Walter Troost

Multiple bremsstrahlung in gauge theories at high energies (I). General formalism for quantum electrodynamics

Multiple bremsstrahlung is studied on the level of tree diagrams for gauge theories. At high energies and in most of the kinematic region, the fermion mass can be neglected. In this case, it is natural to introduce helicity states for both fermions and gauge particles. Our general formalism is given in detail for quantum electrodynamics. In particular, it is expedient to use photon polarization vectors which depend on the fermion helicities. In this way, extensive cancellations between Feynman diagrams are accomplished automatically.

Superconformal algebras in two dimensions with N=4

Abstract We discuss a one-parameter family of d =2 superconformal algebras. They have N =4 supersymmetries and satisfy all the usual requirements. There is one Virasoro algebra, the other generators have dimensions 1 2 , 1 or 3 2 and there is one central extension. A realisation is given on a linear σ-model on a group manifold.

Extended supersymmetric σ-Models on group manifolds (I). The complex structures

Abstract We investigate the possibilities of N-extended rigid supersymmetries in two-dimensional actions, in particular parallelized group manifolds. We give a full classification of all such manifolds with N = 2 or N = 4. We explicitly construct the supersymmetries which are related to complex or quaternionic structures. The N = 4 manifolds are related to Wolf spaces. Only flat spaces allow N > 4. Depending on the dimension N = 1, 2, 4, 8 mod 8.

What is special Kahler geometry

The scalars in vector multiplets of N = 2 supersymmetric theories in four dimensions exhibit ‘special Kahler geometry’, related to duality symmetries, due to their coupling to the vectors. In the literature there is some confusion on the definition of special geometry. We show equivalences of some definitions and give examples which show that earlier definitions are not equivalent, and are not sufficient to restrict the Kahler metric to one that occurs in N = 2 supersymmetry. We treat the rigid as well as the local supersymmetry case. The connection is made to moduli spaces of Riemann surfaces and Calabi-Yau 3-folds. The conditions for the existence of a prepotential translate to a condition on the choice of canonical basis of cycles.

Multiple bremsstrahlung in gauge theories at high energies (II). Single bremsstrahlung

We calculate the helicity amplitudes for the QED processes e+e−→γγγ, μ+μ−γ, and e+e−γ, in the limit of vanishing fermion masses. This is done by introducing explicit polarization vectors for the radiated photons. With the same technique, we also calculate these processes taking into account Z0 exchange. Finally, we present the unpolarized cross sections in which mass terms are retained to describe the radiation of photons in directions parallel to those of the fermions.

Anomalies and the Batalin-Vilkovisky Lagrangian Formalism

Abstract Anomalies can be studied in the framework of the BV lagrangian formalism. They are present whenever there are terms of order ℏ (or higher) in the master equation which cannot be removed by a local counterterm. Regularisation is essential to define those BV expressions which correspond to jacobians and determinants in other approaches. We use a regularisation scheme, motivated by the Pauli-Villars regularisation, which allows one to use the Fujikawa method without being restricted to Fujikawa variables, and which regularises also nonpropagating fields. It leads to finite and local, but in general noncovariant, terms in the master equation at order ℏ. Several explicit examples illustrate the relation between counterterms, canonical transformations and different consistent regulators.

Multiple Bremsstrahlung in Gauge Theories at High-energies. 3. Finite Mass Effects in Collinear Photon Bremsstrahlung

Abstract We present a method for calculating the various spin amplitudes for QED processes in which an arbitrary number of photons is radiated in directions nearly parallel to the fermion directions. This is accomplished by introducing explicit polarization vectors for the photons and by working in the high energy limit, where finite mass effects are treated in leading order.

Extended supersymmetric σ-models on group manifolds (II). Current algebras

Abstract The supersymmetries of σ-models on group manifolds are generated by currents, of which we calculate the operator product expansions. For flat spaces with N > 4 there appear more operators than the usual dimension 2, 3 2 and 1 currents. For N = 2 on any even dimensional group manifold we find the Ademollo et al. algebra. For N = 4 we find a class of new algebras. In all cases except SU(2) ⊗ U(1) and SU(3) the algebra splits in a direct product of several of these new N = 4 algebras, each having a complicated energy-momentum tensor. By including background charges one can restrict the algebras to dimension 2, 3 2 and 1 currents. On the non-compact Wolf spaces one can obtain zero central charge.

Helicity Amplitudes for Massless QED

Abstract The introduction of helicity states, for both fermions and photons, is shown to lead to simple expressions for QED amplitudes, in which an arbitrary number of photons are radiated, provided that the fermion masses can be neglected. As an example, the results are given for the process e + e − →4 γ .

Multiple Bremsstrahlung in Gauge Theories at High-Energies. 4. The Process e+ e- ---> gamma gamma gamma gamma

Abstract We calculate the helicity amplitude and the cross section for the process e + e − → 4 γ in the high-energy limit. The resulting expressions are presented in a form which allows an easy numerical evaluation. They are valid for the kinematical configurations where at most two photons are emitted in directions nearly parallel to the lepton directions.