Chapter 17. Axioms and General Principles of Quantization

R. Shankar

Jessey Wright

Axiomatic quantum field theory is one approach to the project of merging the special theory of relativity with that of ordinary quantum mechanics. The project begins with the postulation of a set of axioms. Axioms should be motivated by reasonable physical principles in a way that illustrates how a given axiom is true. Motivations are often grounded in the principles of the parent theories: ordinary quantum mechanics or the theory of special relativity. Amongst the set of axioms first proposed by Haag and Kastler in 1963 is the axiom of microcausality. Microcausality requires the observables of regions at space-like separation to commute. This thesis seeks to answer the question ‘What principles from the special theory of relativity or ordinary quantum mechanics motivate, or justify, accepting microcausality as an axiom?’ The first chapter will provide the necessary background to investigate this question and the second chapter will undertake that investigation. In conclusion, microcausality cannot be well-motivated by individual principles rooted in the special theory of relativity or ordinary quantum mechanics.

Ahmad Amer

This chapter provides a historical prelude to the development of quantum theory, highlighting the conceptual challenges posed by its foundational axioms. In contrast to the typical approach of starting from axioms and deriving theorems and definitions, the chapter emphasizes that the axioms of quantum mechanics are not intuitively accessible to beginners due to their disconnect from classical reasoning and everyday experience. To bridge this gap, a chronological overview of the experimental discoveries and theoretical advances that led to the formulation of quantum theory is presented. Metadata/Keywords: black body radiation, photoelectric effect, Compton effect, atom, De Broglie waves, Heisenberg uncertainty principle, Bohr's correspondence principle

Elisa Ercolessi

Gerhard Grössing, Johannes Mesa Pascasio, Herbert Schwabl

Changyu Huang, Yong-Chang Huang, Jia-Min Song

This chapter demonstrates the deduction of quantum physics and, in particular, presents its new applications to eigenvalue problems. Specifically, it derives three of the five axiom presumptions of quantum mechanics (QM), for example, deducing the Schrödinger equation in two general ways. It transforms these three axiom presumptions into three theorems of QM, not only resolving the difficulty in understanding them but also yielding new theories and discoveries. For instance, this paper addresses the puzzle of the origin of wave-particle duality, derives operators, eigenvalues, and eigenstates, deduces commutation relations for coordinate and momentum as well as for time and energy, and reveals that QM is essentially a generalized (mechanics) theory of the complex square root of the (real density function of) classical statistical mechanics. The realization that QM is a generalized theory of the complex square root of classical statistical mechanics represents both a groundbreaking discovery and a revolutionary advancement in physics. This insight profoundly influences philosophical perspectives on the development of modern physics, resolves numerous puzzles in QM and quantum information, and provides QM with a scientifically solid foundation. This foundation eliminates the need for basic axiom presumptions and dispels the so-called “strange incomprehensible properties” of QM, as both classical statistical mechanics and its complex square root that have been scientifically validated. Additionally, this chapter uncovers the reason for not taking the time derivative of spatial coordinates in the Schrödinger equation. Consequently, it offers a solution to the puzzle of the origin of first quantization and primarily deduces quantum physics without the strange and incomprehensible properties currently associated with it.