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Homological quantum mechanics

Christoph Chiaffrino
(
- Humboldt U., Berlin
)
,
Olaf Hohm
(
- Humboldt U., Berlin
)
,
Allison F. Pinto
(
- Humboldt U., Berlin
)

Dec 21, 2021

52 pages

Published in:

JHEP 02 (2024) 137

Published: Feb 20, 2024

e-Print:

2112.11495 [hep-th]

DOI:

10.1007/JHEP02(2024)137

Report number:

HU-EP-21/56-RTG

View in:

ADS Abstract Service

reference search14 citations

Citations per year

Abstract: (Springer)

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.

Note:

52 pages, v2: new subsection 4.5, to appear in JHEP

Field Theories in Lower Dimensions
BRST Quantization
Differential and Algebraic Geometry
Nonperturbative Effects
quantum mechanics
cohomology: Batalin-Vilkovisky
algebra: Batalin-Vilkovisky
homotopy
Unruh effect
homology

References(36)

Figures(0)

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