2021/12/21 by Christoph Chiaffrino, Olaf Hohm, Chiaffrino, Christoph +3
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Force Microscopy Techniques and Applications #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Mechanical and Optical Resonators #Nonlinear Dynamics and Pattern Formation #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2112.11495
openalex publication_date 2021/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide a formulation of quantum mechanics based on the cohomology of the Batalin-Vilkovisky (BV) algebra. Focusing on quantum-mechanical systems without gauge symmetry we introduce a homotopy retract from the chain complex of the harmonic oscillator to finite-dimensional phase space. This induces a homotopy transfer from the BV algebra to the algebra of functions on phase space. Quantum expectation values for a given operator or functional are computed by the function whose pullback gives a functional in the same cohomology class. This statement is proved in perturbation theory by relating the perturbation lemma to Wick's theorem. We test this method by computing two-point functions for the harmonic oscillator for position eigenstates and coherent states. Finally, we derive the Unruh effect, illustrating that these methods are applicable to quantum field theory.