Relation of the Inhomogeneous de Sitter Group to the Quantum Mechanics of Elementary Particles

1970 ◽  
Vol 11 (8) ◽  
pp. 2297-2301 ◽  
Author(s):  
J. J. Aghassi ◽  
P. Roman ◽  
R. M. Santilli
Keyword(s):  
Quantum Mechanics ◽  
Elementary Particles ◽  
De Sitter ◽  
Sitter Group

scholarly journals Elementary particles with continuous spin

2017 ◽  
Vol 32 (23n24) ◽  
pp. 1730019 ◽  
Author(s):  
Xavier Bekaert ◽  
Evgeny D. Skvortsov
Keyword(s):  
Degrees Of Freedom ◽  
Isometry Group ◽  
Theoretical Description ◽  
Elementary Particles ◽  
De Sitter ◽  
Continuous Spin ◽  
Sitter Group ◽  
Free Level ◽  
Recent Developments ◽  
Open Issues

Classical results and recent developments on the theoretical description of elementary particles with “continuous” spin are reviewed. At free level, these fields are described by unitary irreducible representations of the isometry group (either Poincaré or anti-de Sitter group) with an infinite number of physical degrees of freedom per space–time point. Their basic group-theoretical and field-theoretical descriptions are reviewed in some details. We mention a list of open issues which are crucial to address for assessing their physical status and potential relevance.

scholarly journals Integration of Dirac’s Efforts to Construct a Quantum Mechanics Which is Lorentz-Covariant

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1270
Author(s):  
Young S. Kim ◽  
Marilyn E. Noz
Keyword(s):  
Quantum Mechanics ◽  
Lie Algebra ◽  
Lorentz Group ◽  
Gaussian Function ◽  
Uncertainty Relations ◽  
De Sitter ◽  
Sitter Group ◽  
Fundamental Symmetry ◽  
Oscillator Wave Function ◽  
Inhomogeneous Lorentz Group

The lifelong efforts of Paul A. M. Dirac were to construct localized quantum systems in the Lorentz covariant world. In 1927, he noted that the time-energy uncertainty should be included in the Lorentz-covariant picture. In 1945, he attempted to construct a representation of the Lorentz group using a normalizable Gaussian function localized both in the space and time variables. In 1949, he introduced his instant form to exclude time-like oscillations. He also introduced the light-cone coordinate system for Lorentz boosts. Also in 1949, he stated the Lie algebra of the inhomogeneous Lorentz group can serve as the uncertainty relations in the Lorentz-covariant world. It is possible to integrate these three papers to produce the harmonic oscillator wave function which can be Lorentz-transformed. In addition, Dirac, in 1963, considered two coupled oscillators to derive the Lie algebra for the generators of the O(3,2) de Sitter group, which has ten generators. It is proven possible to contract this group to the inhomogeneous Lorentz group with ten generators, which constitute the fundamental symmetry of quantum mechanics in Einstein’s Lorentz-covariant world.

ALL CONFORMAL INVARIANT REPRESENTATIONS OF d-DIMENSIONAL ANTI-DE SITTER GROUP

1995 ◽  
Vol 10 (23) ◽  
pp. 1719-1731 ◽  
Author(s):  
R.R. METSAEV
Keyword(s):  
Gauge Invariance ◽  
Conformal Group ◽  
Elementary Particles ◽  
Irreducible Representations ◽  
Conformal Invariant ◽  
De Sitter ◽  
Sitter Group ◽  
Invariant Representations

All the irreducible representations of the anti-de Sitter group which are relevant for elementary particles and which can be realized as irreducible representations of the conformal group are found. It is shown that all these representations correspond to massless representations which arise from considerations of gauge invariance. The problem is studied for arbitrary d>2 dimensional anti-de Sitter group.

scholarly journals p-ADIC AND ADELIC MINISUPERSPACE QUANTUM COSMOLOGY

2002 ◽  
Vol 17 (10) ◽  
pp. 1413-1433 ◽  
Author(s):  
GORAN S. DJORDJEVIĆ ◽  
BRANKO DRAGOVICH ◽  
LJUBIŠA D. NEŠIĆ ◽  
IGOR V. VOLOVICH
Keyword(s):  
Quantum Mechanics ◽  
Cosmological Constant ◽  
Quantum Cosmology ◽  
Quantum Effects ◽  
De Sitter Space ◽  
Cosmological Models ◽  
De Sitter ◽  
Adelic Quantum Mechanics ◽  
Matter Fields

We consider the formulation and some elaboration of p-adic and adelic quantum cosmology. The adelic generalization of the Hartle–Hawking proposal does not work in models with matter fields. p-adic and adelic minisuperspace quantum cosmology is well defined as an ordinary application of p-adic and adelic quantum mechanics. It is illustrated by a few cosmological models in one, two and three minisuperspace dimensions. As a result of p-adic quantum effects and the adelic approach, these models exhibit some discreteness of the minisuperspace and cosmological constant. In particular, discreteness of the de Sitter space and its cosmological constant is emphasized.

The relativistic quantum mechanics of the elementary particles

1949 ◽  
Vol 45 (2) ◽  
pp. 263-274 ◽  
Author(s):  
H. S. Green
Keyword(s):  
Quantum Mechanics ◽  
Density Matrix ◽  
Relativistic Quantum ◽  
Difficult Problem ◽  
Dynamical Variable ◽  
Elementary Particles ◽  
Relativistic Quantum Mechanics ◽  
Principle Of Relativity ◽  
The One ◽  
Real Linear

The search for a theory of the elementary particles which is founded on the well-established principles of quantum mechanics and conforms at the same time with the requirements of the principle of relativity has, in recent years, taken several divergent directions. On the one hand, the second quantization of wave fields derived from a Lagrangian by a variational procedure(1) has succeeded in accounting for the existence and most of the properties of the electron, the photon, and the meson. On the other hand, many generalizations of the Dirac wave equation of the electron(2) have been attempted, with applications to the meson(3) and the proton(4). Heisenberg(5) has considered the much more difficult problem of the interaction between different particles, and has found that the key to the situation is the so-called ‘scattering matrix’, which is nothing other than a limiting form of the relativistic density matrix, as defined in § 2 of this paper. It seems probable that the relativistic density matrix ρ; or statistical operator, as it may be called without reference to representation, will play an important part in relativistic quantum mechanics in the future. It satisfies the same equation as the wave function, but differs from it in being a real linear operator, or a dynamical variable, in the terminology of Dirac.

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.

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