Enhanced Quantization: A Primer

Abstract

Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck's constant \hbar>0, meaning that the classical and quantum world views must actually {\it coexist}. Traditionally, canonical quantization procedures postulate a direct linking of various c-number and q-number quantities that lie in disjoint realms, along with the quite distinct interpretations given to each realm. In this paper we propose a different association of classical and quantum quantities that renders classical theory a natural subset of quantum theory letting them coexist as required. This proposal also shines light on alternative linking assignments of classical and quantum quantities that offer different perspectives on the very meaning of quantization. In this paper we focus on elaborating the general principles, while elsewhere we have published several examples of what this alternative viewpoint can achieve; these examples include removal of singularities in classical solutions to certain models, and an alternative quantization of several field theory models that are trivial when quantized by traditional methods but become well defined and nontrivial when viewed from the new viewpoint.

11 pages, final version accepted for publication

Cited by in corpus (27)

• Smooth Quantum Dynamics of Mixmaster Universe
• Singularity avoidance in a quantum model of the Mixmaster universe
• The Minimum-Uncertainty Squeezed States for for Atoms and Photons in a Cavity
• Covariant Affine Integral Quantization(s)
• Affine Quantization on the Half Line
• Geometric momentum for a particle constrained on a curved hypersurface
• Vibronic framework for quantum mixmaster universe
• Quantum Mixmaster as a model of the Primordial Universe
• Clocks and dynamics in quantum models of gravity
• Canonical quantization on the half-line and in an interval based upon a new concept for the momentum in a space with boundaries
• Primordial gravitational waves in a quantum model of big bounce
• Quantization: History and Problems
• Smooth Bounce in Affine Quantization of Bianchi I
• Quantum and semi-classical aspects of confined systems with variable mass
• Mathematics of the classical and the quantum
• Enhanced quantization on the circle
• Quantum phase space trajectories with application to quantum cosmology
• Affine quantization of Black Holes: thermodynamics, singularity removal and displaced horizons
• Solving oscillations problems through affine quantization
• Mixed Models: Combining Incompatible Scalar Models in Any Spacetime Dimension
• Matrix Models and Large-N Behavior
• Time problem in primordial perturbations
• Solving the Insoluble: A New Rule for Quantization
• A New Rule for Quantization that Resolves All Problems
• Examples of Enhanced Quantization: Bosons, Fermions, and Anyons
• Affine quantization of the dynamical Reissner--Nordström region
• Affine Coherent States in Quantum Cosmology