Canonical Analysis of Brans-Dicke Theory Addresses Hamiltonian Inequivalence between Jordan and Einstein Frames

Abstract

Jordan and Einstein frame are studied under the light of Hamiltonian formalism. Dirac's constraint theory for Hamiltonian systems is applied to Brans-Dicke theory in the Jordan Frame. In both Jordan and Einstein frame, Brans-Dicke theory has four secondary first class constraints and their constraint algebra is closed. We show, contrary to what is generally believed, the Weyl (conformal) transformation, between the two frames, is not a canonical transformation, in the sense of Hamiltonian formalism. This addresses quantum mechanical inequivalence as well. A canonical transformation is shown.

arXiv commentRevised version PRD accepted. 8 pages, Article, latex. Detailed calculations added. Typo corrected

References in corpus (19)

• The (pseudo)issue of the conformal frame revisited
• Question of quantum equivalence between Jordan frame and Einstein frame
• Boundary Terms, Variational Principles and Higher Derivative Modified Gravity
• Conformal transformations in classical gravitational theories and in cosmology
• Hamiltonian Formulation of Palatini f(R) theories a la Brans-Dicke
• A question mark on the equivalence of Einstein and Jordan frames
• Gravity with more or less gauging
• Various Hamiltonian formulations of f(R) gravity and their canonical relationships
• Jordan-Brans-Dicke Quantum Wormholes and Coleman's Mechanism
• Fresh look at the scalar-tensor theory of gravity in Jordan and Einstein frames from undiscussed standpoints
• Bouncing and emergent cosmologies from ADM RG flows
• Frame (In)equivalence in Quantum Field Theory and Cosmology
• Quantum Equivalence of $f(R)$ Gravity and Scalar-tensor Theories in the Jordan and Einstein Frames
• Conformal and Weyl-Einstein gravity: Classical geometrodynamics
• One-loop divergences for $f(R)$ gravity
• Brans-Dicke theory in the local potential approximation
• Affine quantisation of the Brans-Dicke theory: Smooth bouncing and the equivalence between the Einstein and Jordan frames
• On the Canonical Formalism for a Higher-Curvature Gravity
• Einstein or Jordan: seeking answers from the reheating constraints

Cited by in corpus (8)

• Stability criterion for white dwarfs in Palatini $f(R)$ gravity
• Anisotropic and frame dependent chaos of suspended strings from a dynamical holographic QCD model with magnetic field
• 3+1 decomposition in modified gravities within the Palatini formalism and some applications
• Gauge symmetry of unimodular gravity in Hamiltonian formalism
• Jordan and Einstein Frames from the perspective of $\omega =-3/2$ Hamiltonian Brans-Dicke theory
• A pilot study on canonical gravity with mass dimension one fermions
• Dynamical Casimir effect with screened scalar fields
• Casimir Wormholes in Brans-Dicke Theory