Quantum state of fields in $SU(\infty )$ Quantum Gravity ($SU(\infty )$-QGR)

Abstract

Our Universe is ruled by quantum mechanics and should be treated as a quantum system. $SU(\infty )$-QGR is a recently proposed quantum model for the Universe, in which gravity is associated to $SU(\infty )$ symmetry of its Hilbert space. Fragmentation of its infinite dimensional state due to random quantum fluctuations divides the Universe to approximately isolated subsystems. In addition to parameters of their {\it internal} finite rank symmetries, states and dynamics of subsystems are characterized by 4 continuous parameters and the perceived classical spacetime is their effective representation, reflecting quantum states of subsystems and their relative evolution. At lowest order the effective Lagrangian of $SU(\infty )$-QGR~has the form of Yang-Mills gauge theories for both $SU(\infty )$ - gravity - and internal symmetries defined on the aforementioned 4D parameter space. In the present work we study more thoroughly some of the fundamental aspects of $SU(\infty )$-QGR. Specifically, we clarify the impact of the degeneracies of $\mathcal{S}\mathcal{U}(\infty )$ algebra on the construction of the model; describe mixed states of subsystems and their purification; calculate measures of their entanglement to the rest of the Universe; and discuss their role in the emergence of local gauge symmetries. We also describe the relationship between what is called {\it internal space} of $SU(\infty )$ Yang-Mills with the 4D parameter space, and analytically demonstrate irrelevance of the geometry of parameter space for physical observables. Along with these topics, we demonstrate the equivalence of two sets of criteria for compositeness of a quantum system, and show uniqueness of the limit of various algebras leading to $\mathcal{S}\mathcal{U}(\infty )$.

34 pages, 1 figure. version accepted by Academia Quantum; It includes a proposal for testing QGR using coherent lensed astronomical masers

References in corpus (48)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Separability Criterion for Density Matrices
• A computable measure of entanglement
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Nonequilibrium dynamics of closed interacting quantum systems
• Quantifying Coherence
• Thermodynamics of Spacetime: The Einstein Equation of State
• Average Entropy of a Subsystem
• The logarithmic negativity: A full entanglement monotone that is not convex
• Building up spacetime with quantum entanglement
• A Spin Entanglement Witness for Quantum Gravity
• Gravity coupled with matter and foundation of non-commutative geometry
• Reference frames, superselection rules, and quantum information
• Testing Einstein's special relativity with Fermi's short hard gamma-ray burst GRB090510
• Gravitational Dynamics From Entanglement "Thermodynamics"
• Quantum tensor product structures are observable-induced
• Quantum metric-induced nonlinear transport in a topological antiferromagnet
• Generalized Geometric Quantum Speed Limits
• The Trinity of Relational Quantum Dynamics
• Observational constraints on phantom-like braneworld cosmologies
• Nonequilibrium inflaton dynamics and reheating: Back reaction of parametric particle creation and curved spacetime effects
• Notes on the type classification of von Neumann algebras
• A gravitationally lensed water maser in the early Universe
• Quantum Relativity of Subsystems
• Observational constraints on braneworld chaotic inflation
• Understanding nature from experimental observations: a theory independent test for gravitational decoherence
• Quantum field thermalization in expanding backgrounds
• The Cosmological Constant Problem, Dark Energy, and the Landscape of String Theory
• Hilbert-space fragmentation, multifractality, and many-body localization
• Testing the quantum nature of gravity without entanglement
• Physical Purification of Quantum States
• The Conditional Probability Interpretation of the Hamiltonian Constraint
• Constraints on quantum gravity and the photon mass from gamma ray bursts
• Open Quantum System Approach to the Gravitational Decoherence of Spin-1/2 Particles
• Anatomy of the fragmented Hilbert space: eigenvalue tunneling, quantum scars and localization in the perturbed random regular graph
• Comparing Quantum Gravity Models: String Theory, Loop Quantum Gravity, and Entanglement gravity versus $SU(\infty )$-QGR
• The classical-quantum hybrid canonical dynamics and its difficulties with special and general relativity
• Shape dependence of entanglement negativity and mutual information in quantum Hall and critical systems
• Why Matrix theory works for oddly shaped membranes
• A Scheme of Cartan Decomposition for su(N)
• Development of cross-correlation spectrometry and the coherent structures of maser sources
• Making a Quantum Universe: Symmetry and Gravity
• $SU(\infty )$ Quantum Gravity and Cosmology
• Decoherence of a composite particle induced by a weak quantized gravitational field
• Color Glass Condensate in Brane Models or Don't Ultra High Energy Cosmic Rays Probe $10^{15}eV$ Scale ?
• Observation of Hilbert-space fragmentation and fractonic excitations in two-dimensional Hubbard systems
• $\mathbf{SU}(\infty )$-QGR Quantumania: Everything, Everywhere, All At Once
• $SU(\infty )$ Quantum Gravity: Emergence of Gravity in an Infinitely Divisible Quantum Universe