Related papers: First integrals generated by pseudosymmetries in N…
Liouville (super)integrability of a Hamiltonian system of differential equations is based on the existence of globally well-defined constants of the motion, while Lie point symmetries provide a local approach to conserved integrals.…
We consider Hamiltonian systems in first-order multisymplectic field theories. We review the properties of Hamiltonian systems in the so-called restricted multimomentum bundle, including the variational principle which leads to the…
In 2+1-dimensional conformal field theories with a global U(1) symmetry, monopoles can be introduced through a background gauge field that couples to the U(1) conserved current. We use the state-operator correspondence to calculate scaling…
We show that distinct emergent symmetries, such as partial dynamical symmetry and quasi dynamical symmetry, can occur simultaneously in the same or different eigenstates of the Hamiltonian. Implications for nuclear spectroscopy in the…
Nambu mechanics is a generalized Hamiltonian dynamics characterized by an extended phase space and multiple Hamiltonians. In a previous paper [Prog. Theor. Exp. Phys. 2013, 073A01 (2013)] we revealed that the Nambu mechanical structure is…
We propose an N=4 supersymmetric quantum mechanics of a charged particle on a sphere in the background of Dirac magnetic monopole and study the system using the CP(1) model approach. We explicitly calculate the symmetry algebra taking the…
Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics. The derivation is based on a stochastic discrete…
In this paper, we describe the dynamical symmetries of classical supersymmetric oscillators in one and two spatial (bosonic) dimensions. Our main ingredient is a generalized Poisson bracket which is defined as a suitable classical…
The symmetries play important roles in physical systems. We study the symmetries of a Hamiltonian system by investigating the asymmetry of the Hamiltonian with respect to certain algebras. We define the asymmetry of an operator with respect…
In this paper a multi-band envelope-function Hamiltonian for lattice-matched semiconductor heterostructures is derived from first-principles norm-conserving pseudopotentials. The theory is applicable to isovalent or heterovalent…
The holomorphic homogeneous prepotential encoding the special geometry of the special K\"ahler manifolds ${\textstyle SU(1,n)\over \textstyle U(1)\otimes SU(n)}$ is constructed using the symplectic embedding of the isometry group $SU(1,n)$…
We investigate the asymptotic symmetry group of a SU(2)-Yang-Mills theory coupled to a Higgs field in the Hamiltonian formulation. This extends previous work on the asymptotic structure of pure electromagnetism by Henneaux and Troessaert,…
A systematic method to derive the Hamiltonian and Nambu form for the shallow water equations, using the conservation for energy and potential enstrophy, is presented. Different mechanisms, such as vortical flows and emission of gravity…
We obtain by dimensional reduction a $(1+1)$ supersymmetric system introduced in the description of ultracold quantum gases. The correct supercharges are identified and their algebra is constructed. Finally novel static self-dual solutions…
We present a coordinate-free approach for constructing approximate first integrals of generalized slow-fast Hamiltonian systems, based on the global averaging method on parameter-dependent phase spaces with $\mathbb{S}^1 -$symmetry.…
Shell-model states involving several pseudospin doublets and ``intruder'' levels in nuclei, are combined into larger multiplets. The corresponding single-particle spectrum exhibits a supersymmetric pattern whose origin can be traced to the…
In this article we will apply the first- and second-order supersymmetric quantum mechanics to obtain new exactly-solvable real potentials departing from the inverted oscillator potential. This system has some special properties; in…
We develop uniform approximations for the trace formula for non-integrable systems in which SU(2) symmetry is broken by a non-linear term of the Hamiltonian. As specific examples, we investigate H\'enon-Heiles type potentials. Our formalism…
We analyse the problem of defining a Poisson bracket structure on the space of solutions of the equations of motions of first order Hamiltonian field theories. The cases of Hamiltonian mechanical point systems (as a (0 + 1)-dimensional…
We present a numerical technique for calculating path integrals in non-compact U(1) and SU(2) gauge theories. The gauge fields are represented by a superposition of pseudoparticles of various types with their amplitudes and color…