Planck length in classical and quantum Hamiltonian formulations of general relativity

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19630%2F23%3AA0000281" target="_blank" >RIV/47813059:19630/23:A0000281 - isvavai.cz</a>

Result on the web

<a href="https://link.springer.com/article/10.1140/epjc/s10052-023-11909-w" target="_blank" >https://link.springer.com/article/10.1140/epjc/s10052-023-11909-w</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1140/epjc/s10052-023-11909-w" target="_blank" >10.1140/epjc/s10052-023-11909-w</a>

Result language

angličtina

Original language name

Planck length in classical and quantum Hamiltonian formulations of general relativity

Original language description

The physical meaning of the Planck length (l (P)) is investigated in the framework of the unconstrained synchronous variational formulation of classical general relativity (GR). This theoretical setting permits the establishment of manifestly-covariant Lagrangian and Hamiltonian theories for the Einstein field equations of the continuum gravitational field. It is shown that such a formulation is distinguished by the existence of a novel variational contribution expressed by an infinite series summation of suitable 4-scalar terms in which the coupling coefficients are even powers of the Planck length. However, the requirement of realization of a classical GR Hamiltonian theory places stringent constraints on the admissible Planck-length power terms to be retained. In fact, excluding the trivial gauge constant, it is proved that only the O (l(P)(0)) contribution of the series is ultimately permitted, P namely the unique one which is independent of l (P). Therefore, the Planck length is effectively not allowed to appear at the classical level for consistency with the Hamiltonian principle. This places important consequences on the mathematical establishment of the corresponding canonical quantum gravity theory, which is then found to be correct through O (l(P)(2)). Additional implications concern the physical significance of related quantum momenta and their meaning in the semi-classical limit, as well as the role of the Planck length in the same quantum-gravity realm.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10303 - Particles and field physics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2023

Confidentiality

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

Name of the periodical

European Physical Journal C

ISSN

1434-6044

e-ISSN

—

Volume of the periodical

83

Issue of the periodical within the volume

8

Country of publishing house

US - UNITED STATES

Number of pages

11

Pages from-to

„729-1“-„729-11“

UT code for WoS article

001049808300002

EID of the result in the Scopus database

2-s2.0-85168372160