M.J.G. Veltman

Regularization and renormalization of gauge fields

A new regularization and renormalization procedure is presented. It is particularly well suited for the treatment of gauge theories. The method works for theories that were known to be renormalizable as well as for Yang-Mills type theories. Overlapping divergencies are disentangled. The procedure respects unitarity, causality and allows shifts of integration variables. In non-anomalous cases also Ward identities are satisfied at all stages. It is transparent when anomalies, such as the Bell-Jackiw-Adler anomaly, may occur.

One-loop corrections for e+e- annihilation into μ+μ- in the Weinberg model

Abstract Analytical experessions for the e + e − → μ + μ − cross section including all the one-loop radiative corrections in the context of the Weinberg model are presented. The systematic calculation of one-loop diagrams has been carried out using a recently proposed scheme. Numerical results are shown in a region from 40–200 GeV c.m. energy and different values of the scattering angle; they indicate that the percentage corrections are mainly due to soft photons. The only departure from QED-like correction can be seen in a region where the lowest-order cross section is lowered by weak-e.m. interference. In that region hard photon contributions are relatively prominent and perhaps within experimental possibilities.

Scalar one-loop integrals

The completely general one-loop scalar one-, two-, three- and four-point functions are studied. Also an integral occurring in connection with soft bremsstrahlung is considered. Formulas in terms of Spence functions are given. An expansion for Spence functions with complex argument is presented. The whole forms a basis for the calculation of one-loop radiative corrections in the general case, including unstable particles and particles with spin.

Massive and mass-less Yang-Mills and gravitational fields

Massive and mass-less Yang-Mills and gravitational fields are considered. It is found that there is a discrete difference between the zero-mass theories and the very small, but non-zero mass theories. In the case of gravitation,comparison of massive and mass-less theories with experiment, in particular the perihelion movement of Mercury, leads to exclusion of the massive theory. It is concluded that the graviton mass must be rigorously zero.

Limit on mass differences in the Weinberg model

Abstract Within the Weinberg model mass differences between members of a multiplet generate further mass differences between the neutral and charged vector bosons. The experimental situation on the Weinberg model leads to an upper limit of about 800 GeV on mass differences within a multiplet. No limit on the average mass can be deduced.

Combinatorics of gauge fields

Abstract Gauge field theories can be described by many different sets of Feynman rules, depending on the particular gauge chosen. In this paper a prescription for obtaining the Feynman rules in different gauges is given. A rigorous combinatorial proof of the independence of the S -matrix of the chosen gauge is presented. The proof is general and applies to Yang-Mills type theories as well as to gravitation. For renormalizable Yang-Mills type theories it is shown that the renormalized theory is invariant with respect to renormalized gauge transformations.

Two-loop large Higgs mass correction to the ϱ-parameter

Abstract The two-loop correction to the ϱ-parameter in the limit of the large Higgs mass is calculated. Numerically it is found that the two-loop contribution is equal in magnitude, but of opposite sign to the one-loop correction if the Higgs mass is about 137 times the vector boson mass. The calculation suggest a breakdown of perturbation theory if the Higgs mass is larger than 3 TeV. There is no direct correspondence between our results and the poles at n = 3 of the simple non-linear σ-model at the two-loop level.

Neutral currents and the Higgs mechanism

Abstract The consequences of assuming (i) weak and e.m. forces constitute a gauge field theory, and (ii) there are no heavy leptons, are investigated. Relative to the Weinberg model, introduction of a general spontaneous symmetry breaking system leads to a theory with one extra free parameter, namely the neutral vector boson mass. Experimental consequences are indicated. A particular Higgs system containing two multiplets is studied in detail. It is noted that parameters may be chosen such that the cosmological constant is zero before as well as after spontaneous symmetry breakdown.

Diagrammatica : the path to Feynman rules

This author provides an easily accessible introduction to quantum field theory via Feynman rules and calculations in particle physics. His aim is to make clear what the physical foundations of present-day field theory are, to clarify the physical content of Feynman rules. The book begins with a brief review of some aspects of Einsteins theory of relativity that are of particular importance for field theory, before going on to consider the relativistic quantum mechanics of free particles, interacting fields, and particles with spin. The techniques learnt in the chapters are then demonstrated in examples that might be encountered in real accelerator physics. Further chapters contain discussions of renormalization, massive and massless vector fields and unitarity. A final chapter presents concluding arguments concerning quantum electrodynamics. The book includes valuable appendices that review some essential mathematics, including complex spaces, matrices, the CBH equation, traces and dimensional regularization. An appendix containing a comprehensive summary of the rules and conventions used is followed by an appendix specifying the full Lagrangian of the Standard Model and the corresponding Feynman rules. To make the book useful for a wide audience a final appendix provides a discussion of the metric used, and an easy-to-use dictionary connecting equations written with different metrics. Written as a textbook, many diagrams, exercises and examples are included. This book will be used by beginning graduate students taking courses in particle physics or quantum field theory, as well as by researchers as a source and reference book on Feynman diagrams and rules.

Perturbation theory of massive Yang-Mills fields

Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Primitive diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possibility that the theory is renormalizable.