Probing the small distance structure of canonical quantum gravity using the conformal group

Abstract

In canonical quantum gravity, the formal functional integral includes an integration over the local conformal factor, and we propose to perform the functional integral over this factor before doing any of the other functional integrals. By construction, the resulting effective theory would be expected to be conformally invariant and therefore finite. However, also the conformal integral itself diverges, and the effects of a renormalization counter term are considered. It generates problems such as unitarity violation, due to a Landau-like ghost, and conformal anomalies. Adding (massive or massless) matter fields does not change the picture. Various alternative ideas are offered, including a more daring speculation, which is that no counter term should be allowed for at all. This has far-reaching and important consequences, which we discuss. A surprising picture emerges of quantized elementary particles interacting with a gravitational field, in particular gravitons, which are "partly classical". This approach was inspired by a search towards the reconciliation of Hawking radiation with unitarity and locality, and it offers basic new insights there.

22 pages (incl. title page), 1 figure. Substantial changes in the discussion sections, minor errors corrected, and references added

References in corpus (6)

• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• Exactly solvable PT-symmetric Hamiltonian having no Hermitian counterpart
• Entangled quantum states in a local deterministic theory
• A Kinematical Approach to Conformal Cosmology
• Scalar Gravitation and Extra Dimensions
• Quantum gravity without space-time singularities or horizons

Cited by in corpus (31)

• Entanglement entropy of black holes
• A class of elementary particle models without any adjustable real parameters
• Black Holes in Bi-scalar Extensions of Horndeski Theories
• Conformal Gravity and Transformations in the Symmetric Teleparallel Framework
• Stueckelberg breaking of Weyl conformal geometry with applications to gravity
• Weyl $R^2$ inflation with an emergent Planck scale
• New Modified Mimetic Gravity
• Conformally invariant teleparallel theories of gravity
• Mass Generation, the Cosmological Constant Problem, Conformal Symmetry, and the Higgs Boson
• Asymptotically Safe Grand Unification
• Cosmological Perturbations in Conformal Gravity
• RG flow of Weyl-invariant dilaton gravity
• The Conformal Constraint in Canonical Quantum Gravity
• Asymptotic safety and the cosmological constant
• Unimodular gravity with external sources
• Split Weyl transformations in quantum gravity
• Kahler-Einstein metrics emerging from free fermions and statistical mechanics
• Local Conformal Symmetry: the Missing Symmetry Component for Space and Time
• Teleparallel gauge theory of gravity
• Motion of massive particles around a charged Weyl black hole and the geodetic precession of orbiting gyroscopes
• No Conformal Anomaly in Unimodular Gravity
• Exact solution to perturbative conformal cosmology in the recombination era
• Continuity of the torsionless limit as a selection rule for gravity theories with torsion
• Charged (A)dS black hole solutions in conformal teleparallel equivalent of general relativity
• Exact solution to perturbative conformal cosmology from recombination until the current era
• Asymptotic symmetry algebra of conformal gravity
• Solution to the ghost problem in higher-derivative gravity
• Some Cosmological Consequences of Weyl Invariance
• Conformal theory of everything
• Classical and holographic aspects of conformal gravity in four dimensions
• Holography of pp-waves in conformal gravity