scholarly journals A GENERALIZATION OF THE JORDAN-SCHWINGER MAP: THE CLASSICAL VERSION AND ITS q DEFORMATION

1994 ◽  
Vol 09 (31) ◽  
pp. 5541-5561 ◽  
Author(s):  
V.I. MAN’KO ◽  
G. MARMO ◽  
P. VITALE ◽  
F. ZACCARIA
Keyword(s):  
Phase Space ◽  
Lie Algebras ◽  
Three Dimensional ◽  
Poisson Brackets ◽  
Classical Version ◽  
Deformed Algebras

For all three-dimensional Lie algebras the construction of generators in terms of functions on four-dimensional real phase space is given with a realization of the Lie product in terms of Poisson brackets. This is the classical Jordan-Schwinger map, which is also given for the deformed algebras [Formula: see text], ℰq(2) and ℋq(1). The algebra [Formula: see text] is discussed in the same context.

Size of the early universe and GUP

2019 ◽  
Vol 34 (22) ◽  
pp. 1950178
Author(s):  
Ljubisa Nesic ◽  
Darko Radovancevic
Keyword(s):  
Phase Space ◽  
Cosmological Model ◽  
Early Universe ◽  
Generalized Uncertainty Principle ◽  
Poisson Algebra ◽  
Poisson Brackets ◽  
Energy Term ◽  
Classical Version ◽  
One Dimensional ◽  
Potential Energy Term

This paper presents the effects of the Generalized Uncertainty Principle (GUP), i.e. its classical version expressed through the deformed Poisson brackets in the phase–space of a one-dimensional minisuperspace Friedmann cosmological model with a mixture of non-interacting dust and radiation. It is shown, in the case of this model, that starting from the specific representation of the deformed Poisson algebra, which corresponds to the change of the potential energy term of the oscillator, the size of the early universe can be related to its inflationary GUP expansion.

scholarly journals On the Dirac eigenvalues as observables of the on-shell N = 2D = 4 Euclidean supergravity

Open Physics ◽  
2008 ◽  
Vol 6 (4) ◽  
Author(s):  
Ion Vancea
Keyword(s):  
Phase Space ◽  
Equations Of Motion ◽  
Poisson Brackets ◽  
Gauge Transformations

AbstractWe generalize previous works on the Dirac eigenvalues as dynamical variables of Euclidean gravity and N =1 D = 4 supergravity to on-shell N = 2 D = 4 Euclidean supergravity. The covariant phase space of the theory is defined as the space of the solutions of the equations of motion modulo the on-shell gauge transformations. In this space we define the Poisson brackets and compute their value for the Dirac eigenvalues.

A note on the algebra of Poisson brackets

1984 ◽  
Vol 96 (1) ◽  
pp. 45-60 ◽  
Author(s):  
C. J. Atkin
Keyword(s):  
Poisson Bracket ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Symplectic Manifold ◽  
Vector Fields ◽  
Poisson Brackets ◽  
Infinite Dimensional

In a long sequence of notes in the Comptes Rendus and elsewhere, and in the papers [1], [2], [3], [6], [7], Lichnerowicz and his collaborators have studied the ‘classical infinite-dimensional Lie algebras’, their derivations, automorphisms, co-homology, and other properties. The most familiar of these algebras is the Lie algebra of C∞ vector fields on a C∞ manifold. Another is the Lie algebra of ‘Poisson brackets’, that is, of C∞ functions on a C∞ symplectic manifold, with the Poisson bracket as composition; some questions concerning this algebra are of considerable interest in the theory of quantization – see, for instance, [2] and [3].

scholarly journals Examples of S—expansions of Lie Algebras

2021 ◽  
Vol 2090 (1) ◽  
pp. 012067
Author(s):  
G. Javier Rosales
Keyword(s):  
Lie Algebras ◽  
Three Dimensional ◽  
Infinite Dimension ◽  
Dimensional Case ◽  
Finite Dimensional ◽  
Finite Dimensional Case

Abstract In this note, we give examples of S—expansions of Lie algebras of finite and infinite dimension. For the finite dimensional case, we expand all real three-dimensional Lie algebras. In the case of infinite dimension, we perform contractions obtaining new Lie algebras of infinite dimension.

