phymath999: white01 Lagrangian canonicalNoethersymmetries

Wednesday, February 26, 2014

white01 Lagrangian canonicalNoethersymmetries

Canonical

Noether

symmetries

and

commutativity

properties

for

gauge

systems

∗

Abstract
ForadynamicalsystemdeﬁnedbyasingularLagrangian,canonicalNoethersymmetriesarecharacterizedintermsoftheircommutationrelationswiththeevolutionoperatorsofLagrangianandHamiltonianformalisms.Separatecharacterizationsaregiveninphasespace,invelocityspace,andthroughanevolutionoperatorthatlinksbothspaces.

Introduction
Mostphysicaltheoriesimplementthedynamicsasaresultoftheapplicationofavariationalprinciple,thatis,bymeansofaLagrangian.Amongthedynamicalsymmetriesofthesetheories,thatis,transformationsthatmapsolutionsoftheequationsofmotionintosolutions,wecansingleouttheNoethersymmetries,thatis,thecontinuoustransformationsthatleavetheactioninvariant—exceptforboundaryterms.Inaddition,ifweaimtomovethedescriptionofthedy-namicsfromthetangentbundle(velocityspace)TQofitsconﬁgurationspaceQtothecotangentbundle(phasespace)T∗Q,otherdistinctionscanberaised,astowhetherthesymmetrytrans-formationinvelocityspaceisprojectabletophasespaceand,intheaﬃrmativecase,whetherthetransformationinphasespaceiscanonical.Wewillconsidertime-independentLagrangians,asitistheusualcaseinphysicaltheories,butwewillallowtodealwithtime-dependentfunc-tionstocoveralsogaugesymmetries(symmetriesdependinguponarbitraryfunctionsoftime,orspace-timevariablesinﬁeldtheory);thenwewilluseR×TQandR×T∗QinsteadofTQandT∗Q.
Theinﬁnitesimalsymmetriesofanordinarydynamicalsystemarecharacterizedbyaprop-ertyofcommutativity:essentially,thatthetimeevolutionoperatorcommuteswiththeoperatorthatgeneratesthesymmetry.

Canonical Noether symmetries and commutativity properties for ...

arxiv.org › math-ph‎ 翻譯這個網頁

由 X Gracia 著作 - ‎2000 - ‎被引用 12 次 - ‎相關文章

2000年7月27日 - Abstract: For a dynamical system defined by a singular Lagrangian, canonical Noether symmetries are characterized in terms of their ...

~~[PDF]~~

Classical and quantum Lagrangian field theories with boundary

https://www.math.ethz.ch/t3/.../ndb/.../Cattaneo_prodoc.pd...‎ 翻譯這個網頁

由 A Cattaneo 著作 - ‎被引用 16 次 - ‎相關文章

T⇤N by the Legendre mapping. Time evolution is given by a Hamiltonian flow . In particular,. L := graph t1 t0 2 TN ⇥ TN is Lagrangian (canonical relation).

Lagrangian perturbation theory for rotating magnetic stars - MNRAS

mnras.oxfordjournals.org/content/377/2/630.full‎ 翻譯這個網頁

由 K Glampedakis 著作 - ‎2007 - ‎被引用 8 次 - ‎相關文章

They reformulated the stability criterion in terms of the Lagrangian canonical energy functional Ec(ξ, ∂tξ), emphasizing the existence of 'trivial' fluid ...

EUDML | A singular lagrangian model for N-body relativistic ...

https://eudml.org/doc/76224‎ 翻譯這個網頁

由 J Gomis 著作 - ‎1984 - ‎被引用 7 次 - ‎相關文章

... non-separable, interaction, bound stable problem, multitemporal model for N-particles, constrained system, singular Lagrangian, canonical transformation, ...

Lagrangian Quantum Field Theory in Momentum Picture: Free Fields

books.google.com.hk/books?isbn=160456170X - 翻譯這個網頁

Bozhidar Z. Iliev - 2008 - ‎Science

In this book is considered only the Lagrangian (canonical) quantum field theory in which the quantum fields are represented as operators, called field operators, ...

Canonical Noether symmetries and commutativity ... - 百度文库

wenku.baidu.com/view/df0332f57c1cfad6195fa7ea.html - 轉為繁體網頁

2011年9月15日 - For a dynamical system defined by a singular Lagrangian, canonical Noether symmetries are characterized in terms of their commutation ...

~~[PDF]~~

Lagrangian dynamics for a passive tracer in a class of Gaussian ...

https://www.math.ucdavis.edu/~fannjiang/.../rough-OU.pd...‎ 翻譯這個網頁

由 A Fannjianga 著作 - ‎2002 - ‎被引用 19 次 - ‎相關文章

Keywords: Tracer dynamics; Lagrangian canonical process. 1. Introduction. A major problem in uid turbulence is the transport of a passive tracer whose.

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