Functional methods underlying classical mechanics, relativity and quantum theory

8th Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and Fields

Kryukov, A.^1

Department of Mathematics, University of Wisconsin Colleges, 780 Regent Street, Madison, WI 53708, United States^1

关键词: Arbitrary quantum state;    Classical mechanics;    Classical particle;    Dirac delta function;    Functional methods;    Macroscopic particles;    Mathematical frameworks;    Normal probability distributions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/437/1/012020/pdf
DOI  :  10.1088/1742-6596/437/1/012020

来源: IOP

【 摘 要 】

The paper investigates the physical content of a recently proposed mathematical framework that unifies the standard formalisms of classical mechanics, relativity and quantum theory. In the framework states of a classical particle are identified with Dirac delta functions. The classical space is "made" of these functions and becomes a submanifold in a Hilbert space of states of the particle. The resulting embedding of the classical space into the space of states is highly non-trivial and accounts for numerous deep relations between classical and quantum physics and relativity. One of the most striking results is the proof that the normal probability distribution of position of a macroscopic particle (equivalently, position of the corresponding delta state within the classical space submanifold) yields the Born rule for transitions between arbitrary quantum states.