Showing papers in "Lettere Al Nuovo Cimento in 1972"

Analytic renormalization via continuous space dimension

Abstract: In recent ycars analytic techniques have been extensively used in the renormalization of finite-order perturbation theory (1). This letter provides yet another analytic approach, which will be shown immediately to be equivalent to the wcll-knoval additive renormalization by counter terms (2). To place this work in perspective, wc shall s tar t by briefly reviewing the current situation and the motivations for further study. Roughly speaking, renormalization may be described as follows. A generic Feynman integrM is formMly defined by a (possibly diw'~rgent) integral, which is then modified into a well-defined, regularized integral by introducing additional parameters. A specific prescription is then given to remove the regularizing parameters and obtain a finite result, called renormalized integral. Because of their role, the reglflarizh~g parameters may be called generalized cut-offs, even in the schemes, such as analytic renormalization, where they may take complex values. Within any scheme, it must be shown that the difference between the original formal Feynman integral and the renormMized one, can be traced to the introduction of Lagrangian counter terms. This is necessary for the physical interpretat ion of the manipulat ions and also, perhaps more important , to guarantee, at least at a formal level, that the resulting renorrealized pertnrbat ive series originates a uni tary S-matrix. Any almlytic renormalization is an obvious candidate to renormalize the so-called nonrenormalizable theories, where the additive renormalization fails for the occurrence of infinite counter terms. Very recently the equivalence between analytic renormalization and additive renormalization has been proved; each recipe may be transformed into the other one, modu/us a finite renormaliz~ation (a).

Nonmeasurability of the baryon number of a black-hole

Abstract: One of the most astonishing features of gravitational collapse is the presumed (( ideal perfect ion, of the final state. All theoretical evidence favors the Israel-Carter conjecture, which says that the most general final configuration of gravitational collapse is a Kerr-Newman black-hole. If this conjecture is true, then it follows that the only measurable quantum numbers of a black-hole are mass, charge and angular moment u m t h e s e three quantities being the only adjustable parameters appearing in the KerrNewman metric. Any other particularity tha t the collapsing matter had fades away. Now, baryon number, one of the key quantities of particle physics is not in the list. The validity of the Israel-Carter conjecture implies then that the baryon number of a blaek-hole is not observable and consequently, as JOHN WHEELER says (1), that the law of conservation of baryons-i f not violated--is transcended in blaek-hole physics. However, as pointed out by BEKENSTEIN (2), the proofs of increasing generality of the * uniqueness of a black hole ,, given by CARTER (3), HAWKING (4), ISIr (5) and WALD (3), have not explicitly taken into account the possible effect of strong interactions which arc precisely the characteristic interaction of the baryons and which are per excellence the ~ measuring tools , for baryon number. An important step in this direction has been taken by BEKENSTEIN (3) himself who has been able to show tha t no classical meson fields, which meet some regularity conditions, can exist outside of a black-hole. Although this result probably implies tha t a black-hole cannot have any interactions mediated by mesons, even when the quantum nature of the fields is taken into account, an approach dealing with a quantum meson field from the very beginning would help to clarify the matter. Such a t reatment is given below.

More about lorentz transformations and tachyons: answer to the comments by ramachandran, tagare, and kolaskar.

Abstract: I n a no t e (1), RAMACHA~DI~AN et al. h a v e c o m m e n t e d a b o u t a r ecen t , b r ie f l e t t e r b y 0LKHOVSKY a n d one of us (2), r ega rd ing L o r e n t z t r a n s f o r m a t i o n s (LT) a n d fas ter t han l i gh t -pa r t i c l e s (3.~). E v e n if t h e i r c o m m e n t s d id n o t a p p e a r to us to be v e r y p e r t i n e n t , we are grafefu l to t h e m for th i s occasion, since i t allows us to c lar i fy our p r e l i m i n a r y l e t t e r (2), wh ich r e m a i n e d indeed a t t h e surface of t h e p rob lems . I n pa r t i cu la r , we shal l show t h a t ou r p rev ious cons ide ra t ions can be founded m u c h b e t t e r t h a n in ref. (2).