G. Furlan

Sum rules for strong interactions

Abstract Sum rules for strong interactions are derived from analyticity and high energy bounds for the scattering amplitudes of particles endowed with spin. Those bounds, much more stringent than for the spinless case, are strongly suggested by unitarity.

Superconvergence and current algebra

Abstract We consider some general features of the superconvergence sum rules and of their saturation. We treat also the problem of the structure of current algebra sum rules, discussing the presence of non Regge asymptotic behavior. Finally, we discuss current algebra and superconvergence sum rules for higher-spin targets, and their mutual connections.

Stochastic identities in supersymmetric theories

Abstract The correspondence between stochastic quantization and supersymmetry is reobtained for the quantum mechanics case by use of “stochastic identities”. The method is easily generalized to N =1 super Yang-Mills theory in the light cone gauge.

Quantum spinning particle in a curved metric

Abstract We show that the combined use of N=1 supersymmetry and general coordinate invariance allows to completely fix the operator ordering ambiguity for a non-relativistic interacting spinning particle.

Gibbs average in the functional formulation of quantum field theory

Abstract A new formulation of the euclidean functional approach to quantum field theory is proposed. It is based on functional integration over a Gibbs ensemble. This automatically ensures invariance with respect to general field transformations. The new momenta conjugate to the field variables perform naturally the role of the ghost fields required by the general consistency of the theory.

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.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 nonsupersymmetric 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 also have 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 o...

A new supersymmetric extension of conformal mechanics

Abstract In this paper a new supersymmetric extension of conformal mechanics is put forward. The beauty of this extension is that all variables have a clear geometrical meaning and the super-Hamiltonian turns out to be the Lie-derivative of the Hamiltonian flow of standard conformal mechanics. In this paper we also provide a supersymmetric extension of the other conformal generators of the theory and find their “square-roots”. The whole superalgebra of these charges is then analyzed in details. We conclude the paper by showing that, using superfields, a constraint can be built which provides the exact solution of the system.

Stochastic identities in the light cone gauge

Abstract The correspondence between stochastic quantization and supersymmetry is extended to N =1 gauge supersymmetry coupled with matter. This applies to N =2 extended gauge supersymmetry and also to N =1 SUSY in six dimensions. The special role of the light plane gauge is emphasized.

Vacuum effects in quantum field theory

We discuss some consequences of applying a procedure developed in a previous paper, to implement the conformal and general invariance of the functional integral. It is shown that spontaneous breaking of those symmetries is unavoidable; we consider in particular the linear σ-model, in the conformal limit, and the Einstein gravitation and derive some simple relations among the vacuum expectation value, a phenomenological cut-off and the Lagrangian constants.