Beyond quantum.

*(English)*Zbl 1294.81008
Singapore: Pan Stanford Publishing (ISBN 978-981-4411-73-8/hbk; 978-981-4411-74-5/ebook). xvii, 373 p. (2014).

In this book the author studies probabilistic aspects of quantum theory and to what extent it is possible to represent quantum phenomena in terms of classical probability. One of the main ideas discussed is the description of quantum mechanics in terms of a classical statistical theory of random fields.

From the text: “This book is dedicated to Einstein’s vision of physics and specifically his hope for what quantum theory could, and in his view, should be. Two of Einstein’s dreams about the future of quantum theory are particularly realized in this book: reduction of quantum randomness to classical ensemble randomness and the total elimination of particles from QM, that is, the creation of a classical field model of quantum phenomena.”

In Chapter 1 the author shares his views on quantum foundations and reviews a series of conferences on foundations of quantum mechanics which occured in Växjö, Sweden. Also, Prequantum Classical Statistical Field Theory (PCSFT) are introduced.

In Chapter 2, conventional quantum theory fundamentals are reviewed and in Chapter 3, foundations of PCSFT are studied. Chapter 4 discusses prequantum dynamics in terms of hamiltonian formalism and in Chapter 5 it is given a description of quantum mechanics in terms of statistical mechanics of classical fields. In this chapter a prequantum-quantum correspondence is also described, as well as interpretations of models and a discussion of a generalization of quantum mechanics.

Chapter 6 consists of mathematical considerations and Chapter 7 gives a mathematical description for quantum composite systems. Chapter 8 discusses a phenomenological detection model and in Chapter 9 quantum individual events are described.

From the text: “This book is dedicated to Einstein’s vision of physics and specifically his hope for what quantum theory could, and in his view, should be. Two of Einstein’s dreams about the future of quantum theory are particularly realized in this book: reduction of quantum randomness to classical ensemble randomness and the total elimination of particles from QM, that is, the creation of a classical field model of quantum phenomena.”

In Chapter 1 the author shares his views on quantum foundations and reviews a series of conferences on foundations of quantum mechanics which occured in Växjö, Sweden. Also, Prequantum Classical Statistical Field Theory (PCSFT) are introduced.

In Chapter 2, conventional quantum theory fundamentals are reviewed and in Chapter 3, foundations of PCSFT are studied. Chapter 4 discusses prequantum dynamics in terms of hamiltonian formalism and in Chapter 5 it is given a description of quantum mechanics in terms of statistical mechanics of classical fields. In this chapter a prequantum-quantum correspondence is also described, as well as interpretations of models and a discussion of a generalization of quantum mechanics.

Chapter 6 consists of mathematical considerations and Chapter 7 gives a mathematical description for quantum composite systems. Chapter 8 discusses a phenomenological detection model and in Chapter 9 quantum individual events are described.

Reviewer: Carlos F. Lardizabal (Porto Alegre)

##### MSC:

81-02 | Research exposition (monographs, survey articles) pertaining to quantum theory |

81P05 | General and philosophical questions in quantum theory |

81P16 | Quantum state spaces, operational and probabilistic concepts |