Relational Bundle Geometric Formulation of Non-Relativistic Quantum Mechanics

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Relational Bundle Geometric Formulation of Non-Relativistic Quantum Mechanics

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Relational Bundle Geometric Formulation of Non-Relativistic Quantum Mechanics

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA24-10887S" target="_blank" >GA24-10887S: Cartanovy supergeometrie a vyšší Cartanovy geometrie</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS

ISSN

0015-8208

e-ISSN

1521-3978

Svazek periodika

73

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

24

Strana od-do

1-24

Kód UT WoS článku

001597792000001

EID výsledku v databázi Scopus

2-s2.0-105019380008