scholarly journals Higher-Order Dispersive Deformations of Multidimensional Poisson Brackets of Hydrodynamic Type

2018 ◽  
Vol 196 (2) ◽  
pp. 1129-1149
Author(s):  
M. Casati
Keyword(s):  
Higher Order ◽  
Hydrodynamic Type ◽  
Poisson Brackets

On the central extensions of Poisson brackets of hydrodynamic type

2003 ◽  
Vol 36 (9) ◽  
pp. 2261-2269
Author(s):  
Chengming Bai ◽  
Daoji Meng ◽  
Hongbiao Zhang
Keyword(s):  
Hydrodynamic Type ◽  
Poisson Brackets ◽  
Central Extensions

A note on the relativistic invariance of quantized field theories

1950 ◽  
Vol 46 (2) ◽  
pp. 316-318
Author(s):  
J. S. de Wet
Keyword(s):  
Present Author ◽  
Higher Order ◽  
Field Theories ◽  
Poisson Brackets ◽  
Relativistic Invariance ◽  
Field Equations ◽  
Commutation Relations ◽  
Generalized Poisson ◽  
Quantized Field

In an earlier paper (1), which will be referred to as A, the present author has demonstrated the relativistic invariance, for general transformations of coordinates, of the Einstein-Bose and Fermi-Dirac quantizations of linear field equations derived from higher order Lagrangians. The proof consisted of the identification of the commutation relations with the generalized Poisson brackets introduced by Weiss (2) and proving the invariance of the latter.

scholarly journals SECOND-ORDER DEFORMATIONS OF HYDRODYNAMIC-TYPE POISSON BRACKETS

2009 ◽  
Vol 51 (A) ◽  
pp. 75-82
Author(s):  
JAMES T. FERGUSON
Keyword(s):  
Differential Operator ◽  
Poisson Bracket ◽  
Hamiltonian Structure ◽  
Second Order ◽  
Hydrodynamic Type ◽  
Poisson Brackets ◽  
Geometric Type

AbstractThis paper is concerned with the properties of differential-geometric-type Poisson brackets specified by a differential operator of degree 2. It also considers the conditions required for such a Poisson bracket to form a bi-Hamiltonian structure with a hydrodynamic-type Poisson bracket.

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