Symplectic Quantization III: Non-relativistic Limit

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY

Foundations of Physics Pub Date : 2024-07-09 DOI:10.1007/s10701-024-00783-5

Giacomo Gradenigo, Roberto Livi, Luca Salasnich

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引用次数: 0

Abstract

First of all we shortly illustrate how the symplectic quantization scheme (Gradenigo and Livi, Found Phys 51(3):66, 2021) can be applied to a relativistic field theory with self-interaction. Taking inspiration from the stochastic quantization method by Parisi and Wu, this procedure is based on considering explicitly the role of an intrinsic time variable, associated with quantum fluctuations. The major part of this paper is devoted to showing how the symplectic quantization scheme can be extended to the non-relativistic limit for a Schrödinger-like field. Then we also discuss how one can obtain from this non-relativistic theory a linear Schrödinger equation for the single-particle wavefunction. This further passage is based on a suitable coarse-graining procedure, when self-interaction terms can be neglected, with respect to interactions with any external field. In the Appendix we complete our survey on symplectic quantization by discussing how this scheme applies to a non-relativistic particle under the action of a generic external potential.

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交映量子化 III：非相对论极限

首先，我们简要说明交映量子化方案（Gradenigo 和 Livi，Found Phys 51(3):66, 2021）如何应用于具有自相互作用的相对论场论。从帕里西和吴的随机量子化方法中汲取灵感，这一过程基于明确考虑与量子波动相关的内在时间变量的作用。本文的主要内容是展示如何将交映量子化方案扩展到类似薛定谔场的非相对论极限。然后，我们还讨论了如何从这一非相对论中获得单粒子波函数的线性薛定谔方程。在与任何外部场的相互作用方面，当自相互作用项可以被忽略时，这一进一步的过程是基于适当的粗粒化程序。在附录中，我们将讨论这一方案如何应用于一般外部势作用下的非相对论粒子，从而完成我们对交映量子化的研究。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Foundations of Physics 物理-物理：综合

CiteScore

2.70

自引率

6.70%

发文量

104

审稿时长

6-12 weeks

期刊介绍： The conceptual foundations of physics have been under constant revision from the outset, and remain so today. Discussion of foundational issues has always been a major source of progress in science, on a par with empirical knowledge and mathematics. Examples include the debates on the nature of space and time involving Newton and later Einstein; on the nature of heat and of energy; on irreversibility and probability due to Boltzmann; on the nature of matter and observation measurement during the early days of quantum theory; on the meaning of renormalisation, and many others. Today, insightful reflection on the conceptual structure utilised in our efforts to understand the physical world is of particular value, given the serious unsolved problems that are likely to demand, once again, modifications of the grammar of our scientific description of the physical world. The quantum properties of gravity, the nature of measurement in quantum mechanics, the primary source of irreversibility, the role of information in physics – all these are examples of questions about which science is still confused and whose solution may well demand more than skilled mathematics and new experiments. Foundations of Physics is a privileged forum for discussing such foundational issues, open to physicists, cosmologists, philosophers and mathematicians. It is devoted to the conceptual bases of the fundamental theories of physics and cosmology, to their logical, methodological, and philosophical premises. The journal welcomes papers on issues such as the foundations of special and general relativity, quantum theory, classical and quantum field theory, quantum gravity, unified theories, thermodynamics, statistical mechanics, cosmology, and similar.