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College Physics

The basic theoretical formalism of anyon in quantum mechanics

Ren-Gui Zhu

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

The concept of anyons is introduced through discussing the origin of the exchange symmetry of wave functions and the commutation relations of field operators.Moreover,a rigorous proof of the commutation relations of one-dimensional anyonic field operators is presented in detail.The content of this paper is a helpful supplement to the common teaching course of quantum mechanics.

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The concept of anyons is introduced through discussing the origin of the exchange symmetry of wave functions and the commutation relations of field operators.Moreover,a rigorous proof of the commutation relations of one-dimensional anyonic field operators is presented in detail.The content of this paper is a helpful supplement to the common teaching course of quantum mechanics.
Abstract Quantum mechanics is one of the basic theories of modern physics. Here, the famous Schrödinger equation and the differential operators representing mechanical quantities in quantum mechanics are derived, just based on the principle that the translation invariance (symmetry) of a system in Hamiltonian mechanics should be preserved in quantum mechanics. Moreover, according to the form of the differential operators, the commutation relation in quantum mechanics between the generalized coordinate and the generalized momentum can be directly obtained. We believe that the results in this paper are very useful for understanding the physical origin of quantum mechanics.
This chapter, based on the background information of the previous chapter, will review the formalism of quantum mechanics – its fundamental mathematical structure (the basic contents of Hilbert space representation and operator algebra representation) and physical assumptions (kinematics, dynamics, and measurement theory). These are the premise and foundation for discussing the quantum histories interpretation. Then, in combination with the viewpoints of some literature in recent years, we will explore what is the interpretation of quantum mechanics, analyze the relationship between the theory of quantum mechanics and its interpretation, and declare the author’s basic stance on these two issues. These two are the primary issues that all interpretive work in the philosophy of physics will face (not limited to the interpretation of quantum mechanics), and the necessary clarification here is also conducive to the subsequent discussion. Three common terms – theory, formalism, and interpretation – are explicated and differentiated by offering the necessary definitions of their meanings, based on the works of Acuña and Ruetsche. The clarification will help to make the subsequent related discussions more precise.