Students of particle physics often find it difficult to locate resource to learn calculational techniques. Intermediate steps are usually not given in the research literature. To certain extent, this is also the case even in some of the textbooks. In this book of worked problems we have made an effort to provide enough details so that a beginning student will understand the solution in each case. Our hope is that with this step-by-step guidance, students (after first attempting the solution themselves) can develop their skill, and confidence in their ability, to work out particle theory problems.

This collection of problems has evolved from the supplemental material developed for a graduate course that one of us (L.F.L.) has taught over the years at Carnegie Mellon University, and is meant to be a companion volume to our textbook CL (''Gauge Theory of Elementary Particle Physics'', Clarendon Press, Oxford, 1984) rather than a complete assemblage of gauge theory problems. Nevertheless, it has a self-contained format so that even a reader not familiar with CL can use it effectively. All the problems (usually with several parts) have been given a descriptive title. By simply inspecting the table of contents readers should be able to pick out the areas they wish to tackle.

Several new subjects have entered in the field in the fifteen years since the original writing of CL. While we have not revised the book to incorporate them because we would not be able to do them justice, we hope this set of problem/solution presentations is the first step towards remedying the situation. We have incorporated a number of new topics, or have developed further on those that have only been briefly introduced in the original text. Listed below are some of these areas:

• Relations among different renormalization schemes

• Further applications of the path integral formalism

• General relativity as a gauge theory

• Superconductivity as a Higgs phenomenon

• Non-linear sigma model and chiral symmetry

• Path integral derivation of the axial anomaly

• Infrared and collinear divergence in QCD

• Further examples of the parton model phenomenology

• More on gauge theories of lepton number violation

• Group theory of grand unification

• Further examples of solitons

Many people have helped us in preparing this book. Our thanks go particularly to all the students who have taken the course and have worked through a good part of these problems. The original literature has only been referenced casually, and we apologize to the authors whose work we may have neglected to cite.

This book and CL share a page on the World Wide Web at the URL http://www.umsl.edu/~tpcheng/gaugebooks.html. Misprints or other corrections brought to our attention will be posted on this page. We would be grateful for any comments about these books.

T.P.C.

L.F.L.