scholarly journals Bi-Hamiltonian geometry and canonical spectral coordinates for the rational Calogero–Moser system

2017 ◽  
Vol 118 ◽  
pp. 126-137 ◽  
Author(s):  
Gregorio Falqui ◽  
Igor Mencattini
Keyword(s):  
Moser System

scholarly journals Nilpotent integrability, reduction of dynamical systems and a third-order Calogero–Moser system

2019 ◽  
Vol 198 (5) ◽  
pp. 1513-1540
Author(s):  
A. Ibort ◽  
G. Marmo ◽  
M. A. Rodríguez ◽  
P. Tempesta
Keyword(s):  
Dynamical Systems ◽  
Third Order ◽  
Moser System

Superintegrability of the Calogero-Moser system

1983 ◽  
Vol 95 (6) ◽  
pp. 279-281 ◽  
Author(s):  
S. Wojciechowski
Keyword(s):  
Moser System

scholarly journals MORE EVIDENCE FOR THE WDVV EQUATIONS IN ${\mathcal N} = 2$ SUSY YANG–MILLS THEORIES

2000 ◽  
Vol 15 (08) ◽  
pp. 1157-1206 ◽  
Author(s):  
A. MARSHAKOV ◽  
A. MIRONOV ◽  
A. MOROZOV
Keyword(s):  
Field Theory ◽  
Adjoint Representation ◽  
Hyperelliptic Curves ◽  
Fundamental Representation ◽  
Wdvv Equations ◽  
Yang Mills ◽  
Perturbative Regime ◽  
String Models ◽  
Supersymmetric Theories ◽  
Moser System

We consider 4D and 5D [Formula: see text] supersymmetric theories and demonstrate that in general their Seiberg–Witten prepotentials satisfy the Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equations. General proof for the Yang–Mills models (with matter in the first fundamental representation) makes use of the hyperelliptic curves and underlying integrable systems. A wide class of examples is discussed; it contains few understandable exceptions. In particular, in the perturbative regime of 5D theories, in addition to naive field theory expectations some extra terms appear, as happens in heterotic string models. We consider also the example of the Yang–Mills theory with matter hypermultiplet in the adjoint representation (related to the elliptic Calogero–Moser system) when the standard WDVV equations do not hold.

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