Superconnections and internal supersymmetry dynamics.

In previous papers we proposed a theory of internal supersymmetry using the superalgebra su(n/1) to give rise to a unified structure that included quarks and leptons in 2n-5 generations. In the present paper we suggest that the notion of superconnections as introduced by Quillen provides a natural setting for the dynamics of an internally supersymmetric theory with the Higgs field occurring as the "zero-th order part" of the superconnection. The Higgs mechanism enters quadratically into the curvature of the superconnection and hence quartically into the Lagrangian. The supercovariant derivative gives a coupling of the Higgs field to the matter field similar to that put in "by hand" in the Lagrangian of the Weinberg-Salam theory.

The evolutionary role of research.

Every evolutionary process consists in the stochastic occurrence of quasi-random transitions from a given ordered system, with some criteria of stability ensuring that a few of the modified system survive, forming new ordered system that can serve as departure points for a further evolutionary step. In the evolution of human societies, scientific research fulfills the role of the quasi-random mutations.

Classical geometric resolution of the Einstein-Podolsky-Rosen paradox.

I show that, in the geometry of a fiber bundle describing a gauge theory, curvature and parallel transport ensure and impose nonseparability. The "Einstein-Podolsky-Rosen paradox" is thus resolved "classically." I conjecture that the ostentatiously "implausible" features of the quantum treatment are due to the fact that space-time separability, a basic assumption of single-particle nonrelativistic quantum mechanics, does not fit the bundle geometry of the complete physics.

Exterior gauging of an internal supersymmetry and SU(2/1) quantum asthenodynamics.

A formally unitary Lagrangian model gauging an internal supersymmetry is proposed. The even subalgebra is gauged as a Yang-Mills theory, while the odd generators are gauged-according to Freedman's method-by skew tensor fields, equivalent dynamically to scalar Higgs fields. Chiral fermions are incorporated by following Townsend's construction and form irreducible supermultiplets graded by their helicity. The application to quantum asthenodynamics is discussed.

Comparative studies of the aromatization of testosterone and epitestosterone by human placental aromatase.

The aromatization of epitestosterone (17 alpha-hydroxy-4-androsten-3-one) and testosterone by lyophilized human placental microsomes was studied. Upon incubation of epitestosterone, 12% was converted to 17 alpha-estradiol, 15% to 19-keto-epitestosterone (17 alpha-hydroxy-4-oxo-4-androsten-19-al), 10% to 19-hydroxyepitestosterone (17 alpha, 19-dihydroxy-4-androsten-3-one), and about 10% to several unidentified products. A similar incubation with testosterone resulted in 60% conversion to 17 beta-estradiol; 30% was unchanged. At increasing substrate concentrations (0.1-50 microM), the aromatization rate of epitestosterone increased gradually and did not reach a plateau, whereas aromatization rate of testosterone plateaued at about 3 microM. The presence of either testosterone or 17 beta-estradiol in concentrations 0.1-10 times the concentration of epitestosterone inhibited the aromatization of epitestosterone by about 70%, while the aromatization of testosterone was not inhibited by either epitestosterone or 17 alpha-estradiol. Lyophilization of fresh microsomes or storage of the lyophilized microsomes at -20 C greatly reduced the aromatizing activity upon epitestosterone but not upon testosterone. These results suggest that the aromatizing system for epitestosterone is different from that for testosterone.

Internal supersymmetry and unification.

We construct a family of finite-dimensional representations of the superalgebra sl(n/m) that depend on an integer parameter for m > 1 and on a complex parameter, b, for m = 1. We describe some models of elementary particles for sl(2/1), sl(3/1), and sl(5/1). This involves the choice of the parameter b and the choice of the operators I(3) (the third component of the weak left-handed isospin) and U (the weak hypercharge). These must commute, and are related to the electric charge by the usual formula Q = I(3) + (1/2)U. In particular, taking I(3) to be in its standard form in su(2) subset sl(5) subset sl(5/1) and requiring that U commute with color su(3) subset sl(5) subset sl(5/1) leaves three free parameters, two for the choice of U and one for the choice of b. We show that there are just two possible choices of these parameters yielding exactly all 32 quark and lepton charges: the Georgi-Glashow U in su(5), corresponding to U(1,-(2/3)) and arbitrary b and U(0,(1/3)) negated set membership su(5), with b = 2. We provide a general construction of representations of sl(n/1) consisting exactly of sequences of generations of quarks and leptons.

Geometrical gauge theory of ghost and Goldstone fields and of ghost symmetries.

We provide a geometrical identification of the ghost fields, essential to the renormalization procedure in the non-Abelian (Yang-Mills) case. These are some of the local components of a connection on a principal bundle. They multiply the differentials of coordinates spanning directions orthogonal to those of a given section, whereas the Yang-Mills potential multiplies the coordinates in the section itself. In the case of a supergroup, the ghosts become commutative for the odd directions, and represent Nambu-Goldstone fields. We apply the results to chiral "flavor" SU(3)(L) x SU(3)(R) and to SU(2/1). The latter reproduces a highly constrained Weinberg-Salam model.

Gravitational interaction of hadrons and leptons: Linear (multiplicity-free) bandor and nonlinear spinor unitary irreducible representations of SL(4R).

We review two possible affine extensions of gravity connected to the strong interactions. In the metric affine theory, torsion and nonmetricity do not propagate, gravitation is effectively unmodified, and the observed approximate conservation of hadron intrinsic hypermomentum-i.e., scaling, SU(6), and Regge trajectories-is due to the GL(4,R) band-spinor structure of the hadrons. In the second approach, the new gravitational Lagrangian density generates propagating but confined torsion and nonmetricity, presumably the main contributions to quark confinement. Leptons are represented nonlinearly as Poincaré spinors with the metric field as "realizer" and Higgs boson, and are unconfined. We present a construction for all linear multiplicity-free (= bandor) representations of GL(4,R) and in particular the [Formula: see text] fitting the hadron manifield. We also construct the Hilbert space hadron states [irreps (irreducible representations) of GA(4,R)] and the nonlinear realizations of GL(4,R) for lepton fields.

Gravitational interaction of hadrons: Band-spinor representations of GL(n,R).

We demonstrate the existence of double-valued linear (infinite) spinorial representations of the group of general coordinate transformations. We discuss the topology of the group of general coordinate transformations and its subgroups GA(nR), GL(n,R), SL(nr) for n = 2,3,4, and the existence of a double covering. We present the construction of band-spinor representations of GL(n,R) in terms of Harish-Chandra modules.It is suggested that hadrons interact with gravitation as band-spinors of that type. In the metric-affine extension of general relativity, the hadron intrinsic hypermomentum is minimally coupled to the connection, in addition to the coupling of the energy momentum tensor to the vierbeins. The relativistic conservation of intrinsic hypermomentum fits the observed regularities of hadrons: SU(6) ( approximately spin independence), scaling, and complex-J trajectories. The latter correspond to volume-preserving deformations (confinement?) exciting rotational bands.