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 POISSON ALGEBRA OF WILSON LOOPS IN FOUR-DIMENSIONAL YANG-MILLS THEORY

1995 ◽  
Vol 10 (17) ◽  
pp. 2479-2505 ◽  
Author(s):  
S.G. RAJEEV ◽  
O.T. TURGUT
Keyword(s):  
Phase Space ◽  
Gauge Theories ◽  
Poisson Algebra ◽  
Coadjoint Orbit ◽  
Quadratic Algebra ◽  
Wilson Loops ◽  
Poisson Brackets ◽  
Canonical Structure ◽  
Gauge Invariant ◽  
Yang Mills

We formulate the canonical structure of Yang-Mills theory in terms of Poisson brackets of gauge-invariant observables analogous to Wilson loops. This algebra is nontrivial and tractable in a light cone formulation. For U (N) gauge theories the result is a Lie algebra while for SU (N) gauge theories it is a quadratic algebra. We also study the identities satisfied by the gauge-invariant observables. We suggest that the phase space of a Yang-Mills theory is a coadjoint orbit of our Poisson algebra; some partial results in this direction are obtained.

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.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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.

One-dimensional coherent-state representation on a circle in phase space

1994 ◽  
Vol 50 (5) ◽  
pp. 4293-4297 ◽  
Author(s):  
P. Domokos ◽  
P. Adam ◽  
J. Janszky
Keyword(s):  
Phase Space ◽  
Coherent State ◽  
State Representation ◽  
One Dimensional

Local Geometric Projection-Based Noise Reduction for Vibration Signal Analysis in Rolling Bearings

2008 ◽  
Author(s):  
Ruqiang Yan ◽  
Robert X. Gao ◽  
Kang B. Lee ◽  
Steven E. Fick
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Noise Reduction ◽  
Signal Analysis ◽  
Signal To Noise Ratio ◽  
Multifractal Spectrum ◽  
Vibration Signal ◽  
Rolling Bearings ◽  
One Dimensional ◽  
Vibration Signal Analysis

This paper presents a noise reduction technique for vibration signal analysis in rolling bearings, based on local geometric projection (LGP). LGP is a non-linear filtering technique that reconstructs one dimensional time series in a high-dimensional phase space using time-delayed coordinates, based on the Takens embedding theorem. From the neighborhood of each point in the phase space, where a neighbor is defined as a local subspace of the whole phase space, the best subspace to which the point will be orthogonally projected is identified. Since the signal subspace is formed by the most significant eigen-directions of the neighborhood, while the less significant ones define the noise subspace, the noise can be reduced by converting the points onto the subspace spanned by those significant eigen-directions back to a new, one-dimensional time series. Improvement on signal-to-noise ratio enabled by LGP is first evaluated using a chaotic system and an analytically formulated synthetic signal. Then analysis of bearing vibration signals is carried out as a case study. The LGP-based technique is shown to be effective in reducing noise and enhancing extraction of weak, defect-related features, as manifested by the multifractal spectrum from the signal.

scholarly journals Polymer quantum effects on compact stars models

2015 ◽  
Vol 24 (05) ◽  
pp. 1550033 ◽  
Author(s):  
Guillermo Chacón-Acosta ◽  
Héctor H. Hernandez-Hernandez
Keyword(s):  
Semiclassical Approximation ◽  
Generalized Uncertainty Principle ◽  
Compact Object ◽  
Compact Stars ◽  
One Dimensional ◽  
Degenerate Fermi Gas ◽  
Mechanical Models ◽  
Degeneracy Pressure ◽  
Loop Quantization ◽  
Bose Einstein

In this work we study a completely degenerate Fermi gas at zero temperature by a semiclassical approximation for a Hamiltonian that arises in polymer quantum mechanics. Polymer quantum systems are quantum mechanical models quantized in a similar way as in loop quantum gravity, allowing the study of the discreteness of space and other features of the loop quantization in a simplified way. We obtain the polymer modified thermodynamical properties for this system by noticing that the corresponding Fermi energy is exactly the same as if one directly polymerizes the momentum pF. We also obtain the expansion of the corresponding thermodynamical variables in terms of small values of the polymer length scale λ. We apply these results to study a simple model of a compact one-dimensional star where the gravitational collapse is supported by electron degeneracy pressure. As a consequence, polymer corrections to the mass of the object are found. By using bounds for the polymer length found in Bose–Einstein condensates experiments we compute the modification in the mass of the compact object due to polymer effects of order ~ 10-8. This result is similar to the other order found by different approaches such as generalized uncertainty principle (GUP), and that certainly is within the error reported in typical measurements of white dwarf masses.

One-Dimensional Harmonic Oscillator in Quantum Phase Space

2011 ◽  
Vol 110-116 ◽  
pp. 3750-3754
Author(s):  
Jun Lu ◽  
Xue Mei Wang ◽  
Ping Wu
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Quantum Phase ◽  
Space Representation ◽  
Wave Mechanics ◽  
One Dimensional ◽  
Matrix Mechanics ◽  
The Matrix ◽  
Quantum Wave ◽  
The One

Within the framework of the quantum phase space representation established by Torres-Vega and Frederick, we solve the rigorous solutions of the stationary Schrödinger equations for the one-dimensional harmonic oscillator by means of the quantum wave-mechanics method. The result shows that the wave mechanics and the matrix mechanics are equivalent in phase space, just as in position or momentum space.

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