It has recently been shown, by application of statistical mechanical methods to determine the canonical ensemble governing the equilibrium distribution of operator initial values, that complex quantum field theory can emerge as a statistical approximation to an underlying generalized quantum dynamics. This result was obtained by an argument based on a Ward identity analogous to the equipartitio...

We define an (equivariant) quaternionic analytic torsion for antiselfdual vector bundles on quaternionic Kähler manifolds, using ideas by Leung and Yi. We compute this torsion for vector bundles on quaternionic homogeneous spaces with respect to any isometry in the component of the identity, in terms of roots and Weyl groups. 2000 Mathematics Subject Classification: 53C25, 58J52, 53C26, 53C35

We study the orientifold truncation that arises when compactifying type II string theory on Calabi-Yau orientifolds with O3/O7-planes, in the context of supergravity. We look at the N=2 to N=1 reduction of the hypermultiplet sector of N=2 supergravity under the truncation, for the case of very special quaternionic-Kähler target space geometry. We explicitly verify the Kähler structure of the tr...

The non-perturbative corrections to the universal hypermultiplet moduli space metric in the type-IIA superstring compactification on a Calabi-Yau threefold are investigated in the presence of 4d, N=2 supergravity. These corrections come from multiple wrapping of the BPS (Euclidean) D2-branes around certain (BPS) Calabi-Yau 3-cycles, and they are known as the D-instantons. The exact universal hy...

We study the quaternionic linear system which is composed out of terms of the form ln(x) := ∑n p=1 apxbp with quaternionic constants ap, bp and a variable number n of terms. In the first place we investigate one equation in one variable. If n = 2 the corresponding equation, which is normally called Sylvester’s equation will be treated completely by using only quaternionic algebra. For larger n ...

Consider a two-person zero-sum stochastic game with Borel state space S, compact metric action sets A, B and law of motion q such that the integral under q of every bounded Borel measurable function depends measurably on the initial state s and continuously on the actions (a,b) of the players. Suppose the payoff is a bounded function f of the infinite history of states and actions such that f i...

at each point x in M, then M is called a QR-submanifold of r QR-dimension, where ] denotes the complementary orthogonal distribution to ] in TM (cf. [1–3]). Real hypersurfaces, which are typical examples of QR-submanifold with r = 0, have been investigated by many authors (cf. [2–9]) in connection with the shape operator and the induced almost contact 3-structure (for definition, see [10–13]). ...

We introduce new Bézier-like formulas with quaternionic weights for rational curves and surfaces in Euclidean 3-space. They are useful for representation of Möbius invariant geometric objects. Any Bézier curves and surfaces on 2-spheres can be converted to the quaternionic Bézier (QB) form of twice lower degree. Our focus is on bilinear QB-surfaces: we derive their implicitization formula and s...

We begin this review with a brief history of the subject for our exposition shall have little to do with the chronology. In 1960 Sasaki [Sas 1] introduced a geometric structure related to an almost contact structure. This geometry became known as Sasakian geometry and has been studied extensively ever since. In 1970 Kuo [Kuo] refined this notion and introduced manifolds with Sasakian 3-structur...

The pseudo-Riemannian manifold M = (M, g), n ≥ 2 is paraquaternionic Kähler if hol(M) ⊂ sp(n,R)⊕sp(1, R). If hol(M) ⊂ sp(n, R), than the manifold M is called para-hyperKähler. The other possible definitions of these manifolds use certain parallel para-quaternionic structures in End(TM), similarly to the quaternionic case. In order to relate these different definitions we study para-quaternionic...