Gunter Scharf

Causal construction of Yang-Mills theories. - II

SummaryPure quantized Yang-Mills theories are constructed by causalperturbation theory. We study operator gauge transformations which lead in a natural way to the introduction of ghost fields. Considering fermionic as well as bosonic ghosts, we find that only the former save gauge invariance in second order. We work with free quantum fields throughout, so that all expressions are mathematically well defined.

Tunnelling of a large spin: mapping onto a particle problem

The tunnelling of a single quantum spin is studied in the limit of large spin quantum number S. The problem is mapped onto a particle problem on the positive half-line with a Hamiltonian which is invariant under inversion x to 1/x. Not only the ground-state energy but also all the other energy levels and corresponding level splittings (if any) are computed by using the conventional WKB methods for the particle problem and an excellent agreement with numerical data is found.

NON-ABELIAN GAUGE THEORIES AS A CONSEQUENCE OF PERTURBATIVE QUANTUM GAUGE INVARIANCE

We show for the case of interacting massless vector bosons, how the structure of Yang–Mills theories emerges automatically from a more fundamental concept, namely perturbative quantum gauge invariance. It turns out that the coupling in a non-Abelian gauge theory is necessarily of Yang–Mills type plus divergence- and coboundary-couplings. The extension of the method to massive gauge theories is briefly discussed.

On gauge invariance and spontaneous symmetry breaking

We show how the widely used concept of spontaneous symmetry breaking can be explained in causal perturbation theory by introducing a perturbative version of quantum gauge invariance. Perturbative gauge invariance, formulated exclusively by means of asymptotic fields, is discussed for the simple example of Abelian U(1) gauge theory (Abelian Higgs model). Our findings are relevant for the electroweak theory, as pointed out elsewhere.

Scalar QED revisited

SummaryScalar QED is investigated in the framework of causal perturbation theory. This approach which is ultraviolet finite differs from the conventional formalism because the inductive construction starts from the simple first-order interaction, without the term quadratic in the electromagnetic potential. The latter appears in the process of distribution splitting as a consequence of gauge invariance. In this way normalizability, gauge invariance and unitarity can be rigorously proven.

Gauge invariance in finite QED

SummaryGauge invariance is discussed in the causal approach to QED. It is proven that the iterative construction of theS-matrix by the method of Epstein and Glaser can be carried out in such a way that perturbative gauge invariance holds true. The proof rests on a careful analysis of the process of distribution splitting. In case of nontrivial distribution splitting gauge invariance implies the Ward-Takahashi identities.

Gauge invariance of massless QED

Abstract A simple general proof of gauge invariance in QED is given in the framework of causal perturbation theory. It illustrates a method which can also be used in non-abelian gauge theories.

Interacting fields in finite QED

SummaryIn the framework of the causal approach to QED, interacting fields are introduced by functional differentiation of theS-matrix. The properties of these field operators are studied in detail. It is shown that appropriately defined quantum versions of the Dirac and wave equations hold true. As a by-product, the correct operator products for QED are obtained.

Massive gravity as a quantum gauge theory

We present a new point of view on the quantization of the massive gravitational field, namely we use exclusively the quantum framework of the second quantization. The Hilbert space of the many-gravitons system is a Fock space F+ (Hgraviton) where the one-particle Hilbert space Hgraviton carries the direct sum of two unitary irreducible representations of the Poincaré group corresponding to two particles of mass m > 0 and spins 2 and 0, respectively. This Hilbert space is canonically isomorphic to a space of the type Ker(Q)/Im(Q) where Q is a gauge charge defined in an extension of the Hilbert space Hgraviton generated by the gravitational field hμν and some ghosts fields uμ, ũμ (which are vector Fermi fields) and vμ (which is a vector Bose field).Then we study the self interaction of massive gravity in the causal framework. We obtain a solution which goes smoothly to the zero-mass solution of linear quantum gravity up to a term depending on the bosonic ghost field. This solution depends on two real constants as it should be; these constants are related to the gravitational constant and the cosmological constant. In the second order of the perturbation theory we do not need a Higgs field, in sharp contrast to Yang-Mills theory.

Electron positron pair production in the external electromagnetic field of colliding relativistic heavy ions

Abstract. The results concerning the