Hamiltonian Constraint Formulation of Classical Field Theories
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Hamiltonian Constraint Formulation of Classical Field Theories
Original language description
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.
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
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA14-07983S" target="_blank" >GA14-07983S: Vacuum structure in Quantum Field Theories</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
ADVANCES IN APPLIED CLIFFORD ALGEBRAS
ISSN
0188-7009
e-ISSN
1661-4909
Volume of the periodical
27
Issue of the periodical within the volume
1
Country of publishing house
CH - SWITZERLAND
Number of pages
23
Pages from-to
829-851
UT code for WoS article
000396031500053
EID of the result in the Scopus database
2-s2.0-84964404026