Relaxation of first-class constraints and the quantization of gauge theories: from "matter without matter" to the reappearance of time in quantum gravity
arXiv:2402.12437 · doi:10.1016/j.aop.2024.169783
Abstract
We make a conceptual overview of a particular approach to the initial-value problem in canonical gauge theories. We stress how the first-class phase-space constraints may be relaxed if we interpret them as fixing the values of new degrees of freedom. This idea goes back to Fock and Stueckelberg, leading to restrictions of the gauge symmetry of a theory, and it corresponds, in certain cases, to promoting constants of Nature to physical fields. Recently, different versions of this formulation have gained considerable attention in the literature, with several independent iterations, particularly in classical and quantum descriptions of gravity, cosmology, and electromagnetism. In particular, in the case of canonical quantum gravity, the Fock--Stueckelberg approach is relevant to the so-called problem of time. Our overview recalls and generalizes the work of Fock and Stueckelberg and its physical interpretation with the aim of conceptually unifying the different iterations of the idea that appear in the literature and of motivating further research.
arXiv commentv2: conceptual clarifications and brief appendix added; improvements to the text; results unchanged; references updated
References in corpus (38)
- The Dynamics of General Relativity
- The Stueckelberg Field
- New varying speed of light theories
- Dark matter as integration constant in Horava-Lifshitz gravity
- Gauge transformations in the Lagrangian and Hamiltonian formalisms of generally covariant theories
- A Uniqueness Theorem for Constraint Quantization
- On the infrared limit of Horava's gravity with the global Hamiltonian constraint
- Gauge Invariance for Generally Covariant Systems
- Gravity with more or less gauging
- Darkness without dark matter and energy -- generalized unimodular gravity
- Cosmological time and the constants of nature
- Troubles with quantum anistropic cosmological models: Loss of unitarity
- Varying Alpha and the Electroweak Model
- Superpositions of the cosmological constant allow for singularity resolution and unitary evolution in quantum cosmology
- A Zero-Parameter Extension of General Relativity with Varying Cosmological Constant
- Schrodinger Evolution for the Universe: Reparametrization
- Léon Rosenfeld's general theory of constrained Hamiltonian dynamics
- Quantum Cosmology and the Evolution of Inflationary Spectra
- Varying electric charge in multiscale spacetimes
- Jacobi's Principle and the Disappearance of Time
- Square Root Actions, Metric Signature, and the Path-Integral of Quantum Gravity
- BRST Quantization of General Relativity in Unimodular Gauge and Unimodular Gravity
- Quantum cosmology with scalar fields: self-adjointness and cosmological scenarios
- A note on unfree gauge symmetry
- Unfree gauge symmetry in the BV formalism
- Fundamental Constants and the Problem of Time
- Hamiltonian BFV-BRST theory of closed quantum cosmological models
- One real function instead of the Dirac spinor function
- Rosenfeld, Bergmann, Dirac and the Invention of Constrained Hamiltonian Dynamics
- The mass shell of the universe
- Unfree gauge symmetry in the Hamiltonian formalism
- No Drama Quantum Electrodynamics?
- No Drama Quantum Theory? A Review
- Restricted Gauge Theory Formalism and Unimodular Gravity
- General method for including Stueckelberg fields
- Generalized unimodular gravity in Friedmann and Kantowski-Sachs universes
- Vortices, topology and time
- Radiation-dominated bouncing model with slow contraction and inflation