Abstract The purpose of this paper is to shed some fresh light on the long-standing conceptual question origin well-known Poisson bracket structure constraints that govern canonical dynamics generally relativistic field theories, i.e. geometrodynamics. This has long been known be same for a wide class fields inhabit space-time, namely those with non-differential coupling gravity. It also notice...

1.1. General formalism and basic examples. Let A = ⊕ i>0Ai be a graded algebra equipped with a Poisson bracket {·, ·} that has degree −1 because {Ai, Aj} ⊂ Ai+j−1. By a quantization of A one means a pair (A, ι), where • A is a filtered associative unital algebra A = ∪ i>0 A6i. • ι : grA → A is an isomorphism of graded Poisson algebras. Recall that grA := ⊕ i>0 A6i/A6i−1 is a graded algebra. Tha...

We show that the replicator dynamics for zero-sum games arises as a result of non-canonical bracket is hybrid between Poisson Bracket and Nambu Bracket. The resulting parameterized both by skew-symmetric payoff matrix mediating function. function only sometimes conserved quantity, but plays critical role in determination dynamics. As by-product, we this definition natural metric on which phase ...

Abstract. Xu introduced a class of nongraded Hamiltonian Lie algebras. These Lie algebras have a Poisson bracket structure. In this paper, the isomorphism classes of these Lie algebras are determined by employing a “sandwich” method and by studying some features of these Lie algebras. It is obtained that two Hamiltonian Lie algebras are isomorphic if and only if their corresponding Poisson alge...

A LiePoisson bracket is presented for a four-field gyrofluid model with compressible ions and magnetic field curvature, thereby showing the model to be Hamiltonian. In particular, in addition to commonly adopted magnetic curvature terms present in the continuity equations, analogous terms must be retained also in the momentum equations, in order to have a Lie-Poisson structure. The correspondin...

We show that the recently proposed matrix model for M theory obeys the cyclic trace assumptions underlying generalized quantum or trace dynamics. This permits a verification of supersymmetry as an operator calculation, and a calculation of the supercharge density algebra by using the generalized Poisson bracket, in a basis-independent manner that makes no reference to individual matrix elements...