Anti-de Sitterian "massive" elementary systems and their Minkowskian and Newton-Hooke contraction limits

• URL: http://arxiv.org/abs/2307.06690v2
• Date: Wed, 16 Oct 2024 10:44:50 GMT
• Title: Anti-de Sitterian "massive" elementary systems and their Minkowskian and Newton-Hooke contraction limits
• Authors: Mohammad Enayati, Jean-Pierre Gazeau, Mariano A. del Olmo, Hamed Pejhan,
• Abstract summary: We elaborate the definition and properties of "massive" elementary systems in the $(1+3)$-dimensional Anti-de Sitter (AdS$_4$) spacetime. We reveal the dual nature of "massive" elementary systems living in AdS$_4$ spacetime, as each being a combination of a Minkowskian-like elementary system. This duality will take its whole importance in the quantum regime in view of its possible role in the explanation of the current existence of dark matter.
• Score: 0.14999444543328289
• License:
• Abstract: We elaborate the definition and properties of "massive" elementary systems in the $(1+3)$-dimensional Anti-de Sitter (AdS$_4$) spacetime, on both classical and quantum levels. We fully exploit the symmetry group {isomorphic to} Sp$(4,R)$, that is, the two-fold covering of SO$_0(2,3)$ (Sp$(4,\mathbb R) \sim$ SO$_0(2,3)\times \mathbb Z_2$), recognized as the relativity/kinematical group of motions in AdS$_4$ spacetime. In particular, we discuss that the group coset Sp$(4,\mathbb R)/\mathrm{S}\big(\mathrm{U}(1)\times \mathrm{SU}(2)\big)$, as one of the Cartan classical domains, can be interpreted as a phase space for the set of free motions of a test massive particle on AdS$_4$ spacetime; technically, in order to facilitate the computations, the whole process is carried out in terms of complex quaternions. The (projective) unitary irreducible representations (UIRs) of the Sp$(4,R)$ group, describing the quantum version of such motions, are found in the discrete series of the Sp$(4,\mathbb R)$ UIRs. We also describe the null-curvature (Poincar\'{e}) and non-relativistic (Newton-Hooke) contraction limits of such systems, on both classical and quantum levels. On this basis, we unveil the dual nature of "massive" elementary systems living in AdS$_4$ spacetime, as each being a combination of a Minkowskian-like elementary system {with positive proper mass}, with an isotropic harmonic oscillator arising from the AdS$_4$ curvature and viewed as a Newton-Hooke elementary system. This matter-vibration duality will take its whole importance in the quantum regime (in the context of the validity of the equipartition theorem) in view of its possible r\^{o}le in the explanation of the current existence of dark matter.

Related papers

• Theory of Complex Particle without Extra Dimensions [0.0]
  Critical dimension of the complex particle in Minkowski spacetime is $D = 4$, while $D = 2, 4$ or $6$ are permitted in Euclid spacetime. The origin of the restriction to the dimension is the existence of tertiary constraint in the canonical theory, quantization.
  arXiv  Detail & Related papers  (2024-07-02T03:25:13Z)
• Klein-Gordon oscillators and Bergman spaces [55.2480439325792]
  We consider classical and quantum dynamics of relativistic oscillator in Minkowski space $mathbbR3,1$. The general solution of this model is given by functions from the weighted Bergman space of square-integrable holomorphic (for particles) and antiholomorphic functions on the K"ahler-Einstein manifold $Z_6$.
  arXiv  Detail & Related papers  (2024-05-23T09:20:56Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• Quantum charges of harmonic oscillators [55.2480439325792]
  We show that the energy eigenfunctions $psi_n$ with $nge 1$ are complex coordinates on orbifolds $mathbbR2/mathbbZ_n$. We also discuss "antioscillators" with opposite quantum charges and the same positive energy.
  arXiv  Detail & Related papers  (2024-04-02T09:16:18Z)
• Quantum state of fields in $SU(\infty)$ Quantum Gravity ($SU(\infty)$-QGR) [0.0]
  $SU(infty)$-QGR is a recently proposed quantum model for the Universe. $SU(infty)$-QGR has the form of Yang-Mills gauge theories for both $SU(infty)$ - gravity - and internal symmetries defined on the aforementioned 4D parameter space.
  arXiv  Detail & Related papers  (2024-02-28T11:06:45Z)
• Minkowski space from quantum mechanics [0.0]
  Penrose's Spin Geometry Theorem is extended further, from $SU(2)$ and $E(3)$ (Euclidean) to $E(1,3)$ (Poincar'e) invariant elementary quantum mechanical systems.
  arXiv  Detail & Related papers  (2023-09-12T11:48:35Z)
• Correspondence between open bosonic systems and stochastic differential equations [77.34726150561087]
  We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment. A particular system with the form of a discrete nonlinear Schr"odinger equation is analyzed in more detail.
  arXiv  Detail & Related papers  (2023-02-03T19:17:37Z)
• Boundary time crystals in collective $d$-level systems [64.76138964691705]
  Boundary time crystals are non-equilibrium phases of matter occurring in quantum systems in contact to an environment. We study BTC's in collective $d$-level systems, focusing in the cases with $d=2$, $3$ and $4$.
  arXiv  Detail & Related papers  (2021-02-05T19:00:45Z)
• Representation of symmetry transformations on the sets of tripotents of spin and Cartan factors [0.0]
  We prove that in order that the description of the spin will be relativistic, it is not enough to preserve the projection lattice equipped with its natural partial order and denoteity. This, in particular, extends a result of Moln'ar to the wider setting of atomic JBW$*$-triples not containing rank-one Cartan factors.
  arXiv  Detail & Related papers  (2021-01-03T17:21:02Z)
• Scattering data and bound states of a squeezed double-layer structure [77.34726150561087]
  A structure composed of two parallel homogeneous layers is studied in the limit as their widths $l_j$ and $l_j$, and the distance between them $r$ shrinks to zero simultaneously. The existence of non-trivial bound states is proven in the squeezing limit, including the particular example of the squeezed potential in the form of the derivative of Dirac's delta function. The scenario how a single bound state survives in the squeezed system from a finite number of bound states in the finite system is described in detail.
  arXiv  Detail & Related papers  (2020-11-23T14:40:27Z)
• Quantum computation and measurements from an exotic space-time R4 [0.0]
  A valid subgroup $H$ of index $d$ in $G$ leads to a'magic' state $left|psirightrangle$ in $d$-dimensional Hilbert space. A new picture relating a topological quantum computing and exotic space-time is also intended to become an approach of 'quantum gravity'
  arXiv  Detail & Related papers  (2020-01-22T15:16:03Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.