By James D Wells
Springer Verlag
Paperback: £44.99 €52.70 $49.95
E-book: £35.99 €41.64 $39.95
This remarkable and charming book introduces the idea of effective field theories from a novel point of view, making the concepts natural and – in retrospect – inevitable. As the author makes clear, all theories are effective theories. At just 73 pages, it is easily accessible to a graduate student or a bright undergraduate. It will also be welcomed by professional physicists for its readability and clear, compelling style.
In introducing the idea of effective theories, the author begins by considering Galileo’s law for falling bodies, neglecting air resistance. Keeping the symmetries assumed for the problem – here translational invariance – and the idea that the constant downward acceleration might be an approximation to a more complete theory that involves a dependence of g on height above the ground, Wells derives the form of the leading correction by taking into account Newton’s law of gravitation without explicitly invoking the inverse square law. Such an effective theory could have been used to search for an extension to Galileo’s law or to accommodate data, even in the absence of Newton’s more complete theory of gravity. The second chapter continues the discussion of gravity, this time assuming circular orbits (and the simple harmonic oscillator) and the sorts of deviations that might be allowed for, using the ideas of effective theories to analyse deviations from perfect circularity.
Chapter 3 considers effective theories of classical gravity, arguing for the general expectation of perihelion precession and that something like black holes could have been predicted and the Schwarzschild radius estimated before the discovery of general relativity. Using both Lagrangian and Hamiltonian formulations of the problem, this discussion is not only enlightening but a delight to read. The presentation of effective theories in these simple contexts – requiring neither field theory nor even quantum mechanics – makes their meaning, importance and universality clearer than the usual, more advanced introductions.
Assuming some knowledge of the Standard Model, chapter 4 shows how the Fermi theory can be thought of as an effective field theory that approximates it. Here the author considers in some detail the origin of mass and in particular neutrino masses beyond the Standard Model. He then concludes with a discussion of naturalness and the hierarchy problem – all from the viewpoint of effective theories.
The fifth and final chapter is more philosophical in nature, emphasizing how and why effective theories are more than truncations of more comprehensive theory. It also looks at how one can go about choosing between theories, before closing with implications for the LHC.
I was pleasantly surprised by this book. The approach is original and makes the whole concept of effective theories clear and natural. I will be urging all of my students to take an afternoon to read this wonderful introduction – and to think carefully and deeply about the many points that the author makes so well.
