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Quantum Leap: From Dirac and Feynman, Across the Universe to Human Body and Mind, by V. Ivancevic and T. Ivancevic

spontaneously break a symmetry of the system. But the book is essentially a survey of the functional integral method applied to a quantum field description of contemporary condensed matter physics. This enables the author to present a unified approach to much of modern condensed matter physics. This he does clearly – although it may not always be the simplest approach for those less familiar with Lagrangian Field theory. For example, the Hubbard and Bose–Hubbard Models are introduced using the familiar creation and annihilation fermion operators, before applying the field-theoretic analysis; while contrariwise the treatment of BCS superconductivity theory eschews this approach and starts immediately with the (to me at least) more complicated functional integral method. Nevertheless, this is probably more a question of taste, and it is indeed salutary to see such a variety of condensed matter systems, both bosonic and fermionic, treated in a unified way. Bose–Einstein condensation is treated at length, as is superconductivity, and its p-wave equivalent, superfluid He. The book concludes with a very clear discussion of the Quantum Hall Effect, both the integer and fractional cases. Selected chapters of the book are suitable for use in a postgraduate course – indeed the author claims to have done so in an undergraduate course, but I would consider that somewhat optimistic. One unfortunate lacuna is the absence of exercises, which the author states are inappropriate here, as technical details are worked through in the text. This may be so; but it nevertheless lessens the value of the book as a teaching text. There is a very comprehensive bibliography, running to 16 pages, and an index. Whether or not used in the classroom, this book deserves a place in the bookcase of every theoretical physicist who wishes to have a clear exposition of the field theoretic approach to modern condensed matter physics.