相关论文: Nambu structures and integrable 1-forms
We study a type of geometric theory with a non-dynamical one-form field. Its dynamical variables are an $su(2)$ gauge field and a triad of $su(2)$ valued one-forms. Hamiltonian decomposition reveals that the theory has a true Hamiltonian,…
An N-dimensional position-dependent mass Hamiltonian (depending on a parameter \lambda) formed by a curved kinetic term and an intrinsic oscillator potential is considered. It is shown that such a Hamiltonian is exactly solvable for any…
We review the developments of a recently proposed approach to study integrable theories in any dimension. The basic idea consists in generalizing the zero curvature representation for two-dimensional integrable models to space-times of…
We deform classical holomorphic Chern--Simons theory on a Calabi--Yau three-fold $X$ by deforming the complex structure by a deformation parameter $h \in\mathscr{H}^{0,1}(T^{1,0}X)$. The corresponding equations of motion admit new…
This paper examines a generalization of the Camassa-Holm equation from the perspective of integrability. Using the framework developed by Dubrovin on bi-Hamiltonian deformations and the general theory of quasi-integrability, we demonstrate…
Integrability in string/field theories is known to emerge when considering dynamics in the moduli space of physical theories. This implies that one has to look at the dynamics with respect to unusual time variables like coupling constants…
We point out that two classes of deformations of integrable models, developed completely independently, have deep connections and share the same algebraic origin. One class includes the $T\bar T$-deformation of 1+1 dimensional integrable…
We collect some classical results about holomorphic 1-forms of a reduced complex curve singularity. They are used to study the pull-back of holomorphic 1-forms on an isolated complete intersection curve singularity under the normalization…
This review is a collection of various methods and observations relevant to structures in three-dimensional systems similar to those responsible for integrability of two-dimensional systems. Particular focus is given to Nambu structures and…
We discuss deformation quantization of the covariant, light-cone and conformal gauge-fixed p-brane actions (p>1) which are closely related to the structure of the classical and quantum Nambu brackets. It is known that deformation…
The globalization problem arises when local tensor fields possess a given property (such as being symplectic or Poisson) but cannot be consistently extended to a global object due to incompatibilities on chart overlaps. A notable instance…
A large class of physical systems involves the vanishing of a 1-form on a manifold as a constraint on the acceptable states. This means that one is always dealing with the Pfaff problem in those cases. In particular, knowing the degree of…
We study Hamiltonian analysis of three-dimensional advection flow $\mathbf{\dot{x}}=\mathbf{v}({\bf x})$ of incompressible nature $\nabla \cdot {\bf v} ={\bf 0}$ assuming that dynamics is generated by the curl of a vector potential…
Covariant quantization of the Nambu-Goto spinning particle in 2+1-dimensions is studied. The model is relevant in the context of recent activities in non-commutative space-time. From a technical point of view also covariant quantization of…
We prove several conjectures relating the existence of nonvanishing 1- forms to smooth morphisms over abelian varieties, assuming the existence of good minimal models. The proof involves a decomposition result for a family of Calabi-Yau…
The paper suggests new topological lower bounds for the number of zeros of closed 1-forms within a given cohomology class. The main new technical tool is the deformation complex, which allows to pass to a singular limit and reduce the…
The paper deals with the problem of the existence of a normal form for a nearly-integrable real-analytic Hamiltonian with aperiodically time-dependent perturbation decaying (slowly) in time. In particular, in the case of an isochronous…
Flat structure was introduced by K. Saito and his collaborators at the end of 1970's. Independently the WDVV equation arose from the 2D topological field theory. B. Dubrovin unified these two notions as Frobenius manifold structure. In this…
We study Abelian generalized deformations of the usual product of polynomials introduced in hep-th/9602016. We construct an explicit example for the case of $su/2$ which provides a tentative of a quantum-mechanical description of Nambu…
We present local classification results for isolated singularities of functions with respect to a Nambu structure (multi-vector field) of maximal degree, in a neighbourhood of a smooth point of its degeneracy hypersurface. The results…