Hamiltonian Constraint Formulation of Classical Field Theories

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F17%3A00318538" target="_blank" >RIV/68407700:21340/17:00318538 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00006-016-0663-0" target="_blank" >http://dx.doi.org/10.1007/s00006-016-0663-0</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00006-016-0663-0" target="_blank" >10.1007/s00006-016-0663-0</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Hamiltonian Constraint Formulation of Classical Field Theories

Popis výsledku v původním jazyce

Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined via the (Hamiltonian) constraint between multivector-valued generalized momenta, and points in the configuration space. Starting from a variational principle, we derive the local equations of motion, that is, differential equations that determine classical surfaces and momenta. A local Hamilton-Jacobi equation applicable in the field theory then follows readily. In addition, we discuss the relation between symmetries and conservation laws, and derive a Hamiltonian version of the Noether theorem, where the Noether currents are identified as the classical momentum contracted with the symmetry-generating vector fields. The general formalism is illustrated by two examples: the scalar field theory, and the string theory. Throughout the article, we employ the mathematical formalism of geometric algebra and calculus, which allows us to perform completely coordinate-free manipulations.

Název v anglickém jazyce

Hamiltonian Constraint Formulation of Classical Field Theories

Popis výsledku anglicky

Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined via the (Hamiltonian) constraint between multivector-valued generalized momenta, and points in the configuration space. Starting from a variational principle, we derive the local equations of motion, that is, differential equations that determine classical surfaces and momenta. A local Hamilton-Jacobi equation applicable in the field theory then follows readily. In addition, we discuss the relation between symmetries and conservation laws, and derive a Hamiltonian version of the Noether theorem, where the Noether currents are identified as the classical momentum contracted with the symmetry-generating vector fields. The general formalism is illustrated by two examples: the scalar field theory, and the string theory. Throughout the article, we employ the mathematical formalism of geometric algebra and calculus, which allows us to perform completely coordinate-free manipulations.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA14-07983S" target="_blank" >GA14-07983S: Struktura vakua v kvantově polních teoriích</a><br>

Návaznosti

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

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

ADVANCES IN APPLIED CLIFFORD ALGEBRAS

ISSN

0188-7009

e-ISSN

1661-4909

Svazek periodika

27

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

23

Strana od-do

829-851

Kód UT WoS článku

000396031500053

EID výsledku v databázi Scopus

2-s2.0-84964404026