V. De Sabbata

Strong gravity and Dirac numbers

We will consider some relat ions tha t one may obta in in considering the s trong gravi ty . As i t is well known SALA)~ and coworkers (1-:~) are led to consider the g rav i ta t iona l in teract ion media ted via, a heavy meson in analogy to quan tum eleetrodynamics . In the vector model of e lee t rodynamies , the pro ton no longer is the pure carrier of in te rac t ion ; the pho ton in terac ts only wi th leptons d i rec t ly and not wi th protons. The pho ton tu rns into a p-meson which in tu rn interacts wi th the pro ton direct ly (but not leptons) t h a t is:

Strong Gravity and Weak Interactions

The strong gravity contribution to the nucleonic axial-vector form factor is evaluated in the nonrelativistic limit and in the approximation of exactSU3 symmetry. It is suggested also that the anomalous experimental results on the value of the axial coupling constant, in very light nuclei, may be explained as being an effect due to strong gravitational interactions.

Strong gravity with torsion: Some cosmological deduction

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):

The angular momentum of celestial bodies and the fundamental dimensionless constants of nature

SummaryIt is suggested a possible connection between two empirical astrophysical laws concerning the angular momentum of celestial bodies. It is shown that both relations seem to indicate that the fine-structure constant α is the typical dimensionless parameter not only of atomic physics, but also of gravitational physics.

Strong gravity with torsion and the Cabibbo angle

The classical field equations of the strong gravity theory are modified by introducing spin and torsion so as to resemble the field equations of the Einstein-Cartan theory. The effects of the hadronic spin upon the strong metric are evaluated using a semiclassical approximation, and it is pointed out that the torsion contributions are not negligible. A possible interpretation of the Cabibbo angle as a strong gravity correction of the weak semileptonic Lagrangian is suggested.

A « semi-minimal » coupling principle for the electromagnetic field in a space with torsion

In order to preserve local gauge invar iance , i t is well known (1-7) tha t a gauge field cannot be min imal ly coupled to the geome t ry of a space wi th a nonsymmet r i c connect ion such as a R iemann-Car tan space U 4 I f we t ry to make compat ible min imal coupling wi th gauge invar iance in the case of the e lec t romagnet ic (e.m.) field, we are compelled to impose a rb i t ra ry constraints upon torsion (s), or to modify the usual concept of gauge t ransformat ion and to allow torsion propaga t ion in v a c u u m (9). Since in this w a y we get over the l imits of the Eins te in-Car tan theory, where torsion is s t r ic t ly de te rmined by spin dis t r ibut ions and cannot p ropaga te outside ma t t e r (1), i t seems t h a t the only way to recover the e.m. gauge invar iance, in the f ramework of this theory, is to replace the min imal coupl ing principle (MCP) wi th some other empir ical prescription. The s implest hypothesis to preserve gauge invar iance is to assume tha t there is no coupling at all be tween torsion and the e.m. field, i.e. t h a t the Maxwell equat ions , wr i t ten in a ,U4, are exact ly the same as if t hey were wr i t t en in the R iemann space V 4 obta ined f rom U 4 by pu t t ing torsion to zero. This prescr ipt ion finds a ve ry s t rong and na tura l just i f icat ion in the f ramework of the Poincard gauge field theories of g rav i ta t ion (lo), where the gauge fields (like the e.m. potent ia l Ak) are t rea ted as Poineard scalars and then do no t couple to the connect ion; one can say, then, t ha t (1,5.6).

Twistors, torsion and quantization of space-time

SummaryThe analogies between twistors and torsion are developed. TheSL(2,C) group of transformations is used to suggest a unified link between the approaches. The role of space-time defects in the quantization of space-time is clarified and commutation relations between conjugate twistor variables suggested. Finally the incorporation of mass and charge as well as supersymmetry in the formalism is considered.

The role of spin in a Hermitian theory of gravity

SummaryWe propose a Hermitian gravitational theory in which the skew part of the metric tensor is generated by the spin density of matter, and we investigate the gauge invariance of the Lagrangian in the weak-field approximation. We find a close analogy between our second-order Lagrangian and the linearized Lagrangian of an alternative off-shell formulation ofN=1 supergravity.

On the possibility of speed higher than c inside hadronic matter

SummaryThe possibility of light propagation with a speed higher than c through a hadronic medium is related to the breaking of an internal gauge symmetry on a curved metric background with a nonzero cosmological constant.

Torsion contributions to the magnetic field of a spinning charge

In fact , even if torsion does no t di rect ly in terac t wi th the e lect romagnet ic field, there is a coupl ing between torsion and the v i r tua l pairs of fermions, produced according to the v a c u u m polar izat ion effect, which gives rise to the photontorsion in terac t ion (1) displayed in (1) (notice tha t we have assumed a flat metr ic tensor, since we wan t to eva lua te the specific torsion contr ibut ions , apar t f rom the usual R ieman iann terms (2)). We like to stress, in this paper , t ha t an electric charge, in te rac t ing wi th a cons tan t torsionic background, can produce a s tat ic magnet ic field even in its rest system. Consider in fact a poin t l ike charge distr ibut ion, ~ ( x ) ~ e~(x), placed in an ex te rna l torsionic background which we assume generated, according to the Einste inCaf tan theory, by a cons tant semi-classical spin d is t r ibut ion (a) at rest wi th the charge density. We have then Qkuk~0, where u k is the 4-veloci ty vector of the charged part icle.