Cartan connections and momentum maps

2003 ◽  
Author(s):  
Paulette Libermann
Keyword(s):  
Momentum Maps ◽  
Cartan Connections

scholarly journals Momentum Maps and Stochastic Clebsch Action Principles

2017 ◽  
Vol 357 (2) ◽  
pp. 873-912 ◽  
Author(s):  
Ana Bela Cruzeiro ◽  
Darryl D. Holm ◽  
Tudor S. Ratiu
Keyword(s):  
Momentum Maps

scholarly journals The first law of black hole mechanics in the Einstein-Maxwell theory revisited

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Zachary Elgood ◽  
Patrick Meessen ◽  
Tomás Ortín
Keyword(s):  
Black Hole ◽  
Maxwell Theory ◽  
Gauge Invariant ◽  
Momentum Maps ◽  
Field Strengths

Abstract We re-derive the first law of black hole mechanics in the context of the Einstein-Maxwell theory in a gauge-invariant way introducing “momentum maps” associated to field strengths and the vectors that generate their symmetries. These objects play the role of generalized thermodynamical potentials in the first law and satisfy generalized zeroth laws, as first observed in the context of principal gauge bundles by Prabhu, but they can be generalized to more complex situations. We test our ideas on the d-dimensional Reissner-Nordström-Tangherlini black hole.

scholarly journals Parabolic geometries and canonical Cartan connections

2000 ◽  
Vol 29 (3) ◽  
pp. 453-505 ◽  
Author(s):  
Andreas ČAP ◽  
Hermann SCHICHL
Keyword(s):  
Cartan Connections ◽  
Parabolic Geometries

GAUGE-NATURAL NOETHER CURRENTS AND CONNECTION FIELDS

2011 ◽  
Vol 08 (01) ◽  
pp. 177-185 ◽  
Author(s):  
MARCO FERRARIS ◽  
MAURO FRANCAVIGLIA ◽  
MARCELLA PALESE ◽  
EKKEHART WINTERROTH
Keyword(s):  
Variational Problems ◽  
Conserved Quantities ◽  
Cartan Connections ◽  
Natural Bundles

We study geometric aspects concerned with symmetries and conserved quantities in gauge-natural invariant variational problems and investigate implications of the existence of a reductive split structure associated with canonical Lagrangian conserved quantities on gauge-natural bundles. In particular, we characterize the existence of covariant conserved quantities in terms of principal Cartan connections on gauge-natural prolongations.

MULTIPLE LOCAL LAGRANGIANS FOR n-COMPONENT SUPER-KORTEWEG–DE VRIES-TYPE BI-HAMILTONIAN SYSTEMS

2010 ◽  
Vol 25 (05) ◽  
pp. 1069-1078 ◽  
Author(s):  
ÖMER OĞUZ ◽  
DEVRIM YAZICI
Keyword(s):  
Hamiltonian Systems ◽  
Hamiltonian Structure ◽  
Velocity Fields ◽  
Kinetic Term ◽  
Lagrangian Formalism ◽  
Momentum Maps ◽  
Miura Transformation ◽  
De Vries ◽  
Superintegrable Systems

The multiple Lagrangian formalism is constructed for n-component Korteweg–de Vries (KdV) type superintegrable systems. They all admit bi-Hamiltonian structure. The first two Lagrangians are local and degenerate. They contain Clebsch potentials for velocity fields and momentum maps in kinetic term. The first local Lagrangian for n-component supermodified KdV (smKdV) is also obtained by employing the multicomponent super-Miura transformation.

Sign in / Sign up

Export Citation Format

Share Document