Koopman-von Neumann Field Theory

• URL: http://arxiv.org/abs/2507.11541v1
• Date: Tue, 15 Jul 2025 17:59:59 GMT
• Title: Koopman-von Neumann Field Theory
• Authors: James Stokes,
• Abstract summary: Quantum field operators evolve unitarily in the Heisenberg picture so that a quantum Vlasov equation is satisfied as an operator identity.<n>The formalism enables the direct transfer of techniques from quantum information and quantum many-body field theory to classical nonequilibrium statistical mechanics.
• Score: 1.1095601668670758
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The classical many-body problem is reformulated as a bosonic quantum field theory. Quantum field operators evolve unitarily in the Heisenberg picture so that a quantum Vlasov equation is satisfied as an operator identity. The formalism enables the direct transfer of techniques from quantum information and quantum many-body field theory to classical nonequilibrium statistical mechanics. Implications for quantum algorithms are discussed.

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