scholarly journals On the arithmetic and geometry of binary Hamiltonian forms

2013 ◽  
Vol 7 (1) ◽  
pp. 75-115
Author(s):  
Jouni Parkkonen ◽  
Frédéric Paulin
Keyword(s):  
Hamiltonian Forms

scholarly journals Gauge-independent Theory of Symmetry. I.

1964 ◽  
Vol 17 (4) ◽  
pp. 431 ◽  
Author(s):  
LJ Tassie ◽  
HA Buchdahl
Keyword(s):  
Electromagnetic Field ◽  
Single Particle ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Conserved Quantities ◽  
Continuous Symmetry ◽  
Symmetry Properties ◽  
Symmetry Transformations ◽  
Hamiltonian Forms

The invariance of a system under a given transformation of coordinates is usually taken to mean that its Lagrangian is invariant under that transformation. Consequently, whether or not the system is invariant will depend on the gauge used in describing the system. By defining invariance of a system to mean the invariance of its equations of motion, a gauge-independent theory of symmetry properties is obtained for classical mechanics in both the Lagrangian and Hamiltonian forms. The conserved quantities associated with continuous symmetry transformations are obtained. The system of a single particle moving in a given electromagnetic field is considered in detail for various symmetries of the electromagnetic field, and the appropriate conserved quantities are found.

scholarly journals BINARY NONLINEARIZATION OF THE SUPER AKNS SYSTEM

2008 ◽  
Vol 22 (04) ◽  
pp. 275-288 ◽  
Author(s):  
JINGSONG HE ◽  
JING YU ◽  
YI CHENG ◽  
RUGUANG ZHOU
Keyword(s):  
Hamiltonian System ◽  
Spectral Problem ◽  
Integrable Hamiltonian System ◽  
Integrals Of Motion ◽  
Finite Dimensional ◽  
Akns System ◽  
Hamiltonian Forms

We establish the binary nonlinearization approach of the spectral problem of the super AKNS system, and then use it to obtain the super finite-dimensional integrable Hamiltonian system in the supersymmetry manifold ℝ4N|2N. The super Hamiltonian forms and integrals of motion are given explicitly.

scholarly journals A modified chaos-based communication scheme using Hamiltonian forms and observer

2005 ◽  
Vol 23 ◽  
pp. 267-275 ◽  
Author(s):  
D López-Mancilla ◽  
C Cruz-Hernández ◽  
C Posadas-Castillo
Keyword(s):  
Communication Scheme ◽  
Hamiltonian Forms

Hamiltonian Forms for a Hierarchy of Discrete Integrable Coupling Systems

2008 ◽  
Vol 50 (6) ◽  
pp. 1269-1275 ◽  
Author(s):  
Xu Xi-Xiang ◽  
Yang Hong-Xiang ◽  
Lu Rong-Wu
Keyword(s):  
Hamiltonian Forms ◽  
Integrable Coupling

scholarly journals THE KOSZUL–TATE COHOMOLOGY IN COVARIANT HAMILTONIAN FORMALISM

1999 ◽  
Vol 14 (32) ◽  
pp. 2201-2209 ◽  
Author(s):  
LUIGI MANGIAROTTI ◽  
GENNADI SARDANASHVILY
Keyword(s):  
Field Theory ◽  
Explicit Form ◽  
Hamiltonian Formalism ◽  
Projection Operators ◽  
Lagrange Equations ◽  
Tate Cohomology ◽  
Hamilton Equations ◽  
Complete Set ◽  
Hamiltonian Forms

We show that, in the framework of covariant Hamiltonian field theory, a degenerate almost regular quadratic Lagrangian L admits a complete set of non-degenerate Hamiltonian forms such that solutions of the corresponding Hamilton equations, which live in the Lagrangian constraint space, exhaust solutions of the Euler–Lagrange equations for L. We obtain the characteristic splittings of the configuration and momentum phase bundles. Due to the corresponding projection operators, the Koszul–Tate resolution of the Lagrangian constraints for a generic almost regular quadratic Lagrangian is constructed in an explicit form.

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