Classical dynamics from QFT via Stratonovich-Weyl correspondence

Abstract

A bstract : We develop a formalism for extracting relativistic classical dynamics from the S-matrix, in which massive bodies are described on phase space while massless radiation is kept in the Fock space. Our formalism relies on the Stratonovich-Weyl (SW) correspondence between the operator and phase-space formulations of quantum mechanics, as implemented covariantly by the SW quantizer. For localized incoming states, classical observables are given by SW symbols of the appropriate operators evaluated on incoming asymptotic trajectories. In combination with the exponential form of the S-matrix, the observables are naturally given by nested mixed Dirac/commutator brackets involving Magnus amplitudes. The latter are the matrix elements of the logarithm of the S-matrix, and we provide a straightforward algorithm for computing the combinatorial Murua coefficients that control the placement of retarded propagators inside Magnus-amplitude diagrams. This picture is well-suited for gravitational-wave physics applications.

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BibTeX RIS

BibTeX

@article{ochirov2026classical,
  title = {{Classical dynamics from QFT via Stratonovich-Weyl correspondence}},
  author = {Alexander Ochirov and Canxin Shi},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = oct,
  doi = {10.1007/jhep10(2026)215},
  url = {https://link.springer.com/article/10.1007/JHEP10(2026)215},
  note = {CC BY 4.0},
}

RIS

TY  - JOUR
TI  - Classical dynamics from QFT via Stratonovich-Weyl correspondence
AU  - Alexander Ochirov
AU  - Canxin Shi
PY  - 2026
DA  - 2026/10/21
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep10(2026)215
UR  - https://link.springer.com/article/10.1007/JHEP10(2026)215
AB  - A bstract : We develop a formalism for extracting relativistic classical dynamics from the S-matrix, in which massive bodies are described on phase space while massless radiation is kept in the Fock space. Our formalism relies on the Stratonovich-Weyl (SW) correspondence between the operator and phase-space formulations of quantum mechanics, as implemented covariantly by the SW quantizer. For localized incoming states, classical observables are given by SW symbols of the appropriate operators evaluated on incoming asymptotic trajectories. In combination with the exponential form of the S-matrix, the observables are naturally given by nested mixed Dirac/commutator brackets involving Magnus amplitudes. The latter are the matrix elements of the logarithm of the S-matrix, and we provide a straightforward algorithm for computing the combinatorial Murua coefficients that control the placement of retarded propagators inside Magnus-amplitude diagrams. This picture is well-suited for gravitational-wave physics applications.
SN  - 1029-8479
ER  -

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