V. de Alfaro

Conformal Invariance in Quantum Mechanics

SummaryThe properties of a field theory in one over-all time dimension, invariant under the full conformal group, are studied in detail. A compact operator, which is not the Hamiltonian, is diagonalized and used to solve the problem of motion, providing a discrete spectrum and normalizable eigenstates. The role of the physical parameters present in the model is discussed, mainly in connection with a semi-classical approximation.RiassuntoSi studiano le proprietà di una teoria invariante conforme in cui il «campo» dipende solo da una dimensione temporale. Un operatore compatto, che non coincide con l’hamiltoniana, è diagonalizzato ed usato per risolvere il problena del moto. Esso ha uno spettro discreto ed autostati normalizzabili. Si discute il ruolo dei parametri fisici del modello, anche in rapporto ad un’approssimazione semiclassica.РезюмеВ случае одного временного измерения подробно обсуждаются свойства теории поля, инвариантной относительно полностью конформной группы. Диагонализуется компактиый оператор, который не является Гамильтонианом. Этот оператор используется для решения проблемы движения в случае дискретного спектра и нормализуемых собственных состояний. Обсуждается роль физических параметров, присутствующих в модели, в основном, в связи с полуклассическим приближением.

On the neutralino as dark matter candidate. I. Relic abundance

Abstract The neutralino relic abundance is evaluated for a wide range of the neutralino mass, 20 GeV ≤ m x ≤ 1 TeV, by taking into account the full set of final states in the neutralino-neutralino annihilation. The analysis is performed in the Minimal SuSy Standard Model; it is not restricted by stringent GUT assumptions but only constrained by present experimental bounds. We also discuss phenomenological aspects which are employed in the companion paper (Part II. Direct detection) where the chances for a successful search for dark matter neutralino are investigated.

On the neutralino as dark matter candidate. II. Direct detection

Evaluations of the event rates relevant to direct search for dark matter neutralino are presented for a wide range of neutralino masses and for various detector materials of preeminent interest. Differential and total rates are appropriately weighted over the local neutralino density expected on theoretical grounds.

Search for neutralino dark matter with NaI detectors

Theoretical predictions for neutralino dark matter in the framework of the minimal SUSY standard model are compared with recent results of a direct search for dark matter with NaI detectors. Perspectives for a future investigation by this kind of detectors are also discussed.

Indirect search for neutralinos at neutrino telescopes

Abstract Under the assumption that cold dark matter is composed (at least partially) of neutralinos, capture and pair annihilation of these particles in the sun and the earth are evaluated in the framework of the minimal SUSY extension of the standard model (MSSM), taking into account the effects due to the radiative corrections to the masses of the Higgs bosons. The flux of the neutrinos produced in the neutralino-neutralino annihilation and the relevant rate of the muons generated by neutrino conversion in the earth and crossing a detector upwardly are calculated. The present experimental limits from underground detectors are employed to set constraints on the MSSM parameters, and the capabilities of future neutrino telescopes to further explore regions in parameter space are analyzed.

Operator ordering and supersymmetry

Abstract We investigate supersymmetric quantum mechanics in curved space. In particular we discuss, in the framework of the canonical formulation, the role of supersymmetry (SUSY) and of invariance under general coordinate transformations (GCT) in solving the operator ordering ambiguity. It is shown that GCT invariance is instrumental to achieve such result. We also examine the connection with the Weyl ordering of operators and the relevance of our results for the path integral approach.

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 quantum theory

Abstract We offer a systematic treatment of the connection between stochastic quantization and supersymmetry. This is done in the original Nicolai-Parisi-Sourlas approach and by use of the “stochastic identities” which can be derived as a consequence of the supersymmetry invariance both of the action and of the vacuum. We deal extensively with the cases of quantum mechanics, scalar field theory and gauge theory. One of the main results is the presence of a reduced set of stochastic identities even when a local Nicolai transformation does not exist.

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.

Potential model of deuteron photodisintegration and Mandelstam representation

SummaryIn this paper the analytic properties of the fixed angular momentum amplitudes of the deuteron photodisintegration are investigated by a potential model. It is shown that these properties agree with those obtained by a Mandelstam representation with anomalous thresholds, as argued by perturbation arguments. This is an argument in favour of the validity of general dispersion techniques also in nuclear physics.RiassuntoIn questo lavoro vengono studiate le proprietà analitiche dell’ampiezza d’urto di foto disintegrazione del deutone a fissato momento angolare, mediante un modello di teoria del potenziale. Si dimostra che esiste un completo accordo tra le proprietà così ottenute e quelle derivanti dalla rappresentazione di Mandelstam, nel caso in cui siano presenti soglie anomale, ricavate con argomenti perturbativi. Si ha così un argomento in favore della validità generale delle tecniche dispersive, anche in fisica nucleare.