Teichmüller Groupoids,and Monodromy in Conformal Field Theory

We study monodromy representations of the Teichmüller groupoid for the moduli space of pointed compact Riemann surfaces of any genus with first-order infinitesimal structure. To calculate these representations, using arithmetic Schottky-Mumford uniformization theory we construct a real orbifold in the moduli space consisting of fusing and simple moves which gives tangential base points. For a certain vector bundle on the moduli space with projectively flat connection, we show that the monodromy of each fusing move can be expressed as a connection matrix, and give the relations to the monodromy of simple moves. Furthermore, we describe the monodromy representation associated with Tsuchiya-Ueno-Yamadas conformal field theory, and show that this representation can be expressed as the monodromy of the Wess-Zumino-Witten model.     

Photoionisation of atoms and Möller operators

The motion of an hydrogenoïd atom in a laser field is usually given by the time-dependent hamiltonian H(t)=[p?A(t)]²/2+V(r) where V(r) is the atomic potential whileA(t) is to be connected with the laser field. The existence and unicity for the Cauchy problem of the solutions of the corresponding Schrödinger equation are established under mild conditions onA(t) and V(r). The existence of Möller operators is investigated in two cases, namely, when the laser field is a function of time only and when it vanishes asymptotically in time. Special attention is paid for the Coulomb case for which a “distorted” Möller operator is derived. Finally, when the laser field vanishes ast→∞, the photoionisation probability is properly defined by means of the Möller operator $$\Omega (H_{At} ,H) = s - \mathop {\lim }\limits_{t \to \infty } U_{At} (t)^{ - 1} U(t)$$ , whereU(t) is the evolution operator for the system whileU _Att (t) is the evolution operator for the atom.     

Grothendieck–Teichmüller and Batalin–Vilkovisky

It is proven that, for any affine supermanifold M equipped with a constant odd symplectic structure, there is a universal action (up to homotopy) of the Grothendieck–Teichmüller Lie algebra ${\mathfrak{grt}_1}$ on the set of quantum BV structures (i.e. solutions of the quantum master equation) on M.     

Universal Teichmüller space in geometry and physics

Lipman Bers' universal Teichmüller space, classically denoted by T(1), plays a significant role in Teichmüller theory, because all the Teichmüller spaces T(G) of Fuchsian groups G can be embedded into it as complex submanifolds. Recently, T(1) has also become an object of intensive study in physics, because it is a promising geometric environment for a non-perturbative version of bosonic string theory. We provide a non-technical survey of what is currently known about the geometry of T(1) and what is conjectured about its physical meaning. Our bibliography should be rather comprehensive, but we apologize for any unjustified omissions.     

Møller was right

Direct calculation proves that the total energy-momentum vector derived from the Møller energy-momentum complex from 1958 does not transform like a free 4-vector with respect to the Lorentz transformation. This conforms with the conclusion formulated by Møller himself, but it contradicts the result of the critical analysis of Kovacs. Defects in Kovacs argumentation are found.     

Parity-violating M?ller scattering

The A4 collaboration at the MAMI accelerator at Mainz investigates the contribution of strange quarks to the form factors of the nucleon by measuring the parity violating asymmetry A _PV in the cross section of elastic scattering of longitudinally polarized electrons off hydrogen and deuterium. Recently, measurements at backward angles at a four momentum transfer of Q ²?=?0.22 GeV² were completed. Together with previous results at forward angles at the same momentum transfer, the strange electric and magnetic form factors $G_E^s$ and $G_M^s$ can be disentangled.     

Universal Teichmüller Space and DiffS 1/S 1

We point out that the coset space DiffS ¹/S ¹ is a dense complex submanifold of the Universal Teichmüller SpaceS of compact Riemann spaces of genus g1. A holomorphic map ofS into the inifinite dimensional Segal diskD ₁ is constructed. This is the Universal analogue of the map of Teichmüller spaces into the Siegel disk provided by the period matrix. The Kähler potential for the general homogenous metric on DiffS ¹/S ¹ is computed explicitly using the map intoD ₁. Some applications to string theory are discussed.This work was supported in part by the U.S. Department of Energy Contract No. DE-AC02-76ER13065