$SU(\infty)$ Quantum Gravity and Cosmology

• URL: http://arxiv.org/abs/2409.08932v1
• Date: Fri, 13 Sep 2024 15:50:32 GMT
• Title: $SU(\infty)$ Quantum Gravity and Cosmology
• Authors: Houri Ziaeepour,
• Abstract summary: We highlight the structure and main properties of an abstract approach to quantum cosmology and gravity dubbed $SU(infty)$-QGR. We identify the common $SU(infty)$ symmetry and its interaction with gravity. We prove that emergent spacetime has a Lorentzian geometry.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this letter we highlight the structure and main properties of an abstract approach to quantum cosmology and gravity dubbed $SU(\infty)$-QGR. Beginning from the concept of the Universe as an isolated quantum system, the main axiom of the model is the existence of infinite number of mutually commuting observables. Consequently, the Hilbert space of the Universe represents $SU(\infty)$ symmetry. This Universe as a whole is static and topological. Nonetheless, quantum fluctuations induce local clustering in its quantum state and divide it to approximately isolated subsystems representing $G \times SU(\infty)$ symmetry, where $G$ is a generic finite rank internal symmetry for each subsystem that is entangled to the rest of the Universe by the global $SU(\infty)$ symmetry. In addition to parameters characterizing representation of $G$ by subsystems, their states depend on 4 continuous parameters: two of them characterize the representation of $SU(\infty)$, a dimensionful parameter arises from the possibility of comparing representations of $SU(\infty)$ by different subsystems, and the forth parameter is a measurable used as time registered by an arbitrary subsystem chosen as a quantum clock. They introduce a relative dynamics for subsystem formulated by a symmetry invariant effective Lagrangian defined on the (3+1)D parameter space. At lowest quantum order it is a Yang-Mills field theory for both $SU(\infty)$ and internal symmetries. We identify the common $SU(\infty)$ symmetry and its interaction with gravity. Thus, $SU(\infty)$-QGR predicts a spin-1 mediator for quantum gravity. Apparently this is in contradiction with classical gravity. Nonetheless, we show that an observer unable to detect the quantumness of gravity perceives its effect as the curvature of the space of average values of aforementioned parameters. We prove that emergent spacetime has a Lorentzian geometry.

Related papers

• 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 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)
• Quantum Current and Holographic Categorical Symmetry [62.07387569558919]
  A quantum current is defined as symmetric operators that can transport symmetry charges over an arbitrary long distance. The condition for quantum currents to be superconducting is also specified, which corresponds to condensation of anyons in one higher dimension.
  arXiv  Detail & Related papers  (2023-05-22T11:00:25Z)
• $\mathbf {SU(\infty)}$-QGR Quantumania: Everything, Everywhere, All At Once [0.0]
  $SU(infty)$-QGR is a quantum approach to Universe and gravity. Its main assumption is infinite mutually commuting observables in the Universe. When quantumness of gravity is undetectable, it is perceived as curvature of an effective spacetime.
  arXiv  Detail & Related papers  (2023-04-05T21:54:55Z)
• \boldmath $SU(\infty)$ Quantum Gravity: Emergence of Gravity in an Infinitely Divisible Quantum Universe [0.0]
  $SU(infty)$-QGR is a foundationally quantum approach to gravity. It assumes that the Hilbert space of the Universe as a whole represents the symmetry group $SU(infty)$. We show that the global $SU(infty)$ symmetry manifests itself through the entanglement of subsystems with the rest of the Universe.
  arXiv  Detail & Related papers  (2023-01-07T09:19:15Z)
• Uncertainties in Quantum Measurements: A Quantum Tomography [52.77024349608834]
  The observables associated with a quantum system $S$ form a non-commutative algebra $mathcal A_S$. It is assumed that a density matrix $rho$ can be determined from the expectation values of observables. Abelian algebras do not have inner automorphisms, so the measurement apparatus can determine mean values of observables.
  arXiv  Detail & Related papers  (2021-12-14T16:29:53Z)
• Comparing Quantum Gravity Models: String Theory, Loop Quantum Gravity, and Entanglement gravity versus $SU(\infty)$-QGR [0.0]
  We present a new model for Quantum GRavity(QGR) and cosmology, dubbed $SU(infty)$-QGR. We compare it with several QGR proposals, including: string and M-theories, loop quantum gravity and related models, and QGR proposals inspired by holographic principle and quantum entanglement. The purpose is to find their common and analogous features, even if they apparently seem to have different roles and interpretations.
  arXiv  Detail & Related papers  (2021-09-13T07:49:42Z)
• Symmetry from Entanglement Suppression [0.0]
  We show that a minimally entangling $S$-matrix would give rise to global symmetries. For $N_q$ species of qubit, the Identity gate is associated with an $[SU(2)]N_q$ symmetry.
  arXiv  Detail & Related papers  (2021-04-22T02:50:10Z)
• $\PT$ Symmetry and Renormalisation in Quantum Field Theory [62.997667081978825]
  Quantum systems governed by non-Hermitian Hamiltonians with $PT$ symmetry are special in having real energy eigenvalues bounded below and unitary time evolution. We show how $PT$ symmetry may allow interpretations that evade ghosts and instabilities present in an interpretation of the theory within a Hermitian framework.
  arXiv  Detail & Related papers  (2021-03-27T09:46:36Z)
• Fermion and meson mass generation in non-Hermitian Nambu--Jona-Lasinio models [77.34726150561087]
  We investigate the effects of non-Hermiticity on interacting fermionic systems. We do this by including non-Hermitian bilinear terms into the 3+1 dimensional Nambu--Jona-Lasinio (NJL) model.
  arXiv  Detail & Related papers  (2021-02-02T13:56:11Z)
• The Geometry of Time in Topological Quantum Gravity of the Ricci Flow [62.997667081978825]
  We continue the study of nonrelativistic quantum gravity associated with a family of Ricci flow equations. This topological gravity is of the cohomological type, and it exhibits an $cal N=2$ extended BRST symmetry. We demonstrate a standard one-step BRST gauge-fixing of a theory whose fields are $g_ij$, $ni$ and $n$, and whose gauge symmetries consist of (i) the topological deformations of $g_ij$, and (ii) the ultralocal nonrelativistic limit of space
  arXiv  Detail & Related papers  (2020-11-12T06:57:10Z)

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.