Localizable Particles in the Classical Limit of Quantum Field Theory

Feintzeig, Benjamin H.; Librande, J.T.; Soiffer, Rory

doi:10.1007/s10701-021-00458-5

Cited by 2 publications

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The Classical–Quantum Correspondence

Feintzeig

2022

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This Element provides an entry point for philosophical engagement with quantization and the classical limit. It introduces the mathematical tools of C*-algebras as they are used to compare classical and quantum physics. It then employs those tools to investigate philosophical issues surrounding theory change in physics. It discusses examples in which quantization bears on the topics of reduction, structural continuity, analogical reasoning, and theory construction. In doing so, it demonstrates that the precise mathematical tools of algebraic quantum theory can aid philosophers of science and philosophers of physics.

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The Classical–Quantum Correspondence

Feintzeig

2022

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From quantum field theory to quantum mechanics

Sá

Gomes

2021

Eur. Phys. J. C

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The purpose of this article is to construct an explicit relation between the field operators in Quantum Field Theory and the relevant operators in Quantum Mechanics for a system of N identical particles, which are the symmetrised functions of the canonical operators of position and momentum, thus providing a clear relation between Quantum Field Theory and Quantum Mechanics. This is achieved in the context of the non-interacting Klein–Gordon field. Though this procedure may not be extendible to interacting field theories, since it relies crucially on particle number conservation, we find it nevertheless important that such an explicit relation can be found at least for free fields. It also comes out that whatever statistics the field operators obey (either commuting or anticommuting), the position and momentum operators obey commutation relations. The construction of position operators raises the issue of localizability of particles in Relativistic Quantum Mechanics, as the position operator for a single particle turns out to be the Newton–Wigner position operator. We make some clarifications on the interpretation of Newton–Wigner localized states and we consider the transformation properties of position operators under Lorentz transformations, showing that they do not transform as tensors, rather in a manner that preserves the canonical commutation relations. From a complex Klein–Gordon field, position and momentum operators can be constructed for both particles and antiparticles.

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Localizable Particles in the Classical Limit of Quantum Field Theory

Cited by 2 publications

References 47 publications

The Classical–Quantum Correspondence

The Classical–Quantum Correspondence

From quantum field theory to quantum mechanics

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