Publication details
Relational Bundle Geometric Formulation of Non-Relativistic Quantum Mechanics
| Authors | |
|---|---|
| Year of publication | 2025 |
| Type | Article in Periodical |
| Magazine / Source | FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS |
| MU Faculty or unit | |
| Citation | |
| web | https://onlinelibrary.wiley.com/doi/10.1002/prop.70040 |
| Doi | https://doi.org/10.1002/prop.70040 |
| Keywords | Bundle geometry; Cocyclic connection; Physical frame covariance; Quantum mechanics; Relationality |
| Description | A bundle geometric formulation of non-relativistic many-particles Quantum Mechanics is presented. A wave function is seen to be a C-valued cocyclic tensorial 0-form on configuration space-time seen as a principal bundle, while the Schrödinger equation flows from its covariant derivative, with the action functional supplying a (flat) cocyclic connection 1-form on the configuration bundle. In line with the historical motivations of Dirac and Feynman, ours is thus a Lagrangian geometric formulation of QM, in which the Dirac–Feynman path integral arises in a geometrically natural way. Applying the dressing field method, we obtain a relational reformulation of this geometric non-relativistic QM: a relational wave function is realised as a basic cocyclic 0-form on the configuration bundle. In this relational QM, any particle position can be used as a dressing field, i.e., as a “physical reference frame.” The dressing field method naturally accounts for the freedom in choosing the dressing field, which is readily understood as a covariance of the relational formulation under changes of physical reference frame. |
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