Related papers: Canonical (and non-canonical) Transformations: A D…
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…
Renormalization group method is one of the most powerful tool to obtain approximate solutions to differential equations. We apply the renormalization group method to Hamiltonian systems whose integrable parts linearly depend on action…
This paper presents a PDE-based approach to finding an optimal canonical basis with which to represent a nearly integrable Hamiltonian. The idea behind the method is to continuously deform the initial canonical basis in such a way that the…
In this paper we present canonical and canonoid transformations considered as global geometrical objects for Hamiltonian systems. Under the mathematical formalisms of symplectic, cosymplectic, contact and cocontact geometry, the canonoid…
We present a geometric and dynamical approach to the micro-canonical ensemble of classical Hamiltonian systems. We generalize the arguments in \cite{Rugh} and show that the energy-derivative of a micro-canonical average is itself…
In hep-th/0411028 a new manifestly covariant canonical quantization method was developed. The idea is to quantize in the phase space of arbitrary histories first, and impose dynamics as first-class constraints afterwards. The Hamiltonian is…
We show that, when applied to any non-canonical Hamiltonian system, any integrator that is symplectic for canonical Hamiltonian problems is actually conjugate symplectic for the non-canonical structure. This result is useful because it…
Canonical differential calculus is defined for finitely generated abelian group with an involution existing consistently. Two such canonical calculi are found out. Fermionic representation for canonical calculus is defined based on…
We show that a large class of dissipative systems can be brought to a canonical form by introducing complex co-ordinates in phase space and a complex-valued hamiltonian. A naive canonical quantization of these systems lead to non-hermitean…
It is shown how to extend the formal variational calculus in order to incorporate integrals of divergences into it. Such a generalization permits to study nontrivial boundary problems in field theory on the base of canonical formalism.
There are two approaches to time series approximate factor models: the static factor model, where the factors are loaded contemporaneously by the common component, and the Generalised Dynamic Factor Model, where the factors are loaded with…
Canonical functions are a powerful concept with numerous applications in the study of groups, monoids, and clones on countable structures with Ramsey-type properties. In this short note, we present a proof of the existence of canonical…
We present a new Hamiltonian formulation of barotropic Hall magnetohydrodynamics in two complementary approaches based on Dirac's constraint analysis. In one case the Hamiltonian is canonical involving physical variables only but the…
Quantization of energy balance equations, which describe a separatrix -- like motion is presented. The method is based on an exact canonical transformation of the energy--time pair to the action-angle canonical pair, $ (E,t)\to (I,\theta)…
Differential equations are one of the main approaches to evaluate multi-loop Feynman integrals. The construction of a canonical or $\varepsilon$-factorised basis for multi-loop integrals remains a key bottleneck for this approach,…
We express discrete Painlev\'e equations as discrete Hamiltonian systems. The discrete Hamiltonian systems here mean the canonical transformations defined by generating functions. Our construction relies on the classification of the…
Integration of Hamiltonian systems by reduction to action-angle variables has proven to be a successful approach. However, when the solution depends on elliptic functions the transformation to action-angle variables may need to remain in…
The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…
We propose a numerical method for approximate calculations of the time evolution of point particle systems given only the system's Hamiltonian function and initial conditions. The method both generates and solves the equations of motion…
We argue that there is nothing puzzling in the fact that the Hamiltonian formulation of a covariant theory, General Relativity, after a non-covariant change of field variables is not canonically related to the formulation based on the…