On the Classical Origin of Dirac-Like Wave Equations

1972 ◽  
Vol 50 (20) ◽  
pp. 2489-2495 ◽  
Author(s):  
Kenneth Rafanelli
Keyword(s):  
Wave Equations ◽  
Correspondence Principle ◽  
Proper Time ◽  
Group Structure ◽  
Free Particle ◽  
Momentum Tensor ◽  
Spin Angular Momentum ◽  
De Sitter ◽  
Sitter Group ◽  
Algebraic Result

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.

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

2021 ◽  
Author(s):  
Luca Nanni
Keyword(s):  
Mass Spectrum ◽  
Wave Equations ◽  
Relativistic Equation ◽  
Physical Nature ◽  
Physical Reality ◽  
Arbitrary Spin ◽  
Theoretical Physics ◽  
De Sitter ◽  
Sitter Group ◽  
Algebraic Approaches

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.

scholarly journals WEYL INVARIANT STANDARD MODEL AND ITS SYMMETRY BREAKING

2013 ◽  
Vol 10 (06) ◽  
pp. 1350022
Author(s):  
WOLFGANG DRECHSLER
Keyword(s):  
Standard Model ◽  
Symmetry Breaking ◽  
Momentum Tensor ◽  
Mass Scale ◽  
Strong Interactions ◽  
Dirac Fermion ◽  
De Sitter ◽  
Sitter Group ◽  
Fermion Fields ◽  
Weyl Symmetry

A standard model is formulated in a Weyl space, W4, yielding a Weyl covariant dynamics of massless chiral Dirac fermion fields for leptons and quarks as well as the gauge fields involved for the groups D(1) (Weyl), U(1)Y × SU (2)W (electroweak), SU (3)c (color), SO(3, 1) (gravity) and SO(4, 1) (strong interaction, symmetry breaking). The dynamics is based on a gauge and Weyl invariant Lagrangian density [Formula: see text]. Gravitation is included from the beginning as the gauge aspect of the Lorentz group which is here extended in the hadronic sector of the model to the ten-parameter SO(4, 1) de Sitter group. A part of the dynamics is, as usual, a scalar isospinor field ϕ being a section on a bundle related to the electroweak gauge group and to symmetry breaking. In parallel to ϕ on the leptonic side a section [Formula: see text] on the hadronic side is considered as part of the dynamics, governing the symmetry breaking SO(4, 1) → SO(3, 1) and recovering gravitation in the symmetry breaking limit outside the regions in space–time where strong interactions persist. Besides spin, isospin and helicity the Weyl weights determine the form of the contributions of fields in [Formula: see text]. Of particular interest is the appearance of a current–current self-interaction of quark fields allowed by the Weyl weight changing the debate about quark masses. In a second step the D(1)-Weyl symmetry is explicitly broken and a universal mass scale is established through the mass of the ϕ-field appearing in the symmetry breaking Lagrangian [Formula: see text]. The Weyl symmetry breaking is governed by the relation DμΦ2 = 0, where Φ is the norm of ϕ. After D(1) symmetry breaking the masses of the weak bosons and of the electron appear on the scene through the energy–momentum tensor of the ϕ-field.

Wave Equations in the de Sitter Space

1949 ◽  
Vol 76 (2) ◽  
pp. 296-297 ◽  
Author(s):  
Satosi Watanabe
Keyword(s):  
Wave Equations ◽  
De Sitter Space ◽  
De Sitter

Foldy-Wouthuysen transformations, Lorentz transformations and the De Sitter group

Physica ◽  
1969 ◽  
Vol 43 (1) ◽  
pp. 45-49 ◽  
Author(s):  
E. De Vries
Keyword(s):  
Lorentz Transformations ◽  
De Sitter ◽  
Sitter Group

scholarly journals Spherical functions on the de Sitter group

2006 ◽  
Vol 40 (1) ◽  
pp. 163-201 ◽  
Author(s):  
V V Varlamov
Keyword(s):  
Spherical Functions ◽  
De Sitter ◽  
Sitter Group

