coupled to the center of mass motion by only the ''motional Stark Effect,'' which involves the constant of motion scrK. For ionic systems, only one component of the center of mass is coupled to the internal motion.

144 citations

Journal ArticleDOI
TL;DR: In this article, the symmetry properties of a particle interacting with an electromagnetic circularly polarized plane wave were considered and the classical and quantum analysis of the stability group of the plane wave exhibits the origin of the mass shift of the particle.
Abstract: We consider the symmetry properties of a particle interacting with an electromagnetic circularly polarized plane wave. The classical and quantum analysis of the stability group of the plane wave exhibits the origin of the mass shift of the particle. The Chakrabarti’s dynamical representation of the Poincare group is rederived and its physical meaning is given.

133 citations

Journal ArticleDOI
TL;DR: The generalized Inonu-Wigner contraction of the generalized AdS-Lorentz algebras provides the so-called B 4 algebra, which corresponds to the so -called Maxwell algebra as mentioned in this paper.

97 citations

Journal ArticleDOI
TL;DR: In this paper, the standard geometric framework of Einstein gravity with cosmological constant term is extended by adding six four-vector fields associated with the six Abelian tensorial charges in the Maxwell algebra.
Abstract: By gauging the Maxwell spacetime algebra, the standard geometric framework of Einstein gravity with cosmological constant term is extended by adding six four-vector fields ${A}_{\ensuremath{\mu}}^{ab}(x)$ associated with the six Abelian tensorial charges in the Maxwell algebra. In the simplest Maxwell extension of Einstein gravity this leads to a generalized cosmological term that includes a contribution from these vector fields. We also consider going beyond the basic gravitational model by means of bilinear actions for the new Abelian gauge fields. Finally, an analogy with the supersymmetric generalization of gravity is indicated. In an appendix, we propose an equivalent description of the model in terms of a shift of the standard spin connection by the ${A}_{\ensuremath{\mu}}^{ab}(x)$ fields.

96 citations

References
More filters
Journal ArticleDOI
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.
Abstract: It is perhaps the most fundamental principle of Quantum Mechanics that the system of states forms a linear manifold,1 in which a unitary scalar product is defined.2 The states are generally represented by wave functions3 in such a way that φ and constant multiples of φ represent the same physical state. It is possible, therefore, to normalize the wave function, i.e., to multiply it by a constant factor such that its scalar product with itself becomes 1. Then, only a constant factor of modulus 1, the so-called phase, will be left undetermined in the wave function. The linear character of the wave function is called the superposition principle. The square of the modulus of the unitary scalar product (ψ,Φ) of two normalized wave functions ψ and Φ is called the transition probability from the state ψ into Φ, or conversely. This is supposed to give the probability that an experiment performed on a system in the state Φ, to see whether or not the state is ψ, gives the result that it is ψ. If there are two or more different experiments to decide this (e.g., essentially the same experiment, performed at different times) they are all supposed to give the same result, i.e., the transition probability has an invariant physical sense.

2,694 citations

Journal ArticleDOI
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.
Abstract: 1. This paper, although mathematical in content, is motivated by quantumtheoretical considerations. The states of a quantum-mechanical system are usually described by vectors f of norm 1 in some Hilbert space A, and we assume explicitly that to every unit vector f corresponds a state of the system. This correspondence, however, is not one-to-one. In fact, the vectors which describe the same state form a ray f (in Weyl's terminology, cf. [13], p. 4 and p. 20),1 i.e. a set consisting of all vectors f = Tfo where fo is a fixed unit vector in & and r any complex number of modulus 1. (Every vector f in f will be called a representative of the ray f.) We have therefore a one-to-one correspondence between quantum states and rays, and every significant statement in Quantum Theory is a statement about rays. The transition probability from a state f to a state g equals (f, I)'2 where f, g are representatives of the rays f, g respectively. This suggests the introduction of the inner product of two rays by the definition

890 citations

Journal ArticleDOI
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.
Abstract: This paper is devoted to the study of the Galilei group and its representations. The Galilei group presents a certain number of essential differences with respect to the Poincare group. As Bargmann showed, its physical representations, here explicitly constructed, are not true representations but only up‐to‐a‐factor ones. Consequently, in nonrelativistic quantum mechanics, the mass has a very special role, and in fact, gives rise to a superselection rule which prevents the existence of unstable particles. The internal energy of a nonrelativistic system is known to be an arbitrary parameter; this is shown to come also from Galilean invariance, because of a nontrivial concept of equivalence between physical representations. On the contrary, the behavior of an elementary system with respect to rotations, is very similar to the relativistic case. We show here, in particular, how the number of polarization states reduces to two for the zero‐mass case (though in fact there are no physical zero‐mass systems in nonrelativistic mechanics). Finally, we study the two‐particle system, where the orbital angular momenta quite naturally introduce themselves through the decomposition of the tensor product of two physical representations.

213 citations

Journal ArticleDOI
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.
Abstract: Using the Mackey theory of induced representations all the unitary continuous irreducible representations of the 4-dimensional Lie groupG generated by the canonical variables and a positive definite quadratic ‘hamiltonian’ are found. These are shown to be in a one to one correspondence with the orbits underG in the dual spaceG′ to the Lie algebraG ofG, and the representations are obtained from the orbits by inducing from one-dimensional representations provided complex subalgebras are admitted. Thus a construction analogous to that ofKirillov andBernat gives all the representations of this group.

103 citations

Journal ArticleDOI
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.
Abstract: First, a general property of Lie groups is used in the case of the Poincare group in order to define the one particle phase space. It is eight-dimensional in the general case and six-dimensional for a spinless or massless particle.

40 citations