Related papers: Numerical study on a canonized Hamiltonian system …
The Hamiltonian formulation plays the essential role in constructing the framework of modern physics. In this paper, a new form of canonical equations of Hamilton with the complete symmetry is obtained, which are valid not only for the…
Ideal fluid dynamics is studied as a relativistic field theory with particular importance on its hamiltonian structure. The Schwinger condition, whose integrated version yields the stress tensor conservation, is explicitly verified both in…
Without a gauge fixing, canonical variables for the light-front SU(2) gluodynamics are determined. The Gauss law is written in terms of the canonical variables. The system is qualified as a generalized dynamical system with first class…
We use Boulware's Hamiltonian formalism of quadratic gravity theories in order to analyze the classical behaviour of Bianchi cosmological models for a Lagrangian density containing quadratic terms in the curvature. For this purpose we…
We present a variational principle for relativistic hydrodynamics with gauge-anomaly terms for a fluid coupled to an Abelian background gauge field. For this we utilize the Clebsch parametrization of the velocity field. We also set up the…
Motivated by recent discussions on the possible role of quantum computation in plasma simulations, here we present different approaches to Koopman's Hilbert-space formulation of classical mechanics in the context of Vlasov-Maxwell kinetic…
We discuss the quantization of a class of relativistic fluid models defined in terms of one real and two complex conjugate potentials with values on a K\"{a}hler manifold, and parametrized by the K\"{a}hler potential $K(z,\bar{z})$ and a…
We resurrect a standard construction of analytical mechanics dating from the last century. The technique allows one to pass from any dynamical system whose first order evolution equations are known, and whose bracket algebra is not…
The multisymplectic Hamiltonian formalism is a generalization of the Hamiltonian formalism that manifestly preserves covariance in the description of fields and that has been proposed as a possible framework for developing a…
The covariant canonical transformation theory applied to the relativistic Hamiltonian theory of classical matter fields in dynamical space-time yields a novel (first order) gauge field theory of gravitation. The emerging field equations…
We establish kinetic Hamiltonian flows in density space embedded with the $L^2$-Wasserstein metric tensor. We derive the Euler-Lagrange equation in density space, which introduces the associated Hamiltonian flows. We demonstrate that many…
Equations for a perfect fluid can be obtained by means of the variational principle both in the Lagrangian description and in the Eulerian one. It is known that we need additional fields somehow to describe a rotational isentropic flow in…
The multiplicative Hamiltonian flow on the phase space for a system with 1 degree of freedom was constituted from infinite hierarchy Hamiltonian flows. A new type of canonical transformation associated with the multiplicative Hamiltonian…
We propose an alternative for the Clebsch decomposition of currents in fluid mechanics, in terms of complex potentials taking values in a Kahler manifold. We reformulate classical relativistic fluid mechanics in terms of these complex…
The reduced-complexity models developed by Edward Lorenz are widely used in atmospheric and climate sciences to study nonlinear aspect of dynamics and to demonstrate new methods for numerical weather prediction. A set of inviscid Lorenz…
Using canonical quantisation, and eschewing the Schwinger-Keldysh path integral, we derive a version of the Worldline Quantum Field Theory (WQFT) formalism suitable for both scattering and bound configurations of the classical two-body…
Dynamics of ideal fluid with free surface can be effectively solved by perturbing the Hamiltonian in weak nonlinearity limit. However it is shown that perturbation theory, which includes third and fourth order terms in the Hamiltonian,…
This work introduces a Hamiltonian approach to regularization and linearization of central-force particle dynamics through a new canonical extension of the so-called "projective decomposition". The regularization scheme is formulated within…
A Hamiltonian reduction approach is defined, studied, and finally used to derive asymptotic models of internal wave propagation in density stratified fluids in two-dimensional domains. Beginning with the general Hamiltonian formalism of…
The energy and time variables of the elementary classical dynamical systems are described geometrically, as canonically conjugate coordinates of an extended phase-space. It is shown that the Galilei action of the inertial equivalence group…