OBSERVABLE TIME IN QUANTUM COSMOLOGY

1995 ◽  
Vol 04 (01) ◽  
pp. 105-113 ◽  
Author(s):  
V. PERVUSHIN ◽  
T. TOWMASJAN
Keyword(s):  
Quantum Mechanics ◽  
First Principles ◽  
Quantum Cosmology ◽  
Correspondence Principle ◽  
Proper Time ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Conformal Time ◽  
Energy Factor ◽  
Definition Of

We show that the first principles of quantization and the experience of relativistic quantum mechanics can lead to the definition of observable time in quantum cosmology as a global quantity which coincides with the constrained action of the reduced theory up to the energy factor. The latter is fixed by the correspondence principle once one considers the limit of the “dust filled” Universe. The “global time” interpolates between the proper time for dust dominance and the conformal time for radiation dominance.

scholarly journals A CHERN–SIMONS E8 GAUGE THEORY OF GRAVITY IN D = 15, GRAND UNIFICATION AND GENERALIZED GRAVITY IN CLIFFORD SPACES

2007 ◽  
Vol 04 (08) ◽  
pp. 1239-1257 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Gauge Theory ◽  
Grand Unification ◽  
De Sitter ◽  
Sitter Group ◽  
Yang Mills ◽  
Theory Of Gravity ◽  
M Theory ◽  
Chern Simons ◽  
Topological Part ◽  
Gauge Theory Of Gravity

A novel Chern–Simons E8 gauge theory of gravity in D = 15 based on an octicE8 invariant expression in D = 16 (recently constructed by Cederwall and Palmkvist) is developed. A grand unification model of gravity with the other forces is very plausible within the framework of a supersymmetric extension (to incorporate spacetime fermions) of this Chern–Simons E8 gauge theory. We review the construction showing why the ordinary 11D Chern–Simons gravity theory (based on the Anti de Sitter group) can be embedded into a Clifford-algebra valued gauge theory and that an E8 Yang–Mills field theory is a small sector of a Clifford (16) algebra gauge theory. An E8 gauge bundle formulation was instrumental in understanding the topological part of the 11-dim M-theory partition function. The nature of this 11-dim E8 gauge theory remains unknown. We hope that the Chern–Simons E8 gauge theory of gravity in D = 15 advanced in this work may shed some light into solving this problem after a dimensional reduction.

Charged gravastars in f(R,T,RμνTμν) gravity

2021 ◽  
pp. 2150084
Author(s):  
Z. Yousaf ◽  
M. Z. Bhatti
Keyword(s):  
Perfect Fluid ◽  
Energy Momentum Tensor ◽  
Equations Of State ◽  
Mathematical Formulation ◽  
Momentum Tensor ◽  
Spherically Symmetric ◽  
De Sitter ◽  
The Stability ◽  
Physical Features ◽  
Modified Theory

We explore the aspects of the electromagnetism on the stability of gravastar in a particular modified theory, i.e. [Formula: see text] where [Formula: see text], [Formula: see text] is the Ricci scalar and [Formula: see text] is the trace of energy–momentum tensor. We assume a spherically symmetric static metric coupled comprising of perfect fluid in the presence of electric charge. The purpose of this paper is to extend the results of [S. Ghosh, F. Rahaman, B. K. Guha and S. Ray, Phys. Lett. B 767 (2017) 380.] to highlight the effects of [Formula: see text] gravity in the formation of charged gravastars. We demonstrated the mathematical formulation, utilizing different equations of state, for the three respective regions (i.e. inner, shell, exterior) of the gravastar. We have matched smoothly the interior de Sitter and the exterior Reissner–Nordström metric at the hypersurface. At the end we extracted few conclusions by working on the physical features of the charged gravastar, mathematically and graphically.

Sign in / Sign up

Export Citation Format

Share Document