Showing papers in "Lettere Al Nuovo Cimento in 1979"

Model of quantum statistics in terms of a fluid with irregular stochastic fluctuations propagating at the velocity of light: A derivation of Nelson’s equations

Abstract: Wi th in the f rame of t he genera l discussion on the pr inciples and phys ica l con ten t of q u a n t u m mechanics (QM) one the mos t in te res t ing branches since 1952 deals w i th the possible s tochast ic na tu re of i ts associa ted stat is t ics . An increas ing set eI resul ts (~'~) have now es tabl ished s t r iking fo rmal s imilar i t ies w i th classical models of s tochast ic t heo ry such as Markov processes (~,5). Two basic obstacles r e m a i n however , which have p reven ted unt i l now the comple t ion of t he main s ta t i s t ica l in t e rp re ta t ion of QM in t e rms of real phys ica l s tochast ic mot ions . The first obstacle is t he exis tence of a wrong sign (fronl the classical po in t of v iew) in the s tochast ic vers ion of Newton ' s second law: a sign which is clearly necessary to der ive SchrSdingertypc w a v e equat ions . For example in lhe no ta t ions of de la Pef ia and Cet to (a) Newton ' s law takes t he form

On the theoretical reliability of a three-temporal Lorentz transformation

Abstract: Let us consider the following fmldamen ta l postulates of special re la t iv i ty : a) o rd inary space is three-dimensional and Eucl idean, b) light speed is invariant . As ~ direct consequence of a), two general geometr ical requi rements should still be fulfilled even in the relat ivis t ical f ramework: i) Any (pointlike) object which is free (i.e., subjected to no force) has three degrees of freedom when moving in (empty) space. Namely , in order tha t it.s ( ins tantaneous) spat ial posi t ion m a y be univocal ly determined, i t always needs to be assigned a number of three i ndependen t funct ions of t ime. ii) The mot ion of a n y free (pointlike) object can always be characterized by three independent {Cartesian) veloci ty components whose m u t u a l orthogonality requires any variation of each one of t hem to cause by itself no change in the remain ing two components. On the other h,md, by a caroful inspect ion, i t is easy to realise tha t neither (i)) nor (ii)) would seem to be ful ly satisfied by the s t andard k inemat ics of any free photon. In fact, let us suppose, e.g., t ha t ~ given free photon, emi t t ed a.t t ime t = 0 from the origin of (our) frame ]s y, z), is t rave l l ing on the xy-plane. I f the a-co-ordinate is neglected, its motion will be rclar ivis t ieal ly described by the two equat ions

On some spectral problems and isospectral evolutions connected with the classical string problem: II: Evolution equation

Abstract: Needless to say, eq. (1) can be writ ten as S u + v u = 0 by setting ~ = q-t, and u = q 89 so that the spectral problem defined by (1) is also that of S. Besides, it is sound to look for isospectral evolutions since ~ is not determined by the spectrum. Thus, normalizing constants, for instance, are allowed to vary freely. Now let us allow ~ to depend on a parameter t. The well-known Lax's method tells us that the spectrum is invar iant if, for a certain antisymmetric operator B, the evolution of ~ follows the law:

Strong gravity with torsion: Some cosmological deduction

Abstract: Recently i t has been pointed out (1.~) tha t the s t rong-gravi ty theory (3) provides the physical basis for the large-number hypothesis of Dirac (4). The purpose of the present paper is to show that , introducing spin and torsion into the s t rong-gravi ty equations according to the Einstein-Cartan formalism (5), the Dirac law can be extended also to the angular momentum, an4 the total spin of the Universe may be evaluate4 and related to the IIubble radius. If one considers the Universe and a hadron as two physical systems internal ly governed by similar laws, differing only for a scale-factor which carries the Newton gravi ta t ional field into the s trong-gravity field (6.s), one is led to assume tha t the hadronic s trong-gravity potent ia l q~(h)~kfm/rc 2 is of the same order of magnitude as the gravi ta t ional potcnt ial of the Universe ~ ( u ) ~ GM/Rc 2, and the following relat ion is deduced (1.2,6,7):

Eigenvectors of a matrix related to the zeros of hermite polynomials

Abstract: Let x sub(j) indicate the j-th zero of the Hermite polynomial Hsub(n)(x). Define the hermitian matrix L(THETA), of rank n, by the formula Lsub(jK)(THETA) = ..delta..sub(jK)x sub(j)cos THETA + i (1-..delta..sub(jK)) (x sub(j)-x sub(k))/sup -1/ sin THETA. It was recently proved that the eigenvalues of L(0) are independent of THETA (and therefore coincide with the zeros x sub(j)). The eigenvectors corresponding to these eigenvalues are now exhibited.

Tagging direct neutrinos. A first step to neutrino tagging

Abstract: As it is well known, high-energy neutrino investigations are performed by using neutrino beams from ~ and K decays ( 7 : ~ , K ~ ) , that is by letting the pions and the kaons decay over a large distance (the so-called decay length). The possibility of using tagged-neutrino beams in high-energy experiments must have occurred to many people. In tagged-neutrino experiments it should be required that the observed event due to the interaction of the neutrino in the neutrino detector would properly coincide in time with the act of neutrino creation (~--~v, K ~ , K ~ e w : .... ). Of course, in tagged-neutrino experiments the properties of neutrino beams (type, direction and energy) will be much better known than in the experiments performed so far. The main difficulty in designing such a facility is that the effective neutrino source (which is also the source of the charged particles to be detected in coincidence with the neutrino event) has a length equal to the decay length (of the order of hundreds of metres). In spite of the difficulties it seems that sooner or later such facilities will be available at various high-energy accelerators. Naturally such a (( maximum ~) programme would provide an extremely useful facility. Since the main difficulty in designing a tagged-neutrino facility is connected with the (large) scale of the decay length involved, let us turn our attention to such neutrino experiments, in which the decay length is deliberately shortened, that is to (( beam dump ~> experiments. In such experiments direct neutrinos are looked for, that is neutrinos which are neither produced in pion nor in kaon decays. In the present note I am suggesting a relatively simple device, a sort of (~ minimum ~ neutrino tagging programme, which could be put to work without very serious difficulties in beam dump experiments. Direct neutrino experiments have been proposed (L2) a long time ago and were even performed at a very low level of sensitivity (s). At the Neutrino-75 Conference

Rigorous second-order cumulant expansion

Abstract: In several occasions (typically in the quantum-mechanical cases) the random variables of a many-body stochastic process are q-number variables rather than c-numbers. The canonical ensemble part i t ion function, which can be thought of as the moment generating function for the interaction part of the hamil tonian H of the system, is usually computed through a cumulang cluster expansion (1). Suck an expansion however is always performed under the assumption that the interaction part of H might be considered small enough to be kept only up to the first perturbative order. The motivation is twofold. On one hand the interaction energy is indeed often muck smaller than the single-particle energy. On the other hand the interaction part of H is very frequently restricted to a linear combination of pair interaction terms, and the lat ter circumstance allows a very convenient and elegant procedure whereby the problem is reduced to a two-particle problem. Briefly, the argument goes as follows (2). Let