Related papers: The bracket and the evolution operator in covarian…

A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator $\eta_+$ and defining the annihilation and creation operators to be $\eta_+$-pseudo-Hermitian adjoint to each other. The operator…

Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…

It is shown that the new formula for the field theory Poisson brackets arise naturally in the extension of the formal variational calculus incorporating divergences. The linear spaces of local functionals, evolutionary vector fields,…

We review the construction of homological evolutionary vector fields on infinite jet spaces and partial differential equations. We describe the applications of this concept in three tightly inter-related domains: the variational Poisson…

Infinite dimensional Hamiltonian systems appear naturally in the rich algebraic structure of Symplectic Field Theory. Carefully defining a generalization of gravitational descendants and adding them to the picture, one can produce an…

In this paper we extend the geometric formalism of the Hamilton-Jacobi theory for time dependent Mechanics to the case of classical field theories in the k-cosymplectic framework.

We analyze the Poisson structure of the time-dependent mean-field equations for bosons and construct the Lie-Poisson bracket associated to these equations. The latter follow from the time-dependent variational principle of Balian and…

We consider on a symplectic manifold M with Poisson bracket {,} an Hamiltonian H with complete flow and a family Phi=(Phi_1,...,Phi_d) of observables satisfying the condition {{Phi_j,H},H}=0 for each j. Under these assumptions, we prove a…

This work develops a symplectic framework for quantum computing to be applied to classical Hamiltonian systems, exploiting the intrinsic geometric compatibility between unitary quantum evolution and symplectic phase-space dynamics in a…

We introduce a bracket on 1-forms defined on ${\cal J}^{\infty}(S^1, \mathbb{R}^n)$, the infinite jet extension of the space of loops and prove that it satisfies the standard properties of a Poisson bracket. Using this bracket, we show that…

We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong…

For any unitary representation $\rho$ on a finite-dimensional Hilbert space \(V\) with differential \(d\rho : \mathfrak{g} \to \mathfrak{u}(V)\) for the Lie algebra $\mathfrak g$, we consider the Hamiltonian evolution \[ U_X(t) \coloneqq…

The explicit form of evolution operator of the three atoms Tavis-Cummings Model is given.

Let M be a paracompact smooth manifold, A a Weil algebra and M^{A} the associated Weil bundle. In this paper, we give a characterization of hamiltonian field on M^{A} in the case of Poisson manifold and of Symplectic manifold.

A Hamiltonian field theory for the macroscopic Maxwell equations with fully general polarization and magnetization is stated in the language of differential forms. The precise procedure for translating the vector calculus formulation into…

The nonholonomic dynamics can be described by the so-called nonholonomic bracket in the constrained submanifold, which is a non-integrable modification of the Poisson bracket of the ambient space, in this case, of the canonical bracket in…

This article seeks to relate a recent proposal for the association of a covariant Field Theory with a string or brane Lagrangian to the Hamilton-Jacobi formalism for strings and branes. It turns out that since in this special case, the…

A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…

In this paper, we first prove that the kernel of convolution operator, corresponding the composition of pseudo-differential operator and evolution system associated with the symbol depending on time, satisfies the H\"ormander's condition.…

Hamiltonian mechanics of field theory can be formulated in a generally covariant and background independent manner over a finite dimensional extended configuration space. The physical symplectic structure of the theory can then be defined…