The author of this concise, brilliant series of lectures on mathematical methods in quantum mechanics was one of the shining intellects in the field, winning a Nobel prize in 1933 for his pioneering work in the quantum mechanics of the atom. Beyond that, he developed the transformation theory of quantum mechanics (which made it possible to calculate the statistical distribution of certain variables), was one of the major authors of the quantum theory of radiation, codiscovered the Fermi-Dirac statistics, and predicted the existence of the positron.
The four lectures in this book were delivered at Yeshiva University, New York, in 1964. The first, "The Hamiltonian Method," is an introduction to visualizing quantum theory through the use of classical mechanics. The remaining lectures build on that idea. "The Problem of Quantization" shows how one can start with a classical field theory and end up with a quantum field theory. In "Quantization on Curved Surfaces," Dirac examines the possibility of building a relativistic quantum theory on curved surfaces. He deduces that it is not possible, but it should be possible on flat surfaces. In the final lecture, "Quantization on Flat Surfaces," he concludes that "we can set up the basic equations for a quantum theory of the Born-Infeld electrodynamics agreeing with special relativity, but [not] with general relativity." Physics and chemistry students will find this book an invaluable addition to their libraries, as will anyone intrigued by the far-reaching and influential ideas of quantum mechanics.
The Physics of Pretty Mathematics
One of the founders of quantum mechanics and quantum electrodynamics, Paul A. M. Dirac shared the 1933 Nobel Prize in Physics with Erwin Schrödinger, "for the discovery of new productive forms of atomic theory."
In the Author's Own Words:
"A good deal of my research in physics has consisted in not setting out to solve some particular problem, but simply examining mathematical equations of a kind that physicists use and trying to fit them together in an interesting way, regardless of any application that the work may have. It is simply a search for pretty mathematics. It may turn out later to have an application. Then one has good luck."
"The mathematician plays a game in which he himself invents the rules while the physicist plays a game in which the rules are provided by nature, but as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which nature has chosen." — Paul A. M. Dirac
Critical Acclaim for Lectures on Quantum Mechanics:
"Dirac's lovely little book represents a set of lectures Dirac gave in 1964 at Yeshiva University, at a time when the great master could take advantage of hindsight. The Dover edition didn't appear until 2001. The clarity of Dirac's presentation is truly compelling (no mystery at all!). Very little background is required on the part of the reader. Dirac begins with the Hamiltonian method, and then passes to quantization in terms of physics. The mathematics of quantization on curved (and flat) surfaces is clearly presented in the second part of the book." — Palle E.T. Jorgensen, author of Operators and Representation Theory: Canonical Models for Algebras of Operators Arising in Quantum Mechanics, which Dover reprinted in 2008
