On the Semi-Classical Vacuum Structure of the Electroweak Interaction

It is shown that in the semi-classical approximation of the electroweak sector of the Standard Model the moduli space of vacua can be identified with the first de Rham cohomology group of space-time. This gives a slightly different physical interpretation of the occurrence of the well-known Ahoronov-Bohm effect. Moreover, when charge conjugation is taken into account, the existence of a non-trivial ground state of the Higgs boson is shown to be equivalent to the triviality of the electroweak gauge bundle. As a consequence, the gauge bundle of the electromagnetic interaction must also be trivial. Though derived at ``tree level'' the results presented here may also have some consequences for quantizing, e. g., electromagnetism on an arbitrary curved space-time.Comment: 26 pages, no figure

Dynamical torsion in view of a distinguished class of Dirac operators

In this paper we discuss geometric torsion in terms of a distinguished class of Dirac operators. We demonstrate that from this class of Dirac operators a variational problem for torsion can be derived similar to that of Yang-Mills gauge theory. As a consequence, one ends up with propagating torsion even in vacuum as opposed to Einstein-Cartan theory

(Fermionic)Mass Meets (Intrinsic)Curvature

Using the notion of vacuum pairs we show how the (square of the) mass matrix of the fermions can be considered geometrically as curvature. This curvature together with the curvature of space-time, defines the total curvature of the Clifford module bundle representing a ``free'' fermion within the geometrical setup of spontaneously broken Yang-Mills-Higgs gauge theories. The geometrical frame discussed here gives rise to a natural class of Lagrangian densities. It is shown that the geometry of the Clifford module bundle representing a free fermion is described by a canonical spectral invariant Lagrangian density.Comment: 14 page

Unification of Gravity and Yang-Mills-Higgs Gauge Theories

In this letter we show how the action functional of the standard model and of gravity can be derived from a specific Dirac operator. Far from being exotic this particular Dirac operator turns out to be structurally determined by the Yukawa coupling term. The main feature of our approach is that it naturally unifies the action of the standard model with gravity.Comment: 8 pages, late

The functional of super Riemann surfaces -- a "semi-classical" survey

This article provides a brief discussion of the functional of super Riemann surfaces from the point of view of classical (i.e. not "super-) differential geometry. The discussion is based on symmetry considerations and aims to clarify the "borderline" between classical and super differential geometry with respect to the distinguished functional that generalizes the action of harmonic maps and is expected to play a basic role in the discussion of "super Teichm\"uller space". The discussion is also motivated by the fact that a geometrical understanding of the functional of super Riemann surfaces from the point of view of super geometry seems to provide serious issues to treat the functional analytically

On the Determinant of One-Dimensional Elliptic Boundary Value Problems

We discuss the $\zeta-$regularized determinant of elliptic boundary value problems on a line segment. Our framework is applicable for separated and non-separated boundary conditions.Comment: LaTeX, 18 page

The generalized Lichnerowicz formula and analysis of Dirac operators

We study Dirac operators acting on sections of a Clifford module ${\cal E}$\ over a Riemannian manifold $M$. We prove the intrinsic decomposition formula for their square, which is the generalisation of the well-known formula due to Lichnerowicz [L]. This formula enables us to distinguish Dirac operators of simple type. For each Dirac operator of this natural class the local Atiyah-Singer index theorem holds. Furthermore, if $M$\ is compact and {{\petit \rm dim}\;M=2n\ge 4}, we derive an expression for the Wodzicki function $W_{\cal E}$, which is defined via the non-commutative residue on the space of all Dirac operators ${\cal D}({\cal E})$. We calculate this function for certain Dirac operators explicitly. From a physical point of view this provides a method to derive gravity, resp. combined gravity/Yang-Mills actions from the Dirac operators in question.Comment: 25 pages, plain te