Deformations, stable theories and fundamental constants

Mendes, R. Vilela

doi:10.1088/0305-4470/27/24/019

Cited by 96 publications

(180 citation statements)

References 38 publications

Supporting

Mentioning

180

Contrasting

Order By: Relevance

“…The basic starting point there is the old idea of relativity deformations [14][15][16][17][18] to which contraction of the relativity symmetries is the reverse process, so long as one stays within the Lie group/algebra framework. While we have presented some picture of the physics from a sequence of contractions [10], we are currently working on the details of the descriptions of an alternative contraction scheme, via an approach that naturally incorporates symmetries like (3) and̃(3).…”

Section: Discussionmentioning

confidence: 99%

A Quantum Space behind Simple Quantum Mechanics

Chew

Kong

Payne

2017

Advances in High Energy Physics

View full text Add to dashboard Cite

In physics, experiments ultimately inform us about what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the configuration space of a free particle (or the center of mass of a closed system of particles). This configuration space (as well as phase space) can be constructed as a representation space for the relativity symmetry. From the corresponding quantum symmetry, we illustrate the construction of a quantum configuration space, similar to that of quantum phase space, and recover the classical picture as an approximation through a contraction of the (relativity) symmetry and its representations. The quantum Hilbert space reduces into a sum of one-dimensional representations for the observable algebra, with the only admissible states given by coherent states and position eigenstates for the phase and configuration space pictures, respectively. This analysis, founded firmly on known physics, provides a quantum picture of physical space beyond that of a finite-dimensional manifold and provides a crucial first link for any theoretical model of quantum space-time at levels beyond simple quantum mechanics. It also suggests looking at quantum physics from a different perspective.

show abstract

Section: Discussionmentioning

confidence: 99%

A Quantum Space behind Simple Quantum Mechanics

Chew

Kong

Payne

2017

Advances in High Energy Physics

View full text Add to dashboard Cite

show abstract

“…It is important to note that in the standard statistical mechanics of the early Universe, the Bose-Einstein and Fermi-Dirac ensemble densities select a finite subset of microstates from the infinite total number of microstates (22) as the accessible microstates for the system. But, however, the system can access more and more microstates by increasing the energy.…”

Section: A Total Number Of Microstatesmentioning

confidence: 99%

Early universe thermostatistics in curved momentum spaces

Gorji¹,

Hosseinzadeh²,

Nozari³

et al. 2016

Phys. Rev. D

View full text Add to dashboard Cite

The theories known as doubly special relativity are introduced in order to take into account an observer-independent length scale and the speed of light in the framework of special relativity. These theories can be generally formulated on the de Sitter and also recently proposed anti-de Sitter momentum spaces. In the context of these theories, we study the statistical mechanics and to do this, we consider the natural measure on the corresponding extended phase space. The invariant measure on the space of distinct microstates is obtained by restriction of the natural measure of the extended phase space to the physical phase space through the disintegration theorem. Having the invariant measure, one can study the statistical mechanics in an arbitrary ensemble for any doubly special relativity theory. We use the constructed setup to study the statistical properties of four doubly special relativity models. Applying the results to the case of early universe thermodynamics, we show that one of these models that is defined by the cosmological coordinatization of anti-de Sitter momentum space, implies a finite total number of microstates. Therefore, without attribution to any ensemble density and quite generally, we obtain entropy and internal energy bounds for the early radiation dominated universe. We find that while these results cannot be supported by the standard Friedmann equations, they indeed are in complete agreement with the nonsingular effective Friedmann equations that arise in the context of loop quantum cosmology.

show abstract

“…Unfortunately the mathematical rigorous introduction of this length is possible in a quantum gravity theory only. Nevertheless using the theory of deformations of a Lie algebra connected with given physical theory one can show [6]- [9] that a fundamental length is an essential ingredient of an extension of a physical theory.…”

Section: Fundamental Lengthmentioning

confidence: 99%

“…Moving by such a way one can show that: (a) the stabilization from the classical mechanics to the relativistic one is possible by introducing a new fundamental constant -the speed of light c; (b) the stabilization from the classical mechanics to the quantum one is possible with the introduction of a new fundamental constant -the Planck constant ; (c) stabilization from classical relativistic mechanics to an algebra with a fundamental length is possible [6]- [8]. In Ref's [10], [11] (resting on the principles of the deformation idea) it is shown that the Lie algebra for the interface of the gravitational and quantum realms is the stabilized form of the Poincaré-Heisenberg algebra which carries three additional parameters and one from them is the fundamental length.…”

Section: Fundamental Lengthmentioning

confidence: 99%

Soft Singularity and the Fundamental Length

Dzhunushaliev

Myrzakulov²

2006

Found Phys Lett

View full text Add to dashboard Cite

It is shown that some regular solutions in 5D Kaluza-Klein gravity may have interesting properties if one from the parameters is in the Planck region. In this case the Kretschman metric invariant runs up to a maximal reachable value in nature, i.e. practically the metric becomes singular. This observation allows us to suppose that in this situation the problems with such soft singularity will be much easier resolved in the future quantum gravity then by the situation with the ordinary hard singularity (Reissner-Nordström singularity, for example). It is supposed that the analogous consideration can be applied for the avoiding the hard singularities connected with the gauge charges.

show abstract

Deformations, stable theories and fundamental constants

Cited by 96 publications

References 38 publications

A Quantum Space behind Simple Quantum Mechanics

A Quantum Space behind Simple Quantum Mechanics

Early universe thermostatistics in curved momentum spaces

Soft Singularity and the Fundamental Length

Contact Info

Product

Resources

About