Superconductivity and the existence of Nambu's three-dimensional phase space mechanics

1984 ◽  
Vol 104 (2) ◽  
pp. 106-108 ◽  
Author(s):  
Reinaldo Angulo ◽  
Simón Codriansky ◽  
Carlos A. Gonzalez-Bernardo ◽  
Andrés J. Kalnay ◽  
Freddy Perez-M ◽  
...  
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Dimensional Phase Space ◽  
Space Mechanics

scholarly journals Astrometric Tests of Galactic Evolution

1995 ◽  
Vol 166 ◽  
pp. 251-258
Author(s):  
Gerard Gilmore
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Galactic Evolution ◽  
Critical Test ◽  
Current Standard ◽  
High Quality ◽  
Stellar Velocity ◽  
Formation And Evolution ◽  
Standard Models

There are many fundamental aspects of Galactic structure and evolution which can be studied best or exclusively with high quality three dimensional kinematics. Amongst these we note as examples determination of the orientation of the stellar velocity ellipsoid, and the detection of structure in velocity-position phase space. The first of these is the primary limitation at present to reliable and accurate measurement of the Galactic gravitational potential. The second is a critical test of current standard models of Galactic formation and evolution.

ROTATING SYNCHRONIZATION IN THREE-DIMENSIONAL CHAOTIC SYSTEMS

2012 ◽  
Vol 26 (20) ◽  
pp. 1250120 ◽  
Author(s):  
FUZHONG NIAN ◽  
XINGYUAN WANG
Keyword(s):  
Phase Space ◽  
Chaotic Systems ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Phase Space Reconstruction ◽  
Projective Synchronization ◽  
Reconstruction Method ◽  
Self Similarity ◽  
Application Fields ◽  
Three Dimensional Space

Projective synchronization investigates the synchronization of systems evolve in same orientation, however, in practice, the situation of same orientation is only minority, and the majority is different orientation. This paper investigates the latter, proposes the concept of rotating synchronization, and verifies its necessity and feasibility via theoretical analysis and numerical simulations. Three conclusions were elicited: first, in three-dimensional space, two arbitrary nonlinear chaotic systems who evolve in different orientation can realize synchronization at end; second, projective synchronization is a special case of rotating synchronization, so, the application fields of rotating synchronization is more broadly than that of the former; third, the overall evolving information can be reflected by single state variable's evolving, it has self-similarity, this is the same as the basic idea of phase space reconstruction method, it indicates that we got the same result from different approach, so, our method and the phase space reconstruction method are verified each other.

scholarly journals Constraining cluster masses from the stacked phase space distribution at large radii

2019 ◽  
Vol 489 (1) ◽  
pp. 1344-1356
Author(s):  
Akinari Hamabata ◽  
Masamune Oguri ◽  
Takahiro Nishimichi
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Space Distribution ◽  
Line Of Sight ◽  
Mass Dependence ◽  
Mass Measurements ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
Transverse Distance ◽  
Hubble Flow

Abstract Velocity dispersions have been employed as a method to measure masses of clusters. To complement this conventional method, we explore the possibility of constraining cluster masses from the stacked phase space distribution of galaxies at larger radii, where infall velocities are expected to have a sensitivity to cluster masses. First, we construct a two-component model of the three-dimensional phase space distribution of haloes surrounding clusters up to 50 $\, h^{-1}$ Mpc from cluster centres based on N-body simulations. We confirm that the three-dimensional phase space distribution shows a clear cluster mass dependence up to the largest scale examined. We then calculate the probability distribution function of pairwise line-of-sight velocities between clusters and haloes by projecting the three-dimensional phase space distribution along the line of sight with the effect of the Hubble flow. We find that this projected phase space distribution, which can directly be compared with observations, shows a complex mass dependence due to the interplay between infall velocities and the Hubble flow. Using this model, we estimate the accuracy of dynamical mass measurements from the projected phase space distribution at the transverse distance from cluster centres larger than $2\, h^{-1}$ Mpc. We estimate that, by using 1.5 × 105 spectroscopic galaxies, we can constrain the mean cluster masses with an accuracy of 14.5 per cent if we fully take account of the systematic error coming from the inaccuracy of our model. This can be improved down to 5.7 per cent by improving the accuracy of the model.

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