The Radiation Field, at the Origin of the Quantum Canonical Operators

IF 1.2 3区 物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY
A. M. Cetto, L. de la Peña
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Abstract

We show that the electromagnetic radiation field, conventionally introduced as a perturbation in quantum mechanics, is actually at the basis of the operator formalism. We first analyze the linear resonant response of the (continuous) variables x(t), p(t) of a harmonic oscillator to the full radiation field, i.e. the zero-point field plus an applied field playing the role of the driving force, and then extend the analysis to the response of a charged particle bound by a non-linear force, typically an atomic electron. This leads to the establishment of a one-to-one correspondence between the response functions and the respective quantum operators, and to the identification of the quantum commutator with the Poisson bracket of the response functions with respect to the normalized variables of the driving field. To complete the quantum description, a similar procedure is used to obtain the field operators as the response functions to the same normalized variables. The results allow us to draw important conclusions about the physical content of the quantum formalism, in particular about the meaning of the quantum expectation values and the coarse-grained nature of the quantum-mechanical description.

辐射场,量子经典算子的起源
我们的研究表明,电磁辐射场在量子力学中通常是作为扰动引入的,而实际上它是算子形式主义的基础。我们首先分析了谐振子的(连续)变量 x(t)、p(t) 对全辐射场(即零点场加上起驱动力作用的外加场)的线性共振响应,然后将分析扩展到受非线性力约束的带电粒子(通常是原子电子)的响应。这就在响应函数和各自的量子算子之间建立了一一对应的关系,并将量子换向器与响应函数的泊松括号相对于驱动场的归一化变量进行了识别。为了完成量子描述,我们使用了类似的程序来获得场算子,作为对相同归一化变量的响应函数。通过这些结果,我们可以得出有关量子形式主义物理内容的重要结论,特别是量子期望值的含义和量子力学描述的粗粒度性质。
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来源期刊
Foundations of Physics
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.
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