viii PREFACE

objects. Its drawback is that it tethers one to perturbation theory, whereas non-

perturbative arguments would be more satisfying in some situations. Physicists

may also object to it on the grounds that free fields, although mathematically

meaningful, are physically fictitious.

The problem with interacting fields, on the other hand, is exactly the reverse.

Hence, although some might prefer to give them a more prominent role, I sequester

them in the last section of Chapter 6, where the mathematical soundness of the

narrative reaches its nadir, and do not use them at all in Chapter 7 except for a

couple of passing mentions. Their credibility is somewhat enhanced, however, by the

arguments in Chapter 8 using functional integrals, which are also mathematically ill-

defined but intuitively more accessible and seductively close to honest mathematics.

Some physicists like to use functional integrals as the principal route to the main

results, but despite their appeal, I find them a bit too much like sorcery to be relied

on until one already knows where one is going.

This book is meant to be only an introduction to quantum field theory, and it

focuses on the goal of explaining actual physical phenomena rather than studying

formal structures for their own sake. This means that I have largely (though not

entirely) resisted the temptation to pursue mathematical issues when they do not

add to the illumination of the physics, and also that I have nothing to say about the

more speculative areas of present-day theoretical physics such as supersymmetry

and string theory. Even within these restrictions, there are many important topics

that are mentioned only briefly or omitted entirely — most notably, the renor-

malization group. My hope is that this book will better prepare those who wish

to go further to tackle the physics literature. References to sources where further

information can be obtained on various topics are scattered throughout the book.

Here, however, I wish to draw the reader’s attention to three physics books whose

quality of writing I find exceptional.

First, everyone with any interest in quantum electrodynamics should treat

themselves to a perusal of Feynman’s QED [38], an amazingly fine piece of pop-

ular exposition. On a much more sophisticated level, but still with a high ratio

of physical insight to technical detail, Zee’s Quantum Field Theory in a Nutshell

[138] makes very good reading. (Both of these books adopt the functional integral

approach.) And finally, for a full-dress treatment of the subject, Weinberg’s The

Quantum Theory of Fields [131], [132], [133] is the sort of book for which the

overworked adjective “magisterial” is truly appropriate. Weinberg does not aim for

a mathematician’s level of rigor, but he has a mathematician’s respect for careful

reasoning and for appropriate levels of generality, and his approach has influenced

mine considerably. I will warn the reader, however, that Weinberg’s notation is at

variance with standard usage in some respects. Most notably, he takes the Lorentz

metric (which he denotes by

ημν)

to have signature − + ++ rather than the usual

+ −−−, and since he wants his Dirac matrices

γμ

to satisfy

{γμ,γν}

=

2ημν

, what

he calls

γμ

is what most people call

−iγμ.1

I call this book a tourist guide for mathematicians. This is meant to give the

impression not that it is easy reading (it’s not) but that the intended audience

consists of people who approach physics as tourists approach a foreign country, as

a place to enjoy and learn from but not to settle in permanently. It is also meant to

1There

is yet a third convention for defining Dirac matrices, found in Sakurai [103] among

other places.