On Integrability and Pseudo-Hermitian Systems with Spin-Coupling Point Interactions

We study the pseudo-Hermitian systems with general spin-coupling point interactions and give a systematic description of the corresponding boundary conditions for PT-symmetric systems. The corresponding integrability for both bosonic and fermionic many-body systems with PT-symmetric contact interactions is investigated.Comment: 7 page

The confidence channel for the transmission of shocks

It is widely known that agents confidence is closely linked to macroeconomic cycles. A confidence channel may therefore have a significant impact in accelerating and amplifying the transmission of shocks accross borders. We endeavor to find empirical proof of the existence of a confidence channel between G7 countries (and Spain). This paper centers around the concept of a contagion of confidence from “large countries” to “small countries”. I apply instrumental-variable regressions to OECD standardized Consumers and Business Confidence measures, in order to investigate the relationship between the confidence series of all G7 countries, and Spain. Macroeconomic variables are included in these regressions to control for domestic causes of confidence changes. We find that, even after having controlled for domestic macroeconomic causes of confidence level variations, the level of confidence of agents in large countries does have an influence on the level of confidence of agents in smaller countries.confidence channel, contagion, confidence shock.

Symplectic Geometry on Quantum Plane

A study of symplectic forms associated with two dimensional quantum planes and the quantum sphere in a three dimensional orthogonal quantum plane is provided. The associated Hamiltonian vector fields and Poissonian algebraic relations are made explicit.Comment: 12 pages, Late

Point Interactions: PT-Hermiticity and Reality of the Spectrum

General point interactions for the second derivative operator in one dimension are studied. In particular, ${\mathcal P \mathcal T}$-self-adjoint point interactions with the support at the origin and at points $\pm l$ are considered. The spectrum of such non-Hermitian operators is investigated and conditions when the spectrum is pure real are presented. The results are compared with those for standard self-adjoint point interactions.Comment: 17 page

A Note on Pseudo-Hermitian Systems with Point Interactions and Quantum Separability

We study the quantum entanglement and separability of Hermitian and pseudo-Hermitian systems of identical bosonic or fermionic particles with point interactions. The separability conditions are investigated in detail.Comment: 6 page

BRST Structures and Symplectic Geometry on a Class of Supermanifolds

By investigating the symplectic geometry and geometric quantization on a class of supermanifolds, we exhibit BRST structures for a certain kind of algebras. We discuss the undeformed and q-deformed cases in the classical as well as in the quantum cases.Comment: 14 pages, Late