A New Superconformal Mechanics

In this paper we propose a new supersymmetric extension of conformal mechanics. The Grassmannian variables that we introduce are the basis of the forms and of the vector-fields built over the symplectic space of the original system. Our supersymmetric Hamiltonian itself turns out to have a clear geometrical meaning being the Lie-derivative of the Hamiltonian flow of conformal mechanics. Using superfields we derive a constraint which gives the exact solution of the supersymmetric system in a way analogous to the constraint in configuration space which solved the original non-supersymmetric model. Besides the supersymmetric extension of the original Hamiltonian, we also provide the extension of the other conformal generators present in the original system. These extensions have also a supersymmetric character being the square of some Grassmannian charge. We build the whole superalgebra of these charges and analyze their closure. The representation of the even part of this superalgebra on the odd part turns out to be integer and not spinorial in character.Comment: Superfield re-define

Functional Approach to Classical Yang-Mills Theories

Sometime ago it was shown that the operatorial approach to classical mechanics, pioneered in the 30's by Koopman and von Neumann, can have a functional version. In this talk we will extend this functional approach to the case of classical field theories and in particular to the Yang-Mills ones. We shall show that the issues of gauge-fixing and Faddeev-Popov determinant arise also in this classical formalism.Comment: 4 pages, Contribution to the Proceedings of the International Meeting "Quantum Gravity and Spectral Geometry" (Naples, July 2-7, 2001

Universal Local symmetries and non-superposition in classical mechanics

In the Hilbert space formulation of classical mechanics (CM), pioneered by Koopman and von Neumann (KvN), there are potentially more observables that in the standard approach to CM. In this paper we show that actually many of those extra observables are not invariant under a set of universal local symmetries which appear once the KvN is extended to include the evolution of differential forms. Because of their non-invariance, those extra observables have to be removed. This removal makes the superposition of states in KvN, and as a consequence also in CM, impossible

A Dynamical Mechanism for the Selection of Physical States in `Geometric Quantization Schemes'

Geometric quantization procedures go usually through an extension of the original theory (pre-quantization) and a subsequent reduction (selection of the physical states). In this context we describe a full geometrical mechanism which provides dynamically the desired reduction.Comment: 6 page

Chiral Anomalies via Classical and Quantum Functional Methods

In the quantum path integral formulation of a field theory model an anomaly arises when the functional measure is not invariant under a symmetry transformation of the Lagrangian. In this paper, generalizing previous work done on the point particle, we show that even at the classical level we can give a path integral formulation for any field theory model. Since classical mechanics cannot be affected by anomalies, the measure of the classical path integral of a field theory must be invariant under the symmetry. The classical path integral measure contains the fields of the quantum one plus some extra auxiliary ones. So, at the classical level, there must be a sort of "cancellation" of the quantum anomaly between the original fields and the auxiliary ones. In this paper we prove in detail how this occurs for the chiral anomaly.Comment: 26 pages, Latex, misprint fixed, a dedication include

Is classical reality completely deterministic?

The concept of determinism for a classical system is interpreted as the requirement that the solution to the Cauchy problem for the equations of motion governing this system be unique. This requirement is generally assumed to hold for all autonomous classical systems. We give counterexamples of this view. Our analysis of classical electrodynamics in a world with one temporal and one spatial dimension shows that the solution to the Cauchy problem with the initial conditions of a particular type is not unique. Therefore, random behavior of closed classical systems is indeed possible. This finding provides a qualitative explanation of how classical strings can split. We propose a modified path integral formulation of classical mechanics to include indeterministic systems.Comment: Replace the paper with a revised versio

Optimal portfolio choice with path dependent labor income: the infinite horizon case

We consider an infinite horizon portfolio problem with borrowing constraints, in which an agentreceives labor income which adjusts to financial market shocks in a path dependent way. Thispath-dependency is the novelty of the model, and leads to an infinite dimensional stochasticoptimal control problem. We solve the problem completely, and find explicitly the optimalcontrols in feedback form. This is possible because we are able to find an explicit solutionto the associated infinite dimensional Hamilton-Jacobi-Bellman (HJB) equation, even if stateconstraints are present. To the best of our knowledge, this is the first infinite dimensionalgeneralization of Merton’s optimal portfolio problem for which explicit solutions can be found.The explicit solution allows us to study the properties of optimal strategies and discuss theirfinancial implications

Bilateral Severe Corneal Ulcer in a Patient with Lung Adenocarcinoma Treated with Gefitinib

We describe the case of Gefitinib-related bilateral corneal perforation. An 86-year-old female patient had bilateral painless and progressive vision loss due to neurotrophic corneal ulcer, following a 2-month treatment with Gefitinib, a selective epidermal growth factor receptor (EGFR) tyrosine kinase inhibitor for metastatic adenocarcinoma of the lung with confirmed EGFR gene mutation. She had no signs of ocular infection, inflammation, or lid problems to account for the development of corneal damage. Neurotrophic ulcer evolved into a frank perforation in one eye and an impending perforation on the other eye. EGFR inhibitors have been associated with dry eye, epithelial erosions, ulcerative keratitis, and corneal edema. However, to the best of our knowledge, this is the first case of bilateral severe corneal ulcer due to Gefitinib. The patient went on to have bilateral corneal graft surgery. This case aims to raise awareness among ophthalmologists and oncologists of the association between EGFR inhibitors, corneal neurotrophic ulcers, and possible evolution in corneal perforation

Hamilton Jacobi Bellman equations in infinite dimensions with quadratic and superquadratic Hamiltonian

We consider Hamilton Jacobi Bellman equations in an inifinite dimensional Hilbert space, with quadratic (respectively superquadratic) hamiltonian and with continuous (respectively lipschitz continuous) final conditions. This allows to study stochastic optimal control problems for suitable controlled Ornstein Uhlenbeck process with unbounded control processes

Electrical Characterization of Thin-Film Transistors Based on Solution-Processed Metal Oxides

This chapter provides a brief introduction to thin-film transistors (TFTs) based on transparent semiconducting metal oxides (SMOs) with a focus on solution-processed devices. The electrical properties of TFTs comprising different active layer compositions (zinc oxide, aluminum-doped zinc oxide and indium-zinc oxide) produced by spin-coating and spray-pyrolysis deposition are presented and compared. The electrical performance of TFTs is evaluated from parameters as the saturation mobility (μsat), the TFT threshold voltage (Vth) and the on/off current (Ion/Ioff) ratio to demonstrate the dependence on the composition of the device-active layer and on ambient characterization conditions (exposure to UV radiation and to air)