Related papers: On the local Hamiltonian structure of vector field…
Smooth vector fields on $\mathbb{R}^n$ can be decomposed into the sum of a gradient vector field and divergence-free (solenoidal) vector field under suitable hypotheses. This is called the Helmholtz-Hodge decomposition (HHD), which has been…
In the time evolution of fluids, the topologies of fluids can be changed by the creations and annihilations of singular points and by switching combinatorial structures of separatrices. In this paper, to describe the possible generic time…
We consider all compatible topologies of an arbitrary finite-dimensional vector space over a non-trivial valuation field whose metric completion is a locally compact space. We construct the canonical lattice isomorphism between the lattice…
We develop a Hamiltonian theory for 2D soliton equations. In particular, we identify the spaces of doubly periodic operators on which a full hierarchy of commuting flows can be introduced, and show that these flows are Hamiltonian with…
We propose a suitable formulation of the Hamiltonian formalism for Field Theory in terms of Hamiltonian connections and multisymplectic forms where a composite fibered bundle, involving a line bundle, plays the role of an extended…
The effective Hamiltonian, as obtained from applying the Hamiltonian flow equations to front form QED, are solved numerically for positronium. Both the exchange and the annihilation channels are included. The impact of different similarity…
We introduce a class of Hamiltonian scattering systems which can be reduced to the "normal form" $\dot P=0$, $\dot Q=P$, by means of a global canonical transformation $ (P,Q)=A(p,q), p,q\in R^n$, defined through asymptotic properties of 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…
The usual implement procedure for the reconstruction of secular equation for an effective Hamiltonian has been discussed and improved. A relative characteristic polynomial has been introduced for the effective Hamiltonian, to obtain a…
It has been a long standing question how to extend the canonical Poisson bracket formulation from classical mechanics to classical field theories, in a completely general, intrinsic, and canonical way. In this paper, we provide an answer to…
An exact result for the reduced density matrix on a finite interval for a $1+1$ dimensional free real scalar field in the ground state is presented. In the massless case, the Williamson decomposition of the appearing kernels is explicitly…
For a linear non-Hermitian system, I demonstrate that a Hamiltonian can be constructed such that the non-Hermitian equations can be expressed exactly in the form of Hamilton's canonical equations. This is first shown for discrete systems…
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…
The canonical front form Hamiltonian for non-Abelian SU(N) gauge theory in 3+1 dimensions is mapped non-perturbatively on an effective Hamiltonian which acts only in the Fock space of a quark and an antiquark. Emphasis is put on dealing…
In many Lagrangian field theories one has a Poisson bracket defined on the space of local functionals. We find necessary and sufficient conditions for a transformation on the space of local functionals to be canonical in three different…
We discuss in this paper the canonical structure of classical field theory in finite dimensions within the {\it{pataplectic}} hamiltonian formulation, where we put forward the role of Legendre correspondance. We define the Poisson…
We establish the Hamiltonian analysis and the canonical path integral for a local formulation of vacuum energy sequestering. In particular, by considering the state of the universe as a superposition of vacuum states corresponding to…
An outstanding property of any Hamiltonian system is the symplecticity of its flow, namely, the continuous trajectory preserves volume in phase space. Given a symplectic but discrete trajectory generated by a transition matrix applied at a…
In this paper we construct multiparametric families of two dimensional metrics with polynomial first integral. Such integrable geodesic flows are described by solutions of some semi-Hamiltonian hydrodynamic type system. We find infinitely…
We study log canonical models of foliated surfaces of general type. In particular, we show that log canonical models of general type and their minimal partial du Val resolutions are bounded. Moreover, we show the valuative criteria of…