Enhanced Quantization

Particles, Fields & Gravity

This pioneering book addresses the question: Are the standard procedures of canonical quantization fully satisfactory, or is there more to learn about assigning a proper quantum system to a given classical system? As shown in this book, the answer to this question is: The standard procedures of canonical quantization are not the whole story!

This book offers alternative quantization procedures that complete the story of quantization. The initial chapters are designed to present the new procedures in a clear and simple manner for general readers. As is necessary, systems that exhibit acceptable results with conventional quantization lead to the same results when the new procedures are used for them. However, later chapters examine selected models that lead to unacceptable results when quantized conventionally. Fortunately, these same models lead to acceptable results when the new quantization procedures are used.

Contents:

• Introduction and Overview

• Selected Topics in Classical and Quantum Mechanics:

  • Selected Topics in Classical Mechanics
  • Selected Topics in Quantum Mechanics

• Enhanced Quantization of Simple Systems:

  • Essentials of Enhanced Quantization
  • Enhanced Affine Quantization and the Initial Cosmological Singularity

• Enhanced Quantization of Some Complex Systems:

  • Examples of Enhanced Quantization: Bosons, Fermions, and Anyons
  • Enhanced Quantization of Rotationally Invariant Models

• Enhanced Quantization of Ultralocal Field Theories:

  • Enhanced Quantization of Ultralocal Models

• Enhanced Quantization of Covariant Scalars and Gravity:

  • Enhanced Quantization of Covariant Scalar Field Models
  • Enhanced Quantization of Gravity

Readership: Graduate students and researchers in quantum mechanics.
Key Features:

• Solutions for previously insoluble problems
• Nontrivial behavior for scalar fields
• Novel quantization procedures