Relational Bundle Geometric Formulation of Non-Relativistic Quantum Mechanics
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F25%3A00144617" target="_blank" >RIV/00216224:14310/25:00144617 - isvavai.cz</a>
Result on the web
<a href="https://onlinelibrary.wiley.com/doi/10.1002/prop.70040" target="_blank" >https://onlinelibrary.wiley.com/doi/10.1002/prop.70040</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/prop.70040" target="_blank" >10.1002/prop.70040</a>
Alternative languages
Result language
angličtina
Original language name
Relational Bundle Geometric Formulation of Non-Relativistic Quantum Mechanics
Original language 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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA24-10887S" target="_blank" >GA24-10887S: Cartan supergeometries and Higher Cartan geometries</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS
ISSN
0015-8208
e-ISSN
1521-3978
Volume of the periodical
73
Issue of the periodical within the volume
12
Country of publishing house
DE - GERMANY
Number of pages
24
Pages from-to
1-24
UT code for WoS article
001597792000001
EID of the result in the Scopus database
2-s2.0-105019380008