Quantum Darboux theorem

被引:1
作者
Corradini, O. [1 ,2 ]
Latini, E. [2 ,3 ]
Waldron, Andrew [4 ]
机构
[1] Univ Modena & Reggio Emilia, Dipartimento Sci Fis Informat & Matemat, Via Campi 213-A, I-41125 Modena, Italy
[2] Ist Nazl Fis Nucl, Sez Bologna, Via Irnerio 46, I-40126 Bologna, Italy
[3] Univ Bologna, Dipartimento Matemat, Piazza Porta S Donato 5, I-40126 Bologna, Italy
[4] Univ Calif Davis, Ctr Quantum Math & Phys QMAP, Dept Math, Davis, CA 95616 USA
关键词
DEFORMATION QUANTIZATION; RELATIVISTIC SYSTEMS; DYNAMICAL-SYSTEMS; CONTACT GEOMETRY; 1ST-CLASS; BOSON;
D O I
10.1103/PhysRevD.103.105021
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
The problem of computing quantum mechanical propagators can be recast as a computation of a Wilson line operator for parallel transport by a flat connection acting on a vector bundle of wave functions. In this picture, the base manifold is an odd-dimensional symplectic geometry, or quite generically a contact manifold that can be viewed as a "phase-spacetime," while the fibers are Hilbert spaces. This approach enjoys a "quantum Darboux theorem" that parallels the Darboux theorem on contact manifolds which turns local classical dynamics into straight lines. We detail how the quantum Darboux theorem works for anharmonic quantum potentials. In particular, we develop a novel diagrammatic approach for computing the asymptotics of a gauge transformation that locally makes complicated quantum dynamics trivial.
引用
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页数:19
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