Cartan connections and momentum maps

2003 ◽  
Author(s):  
Paulette Libermann
2017 ◽  
Vol 357 (2) ◽  
pp. 873-912 ◽  
Author(s):  
Ana Bela Cruzeiro ◽  
Darryl D. Holm ◽  
Tudor S. Ratiu
Keyword(s):  

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Zachary Elgood ◽  
Patrick Meessen ◽  
Tomás Ortín

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.


2000 ◽  
Vol 29 (3) ◽  
pp. 453-505 ◽  
Author(s):  
Andreas ČAP ◽  
Hermann SCHICHL

2011 ◽  
Vol 08 (01) ◽  
pp. 177-185 ◽  
Author(s):  
MARCO FERRARIS ◽  
MAURO FRANCAVIGLIA ◽  
MARCELLA PALESE ◽  
EKKEHART WINTERROTH

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.


2010 ◽  
Vol 25 (05) ◽  
pp. 1069-1078 ◽  
Author(s):  
ÖMER OĞUZ ◽  
DEVRIM YAZICI

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.


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