Related papers: On Generalized Nambu Mechanics
The barotropic ideal fluid with step and delta-function discontinuities coupled to Einstein's gravity is studied. The discontinuities represent star surfaces and thin shells; only non-intersecting discontinuity hypersurfaces are considered.…
We review some aspects of Nambu mechanics on the basis of the works previously published separately by the present author. Main focuses are on three themes, its various symmetry structures, their possible relevance to string/M theory, and a…
The link between 3D spaces with (in general, non-constant) curvature and quantum deformations is presented. It is shown how the non-standard deformation of a sl(2) Poisson coalgebra generates a family of integrable Hamiltonians that…
A ternary Nambu-Poisson algebra (which we call a Nambu-Poisson algebra in the paper) is the underlying algebraic structure of Nambu-Poisson manifolds of order $3$ that appeared in the generalized Hamiltonian mechanics. First, we consider…
A formulation of quantum mechanics is introduced based on a $2D$-dimensional phase-space wave function $\text{\reflectbox{\text{p}}}\mkern-3mu\text{p}\left(q,p\right)$ which might be computed from the position-space wave function…
We present a full study of the 3-body problem in gravity in flat (2+1)-dimensional space-time, and in the nonrelativistic limit of small velocities. We provide an explicit form of the ADM Hamiltonian in a regular coordinate system and we…
We develop a geometric approach to Poisson electrodynamics, that is, the semi-classical limit of noncommutative $U(1)$ gauge theory. Our framework is based on an integrating symplectic groupoid for the underlying Poisson brackets, which we…
A variational formulation for nonequilibrium thermodynamics was recently proposed in \cite{GBYo2017a,GBYo2017b} for both discrete and continuum systems. This formulation extends the Hamilton principle of classical mechanics to include…
Basic idea presented in Parts (I) and (II) for the deformed boson scheme is applied to the case of the su(2,1)-algebra for describing many-body systems consisting of three kinds of boson operators. A possible form of the coherent state for…
A carefully motivated symmetric variant of the Poisson bracket in ordinary (not Grassmann) phase space variables is shown to satisfy identities which are in algebraic correspondence with the anticommutation postulates for quantized Fermion…
The theory of the usual, constrained p-branes is embedded into a larger theory in which there is no constraints. In the latter theory the Fock-Schwinger proper time formalism is extended from point-particles to membranes of arbitrary…
A geometric analysis of the Shake and Rattle methods for constrained Hamiltonian problems is carried out. The study reveals the underlying differential geometric foundation of the two methods, and the exact relation between them. In…
We present novel Hamiltonian descriptions of some three-dimensional systems including two well-known systems describing the three-wave-interaction problem and some well-known chaotic systems, namely, the Chen, L\"u, and Qi systems. We show…
We parameterize the phase space density by time dependent diffeomorphic, Poisson preserving transformations on phase space acting on a reference density solution. We can look at these as transformations which fix time on the extended space…
We show that classical thermodynamics has a formulation in terms of Hamilton-Jacobi theory, analogous to mechanics. Even though the thermodynamic variables come in conjugate pairs such as pressure/volume or temperature/entropy, the phase…
The Poisson structures for 3D systems possessing one constant of motion can always be constructed from the solution of a linear PDE. When two constants of the motion are available the problem reduces to a quadrature and the structure…
In the present paper we have developed a Non-Commutative (NC) generalization of perfect fluid model from first principles, in a Hamiltonian framework. The noncommutativity is introduced at the Lagrangian (particle) coordinate space brackets…
The Poisson structure arising in the Hamiltonian approach to the rational Gaudin model looks very similar to the so-called modified Reflection Equation Algebra. Motivated by this analogy, we realize a braiding of the mentioned Poisson…
We present the Dirac Hamiltonian formalism for a pair of $1$-form fields with a topological-like potential coupled to first-order gravity in three-dimensional spacetime. By considering the complete phase space, we derive the full structure…
A class of two dimensional field theories, based on (generically degenerate) Poisson structures and generalizing gravity-Yang-Mills systems, is presented. Locally, the solutions of the classical equations of motion are given. A general…