Related papers: Antibrackets, Supersymmetric $\sigma$-Model and Lo…

We discuss the target space pseudoduality in supersymmetric sigma models on symmetric spaces using two different methods, orthonormal coframe and component expansion. These two methods yield similar results to the classical cases with the…

Directional notions in topology and analysis naturally lead to nonsymmetric structures such as quasi-metrics, quasi-uniformities, and modular spaces. In these settings, classical notions of connectedness and completion based on symmetric…

Instead of the conventional construction of symmetric and antisymmetric states by abruptly projecting with the symmetrizer or antisymmetrizer, this paper investigates rapid but continuous symmetrization via environment-induced decoherence.…

We investigate various types of symmetries and their mutual relationships in Hamiltonian systems defined on manifolds with different geometric structures: symplectic, cosymplectic, contact and cocontact. In each case we pay special…

Dynamical localization, i.e. the absence of secular spreading of a quantum or classical wave packet, is usually associated to Hamiltonians with purely point spectrum, i.e. with a normalizable and complete set of eigenstates, which show…

Models of disorder with a direction (constant imaginary vector-potential) are considered. These non-Hermitian models can appear as a result of computation for models of statistical physics using transfer matrix technique or describe…

In the broad context of physics ranging from classical experimental optics to quantum mechanics of unitary as well as non-unitary systems there emerge interesting phenomena related to the presence of the so called Kato's exceptional points…

Harmonic maps from Riemann surfaces arise from a conformally invariant variational problem. Therefore, on one hand, they are intimately connected with moduli spaces of Riemann surfaces, and on the other hand, because the conformal group is…

We discuss the properties of superintegrable Hamiltonian systems, in particular those that admit separation of variables in cartesian coordinates. We show that the superintegrability of such potentials is equivalent to the isochronicity of…

We describe the symplectic structure and Hamiltonian dynamics for a class of Grassmannian manifolds. Using the two dimensional sphere ($S^2$) and disc ($D^2$) as illustrative cases, we write their path integral representations using…

This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…

The mathematical framework for an exact quantization of the two-dimensional coset space sigma-models coupled to dilaton gravity, that arise from dimensional reduction of gravity and supergravity theories, is presented. Extending previous…

Gauged linear sigma models with (0,2) supersymmetry allow a larger choice of couplings than models with (2,2) supersymmetry. We use this freedom to find a fully linear construction of torsional heterotic compactifications, including models…

The connection between symmetries and linearizations of discrete-time dynamical systems is being inverstigated. It is shown, that existence of semigroup structures related to the vector field and having linear representations enables…

We investigate the dynamics of nonclassical states of light in coupled optical structures and we demonstrate a number of intriguing features associated with such arrangements. By diagonalizing the system's Hamiltonian, we show that these…

The concept of supersymmetry developed in particle physics has been applied to various fields of modern physics. In quantum mechanics, the supersymmetric systems refer to the systems involving two supersymmetric partner Hamiltonians, whose…

Reversible part of evolution equations of physical systems is often generated by a Poisson bracket. We discuss geometric means of construction of Poisson brackets and their mutual coupling (direct, semidirect and matched-pair products) as…

Partial symmetries are described by generalized group structures known as symmetric inverse semigroups. We use the algebras arising from these structures to realize supersymmetry in (0+1) dimensions and to build many-body quantum systems on…

The Hamiltonian and Lagrangian formalisms offer two perspectives on quantum field theory. This paper sets up a framework to compare these approaches for the supersymmetric sigma model. The goal is to use techniques from physics to construct…

This article studies some features of quantum field theories with internal supersymmetry, focusing mainly on 2-dimensional non-linear sigma models which take values in a coset superspace. It is discussed how BRST operators from the target…