Measurements to test the neutrality of matter by acoustic means are reported. The apparatus is based on a spherical capacitor filled with gaseous SF_6 excited by an oscillating electric field. The apparatus has been calibrated measuring the electric polarizability. Assuming charge conservation in the β decay of the neutron, the experiment gives a limit of \epsilon_{p−e} <= 1 × 10−21 for the electron-proton charge difference, the same limit holding for the charge of the neutron. Previous measurements are critically reviewed and found to be inaccurate
The consequences of the invariance of the superpotential under the complexifϊcation G c of the internal symmetry group on the determination of the possible patterns of symmetry and supersymmetry breaking are established in a globally supersymmetric theory. In particular, in the case of global internal symmetry we show that a vacuum associaated to a point z, where G/ φ G\ is always degenerate with a vacuum associated to a point z', where G\, = G z c ; all the other degeneracies of the minimum of the potential on an orbit of G c are also determined and shown to be completely removed when the internal symmetry is gauged. The zeroes of the D-term of a supersymmetric gauge theory are characterized as the points of the closed orbits of G c which are at minimum distance from the origin; at these pointsIt is rigorously proved that the minimum of the potential is zero if the gradient of the superpotential vanishes somewhere. It is also shown that the D-term necessarily vanishes at the minimum of the potential if the direction of spontaneous supersymmetry breaking is invariant by G.
If {p_1(x), ..., p_q(x)} is a minimal integrity basis of the ideal of polynomial invariants of a compact coregular linear group G, the orbit map p=(p_1(x) .... ,p_q(x)):R^n->R^q,\ud
yields a diffeomorphic image S = p(R^n) \subset R^q of the orbit space R^n/G. Starting from this fact, we point out some properties which are common to the orbit spaces of all the compact coregular linear groups of transformations of R^n. In particular we show that a contravariant metric matrix P(p) can be defined in the interior of S, as\ud
a polynomial function of (p_1, ...,p_q). We prove that the matrix P(p), which characterizes the set S, as it is positive semi-definite only for p \in S, can be determined as a solution of a canonical differential equation, which, for every compact coregular linear group, depends only on the number q and on the degrees of the elements of the minimal integrity bases. This allows to determine all the\ud
isomorphism classes of the orbit spaces of the compact coregular linear groups through a determination of the equivalence classes of the corresponding matrices\ud
P(p). For q<3 (orbit spaces with dimensions < 3), the solutions P(p) of the canonical equation are explicitly determined and the number of their equivalence\ud
classes is shown to be finite. It is also shown that, with a convenient choice of the minimal integrity basis, the polynomial matrix elements of P(p) have only integer\ud
coefficients. Arguments are given in favour of the conjecture that our conclusions hold true for all values of q. Our results are relevant and lead to universality properties in the physics of spontaneous symmetry breaking
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