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arXiv:2111.00211

Classical Limit of Yukawa theory from quantum state perspective

Qi Chen, Kaixun Tu, Qing Wang

Published Oct 30, 2021• 0 citations
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Abstract

We derive the quantum states corresponding to classical scalar fields in the representation expanded by the eigenstates of quantum field operators. This allows us to directly observe the spatial entanglement structure of quantum states and explore the differences and relationships between quantum superposition and classical superposition. We find that if two classical fields are identical in a certain spatial region, then their corresponding quantum states have the same reduced density matrix in that region. This indicates that knowing the classical field in a local region is sufficient to derive the reduced density matrix for that region. According to the correspondence between classical quantities and quantum states, we derive the equation of motion of the classical theory from the evolution of quantum states in Yukawa theory. This leads to the relativistic classical Yukawa theory, and we further obtain the relativistic corrections to the Yukawa potential.

DOI
10.48550/arxiv.2111.00211

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According to Heisenberg correspondence principle,quantum matrix element of a Hermitian operator reduces to the coefficient of Fourier expansion of the corresponding classical quantity in the classical limit.Applying HCP to Dirac equations in relativistic realm,for the relativistic free particle or the charged particle moving in a constant magnetic field,it is shown that quantum operators in Dirac theory reduces to the classical quantities in the classical limit and the classical limit of quantum expectation value is the time average of the classical quantity.
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