A summary on symmetries and conserved quantities of autonomous Hamiltonian systems

Autor: Narciso Román-Roy
Přispěvatelé: Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions
Jazyk: angličtina
Rok vydání: 2020
Předmět:
High Energy Physics - Theory
Control and Optimization
Field theory (Physics)
Conserved quantities
FOS: Physical sciences
Matemàtiques i estadística::Matemàtica aplicada a les ciències [Àrees temàtiques de la UPC]
01 natural sciences
Noether theorem
Hamiltonian system
symbols.namesake
0103 physical sciences
Nonlinear systems
70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics [Classificació AMS]
70 Mechanics of particles and systems::70S Classical field theories [Classificació AMS]
37J15
37K05
53D05
70H05
70S05
70S10
0101 mathematics
Hamiltonian systems
Camps
Teoria dels (Física)
Mathematics::Symplectic Geometry
70 Mechanics of particles and systems::70K Nonlinear dynamics [Classificació AMS]
Mathematical Physics
Mathematical physics
Symplectic manifolds
Physics
Conservation law
Sistemes no lineals
Applied Mathematics
010102 general mathematics
Mathematical Physics (math-ph)
Conserved quantity
High Energy Physics - Theory (hep-th)
Hamiltonian formalism
Mechanics of Materials
Hamilton
Sistemes de
Homogeneous space
symbols
010307 mathematical physics
Geometry and Topology
Noether's theorem
Hamiltonian (quantum mechanics)
Symplectic geometry
Symmetries
Zdroj: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
Popis: A complete geometric classification of symmetries of autonomous Hamiltonian mechanical systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results and properties about the symmetries of the Hamiltonian and of the symplectic form and then some new kinds of non-symplectic symmetries and their conserved quantities are introduced and studied.
Comment: 11 pages. The paper has been substantially shortened. The bibliography has been updated
Databáze: OpenAIRE
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