scholarly journals On the Group-Theoretical Approach to Relativistic Wave Equations for Arbitrary Spin

Author(s):  
Luca Nanni

Formulating a relativistic equation for particles with arbitrary spin remains an open challenge in theoretical physics. In this study, the main algebraic approaches used to generalize the Dirac and Kemmer–Duffin equations for particles of arbitrary spin are investigated. It is proved that an irreducible relativistic equation formulated using spin matrices satisfying the commutation relations of the de Sitter group leads to inconsistent results, mainly as a consequence of violation of unitarity and the appearance of a mass spectrum that does not reflect the physical reality of elementary particles. However, the introduction of subsidiary conditions resolves the problem of unitarity and restores the physical meaning of the mass spectrum. The equations obtained by these approaches are solved and the physical nature of the solutions is discussed.

1972 ◽  
Vol 50 (20) ◽  
pp. 2489-2495 ◽  
Author(s):  
Kenneth Rafanelli

We investigate the group structure of the intrinsic dynamical variables describing the relativistic motions of the classical pure gyroscope. It is shown that the 10 elements of this group, the 6 components of the spin angular momentum tensor, and the four-velocity components have Poisson bracket relations among themselves characteristic of the Lie algebra of the De Sitter group. This algebraic result allows a complete description of the free particle motions to be deduced from a proper-time Hamiltonian linear in the four-momentum components. Thus we are led, via the correspondence principle, to a classical understanding of the origin of the algebraic and dynamical properties characteristic of Dirac-like relativistic wave equations.


1998 ◽  
Vol 10 (08) ◽  
pp. 1079-1109 ◽  
Author(s):  
Mourad Laoues

Various properties of two kinds of massless representations of the n-conformal (or (n+1)-De Sitter) group [Formula: see text] are investigated for n≥2. It is found that, for space-time dimensions n≥3, the situation is quite similar to the one of the n=4 case for Sn-massless representations of the n-De Sitter group [Formula: see text]. These representations are the restrictions of the singletons of [Formula: see text]. The main difference is that they are not contained in the tensor product of two UIRs with the same sign of energy when n>4, whereas it is the case for another kind of massless representations. Finally some examples of Gupta–Bleuler triplets are given for arbitrary spin and n≥3.


1977 ◽  
Vol 30 (1) ◽  
pp. 1 ◽  
Author(s):  
HS Green

It is pointed out that existing field equations for particles of higher spin are unsuitable' for the formulation of field theories with interaction. ' A generalization of the Dirac and Kemmer matrices is discussed in terms of finite-dimensional representations of the de, Sitter group. ' It is shown how to formulate a general field theory in such a way as to exhibit a corresponding dynamical symmetry. The resulting field equation resembles Bhabha's, but is self-consistent in its applications to interacting particles and has a different type of mass spectrum. In the Appendix, it is shown that'within any'irreducible representation of the Poincare group there are finite-dimensional representations of the'Lorentz group'labelled (s, � s).


2017 ◽  
Vol 9 (6) ◽  
pp. 1
Author(s):  
Maurizio Michelini

Rejecting some old misconceptions (such as the “pulling” gravitation that ravaged classical physics) the Inertial-Gravitational theory supported by the Micro-quanta paradigm incorporates both the relativistic concepts of Mass - Momentum - Energy and the quantic Inertial Model of the particle mass. The flux of micro-quanta supports primarily the physical interaction that generates the Inertial forces defined by Newton. Scholars believing that Inertial forces originate from the properties of the empty space, do not pertain to the community of physicists believing on Newton’s Inertial Law. This great ancient physicist admitted he was unable to explicit the physical nature of his Law of Inertia (“Hypotheses non fingo”). However, marking the difference between “empty” and “absolute” space, he remained in his conviction that some unknown physical reality originates (in the absolute space) the inertial forces upon accelerated masses. At present, Micro-quanta paradigm describes the quantic objects that generate through collisions the physical inertial forces on particles. Since the flux of micro-quanta fills all space, there is no need to refer these collisions to some external System of reference. The relative velocity between quanta and particles comes out from the momentum that micro-quanta confer to particles. By this reason the Micro-quanta paradigm defines on pure dynamical bases the relativistic formalism that Special relativity derived from kinematics, so creating flaws that produced the well known paradoxes. To reveal the micro-quanta it's not necessary to devise particular experiments. The technique of the accelerometers has given many evidences of the physical reality guessed by Newton to explain inertial forces exerted on masses. Since the action of micro-quanta is always manifested in statistical terms, classical and relativistic physics allowed to describe Inertia and Gravitation without knowing the quantic nature of these phenomena. The micro-quanta Paradigm shows in particular the proportionality between cross section and mass (ratio Au) of all particles colliding with micro-quanta. To the aim of calculating the transmission across matter of micro-quanta and neutrinos (which show the same nature) the only unknown quantity is the numerical value of the ratio Au. Recalling that micro-quanta flux fills all space, it appears also interesting to search about neutrino collisions with micro-quanta flux as possible cause of the oscillations phenomena that occur during neutrino travels across the (so called) astronomic “empty” space. A quantitative indication on the ratio Ao is found in this paper from an experimental measurement of the solar neutrino flux interacting with the Earth mass in the course of the Borexino research carried out at Gran Sasso National Laboratory.


1949 ◽  
Vol 76 (2) ◽  
pp. 296-297 ◽  
Author(s):  
Satosi Watanabe

2006 ◽  
Vol 03 (07) ◽  
pp. 1349-1357 ◽  
Author(s):  
V. V. KOZLOV ◽  
I. V. VOLOVICH

The eigenvalue problem for the square integrable solutions is studied usually for elliptic equations. In this paper we consider such a problem for the hyperbolic Klein–Gordon equation on Lorentzian manifolds. The investigation could help to answer the question why elementary particles have a discrete mass spectrum. An infinite family of square integrable solutions for the Klein–Gordon equation on the Friedman type manifolds is constructed. These solutions have a discrete mass spectrum and a finite action. In particular the solutions on de Sitter space are investigated.


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