相关论文: Faddeev-Jackiw quantization of topological invaria…

We prove the existence of equilibrium states for geometric potentials in a class of piecewise weakly convex interval maps. This class includes systems with indifferent fixed points and non-Markov partitions. Under additional hypotheses we…

We give a generally covariant description, in the sense of symplectic geometry, of gauge transformations in Batalin-Vilkovisky quantization. Gauge transformations exist not only at the classical level, but also at the quantum level, where…

Whereas in a coordinate-dependent setting the Euler-Lagrange equations establish necessary conditions for solving variational problems in which both the integrands of functionals and the resulting paths are assumed to be sufficiently…

A gauge invariant quantization in a closed integral form is developed over a linear phase space endowed with an inhomogeneous Faraday electromagnetic tensor. An analog of the Groenewold product formula (corresponding to Weyl ordering) is…

Any solution to the Yang-Baxter equation yields a family of representations of braid groups. Under certain conditions, identified by Turaev, the appropriately normalized trace of these representations yields a link invariant. Any…

Given a nondegenerate harmonic structure, we prove a Poincar\'e-type inequality for functions in the domain of the Dirichlet form on nested fractals. We then study the Hajlasz-Sobolev spaces on nested fractals. In particular, we describe…

In this paper we analyze two higher-derivative theories, the generalized electrodynamics and the Alekseev-Arbuzov-Baikov's effective Lagrangian from the point of view of Faddeev-Jackiw sympletic approach. It is shown that the full set of…

We derive formulas and algorithms for Kitaev's invariants in the periodic table for topological insulators and superconductors for finite disordered systems on lattices with boundaries. We find that K-theory arises as an obstruction to…

We study the physical content of quadratic diff-invariant Lagrangians in arbitrary dimensions by using covariant symplectic techniques. This paper extends previous results in dimension four. We discuss the difference between the even and…

Kitaev's quantum double models in 2D provide some of the most commonly studied examples of topological quantum order. In particular, the ground space is thought to yield a quantum error-correcting code. We offer an explicit proof that this…

Two-dimensional Euler insulators are novel kind of systems that host multi-gap topological phases, quantified by a quantised first Euler number in their bulk. Recently, these phases have been experimentally realised in suitable…

Zeta-function regularization is applied to complete a recent analysis of the quantized electromagnetic field in the presence of boundaries. The quantum theory is studied by setting to zero on the boundary the magnetic field, the…

We show that the space of observables of test particles carries a natural Jacobi structure which is manifestly invariant under the action of the Poincar\'{e} group. Poisson algebras may be obtained by imposing further requirements. A…

We provide a classification of type AII topological quantum systems in dimension d=1,2,3,4. Our analysis is based on the construction of a topological invariant, the FKMM-invariant, which completely classifies "Quaternionic" vector bundles…

By considering spaces of directed Jacobi diagrams, we construct a diagrammatic version of the Etingof-Kazhdan quantization of complex semisimple Lie algebras. This diagrammatic quantization is used to provide a construction of a directed…

Master character of the multidimensional homogeneous Euler equation is discussed. It is shown that under restrictions to the lower dimensions certain subclasses of its solutions provide us with the solutions of various hydrodynamic type…

We construct finite dimensional families of non-steady solutions to the Euler equations, existing for all time, and exhibiting all kinds of qualitative dynamics in the phase space, for example: strange attractors and chaos, invariant…

The Cauchy problem is studied for the self-adjoint and non-self-adjoint Schroedinger equations. We first prove the existence and uniqueness of solutions in the weighted Sobolev spaces. Secondly we prove that if potentials are depending…

Given a finite dimensional representation of a semisimple Lie algebra there are two ways of constructing link invariants: 1) quantum group invariants using the R-matrix, 2) the Kontsevich universal link invariant followed by the Lie algebra…

We establish an equivariant generalization of the Novikov inequalities which allow to estimate the topology of the set of critical points of a closed basic invariant form by means of twisted equivariant cohomology of the manifold. We apply…