Well suited as a textbook in the emerging field of stochastic limit, which is a new mathematical technique developed for solving nonlinear problems in quantum theory.

The principal intent of this monograph is to present in a systematic and self-con tained fashion the basic tenets, ideas and results of a framework for the consistent unification of relativity and quantum theory based on a quantum concept of spacetime, and incorporating the basic principles of the theory of stochastic spaces in combination with those of Born's reciprocity theory. In this context, by the physicial consistency of the present framework we mean that the advocated approach to relativistic quantum theory relies on a consistent probabilistic interpretation, which is proven to be a direct extrapolation of the conventional interpretation of nonrelativistic quantum mechanics. The central issue here is that we can derive conserved and relativistically convariant probability currents, which are shown to merge into their nonrelativistic counterparts in the nonrelativistic limit, and which at the same time explain the physical and mathe matical reasons behind the basic fact that no probability currents that consistently describe pointlike particle localizability exist in conventional relativistic quantum mechanics. Thus, it is not that we dispense with the concept oflocality, but rather the advanced central thesis is that the classical concept of locality based on point like localizability is inconsistent in the realm of relativistic quantum theory, and should be replaced by a concept of quantum locality based on stochastically formulated systems of covariance and related to the aforementioned currents.

The principal intent of this monograph is to present in a systematic and self-con tained fashion the basic tenets, ideas and results of a framework for the consistent unification of relativity and quantum theory based on a quantum concept of spacetime, and incorporating the basic principles of the theory of stochastic spaces in combination with those of Born's reciprocity theory. In this context, by the physicial consistency of the present framework we mean that the advocated approach to relativistic quantum theory relies on a consistent probabilistic interpretation, which is proven to be a direct extrapolation of the conventional interpretation of nonrelativistic quantum mechanics. The central issue here is that we can derive conserved and relativistically convariant probability currents, which are shown to merge into their nonrelativistic counterparts in the nonrelativistic limit, and which at the same time explain the physical and mathe matical reasons behind the basic fact that no probability currents that consistently describe pointlike particle localizability exist in conventional relativistic quantum mechanics. Thus, it is not that we dispense with the concept oflocality, but rather the advanced central thesis is that the classical concept of locality based on point like localizability is inconsistent in the realm of relativistic quantum theory, and should be replaced by a concept of quantum locality based on stochastically formulated systems of covariance and related to the aforementioned currents.

The main purpose of this volume is to emphasize the multidisciplinary aspects of this very active new line of research in which concrete technological and industrial realizations require the combined efforts of experimental and theoretical physicists, mathematicians and engineers. Contents: Coherent Quantum Control of o-Atoms through the Stochastic Limit (L Accardi et al.); Recent Advances in Quantum White Noise Calculus (L Accardi & A Boukas); Joint Extension of States of Fermion Subsystems (H Araki); Fidelity of Quantum Teleportation Model Using Beam Splittings (K-H Fichtner et al.); Quantum Logical Gates Realized by Beam Splittings (W Freudenberg et al.); Noncanonical Representations of a Multi-dimensional Brownian Motion (Y Hibino); Information, Innovation and Elemental Random Field (T Hida); Generalized Sectors and Adjunctions to Control MicroOCoMacro Transitions (I Ojima); Saturation of an Entropy Bound and Quantum Markov States (D Petz); An Infinite Dimensional Laplacian Acting on Some Class of L(r)vy White Noise Functionals (K Sait); Structure of Linear Processes (S Si & W W Htay); Group Theory of Dynamical Maps (E C G Sudarshan); Quantum Entanglement, Purification, and Linear-optics Quantum Gates with Photonic Qubits (P Walther & A Zeilinger); On Quantum Mutual Type Measures and Capacity (N Watanabe); and other papers. Readership: Researchers in quantum physics and theoretical physics."

This introductory survey of stochastic methods and techniques in quantum physics, functional analysis, probability theory, communications, and electrical engineering also serves as a useful and comprehensive reference volume. 1979 edition.

From the reviews: "The text is almost self-contained and requires only an elementary knowledge of probability theory at the graduate level. The book under review is recommended to mathematicians, physicists and graduate students interested in mathematical physics and stochastic processes. Furthermore, some selected chapters can be used as sub-textbooks for advanced courses on stochastic processes, quantum theory and quantum chemistry." ZAA

Thi's book collects the contributions to the NATO Advanced Research WJrkshop on "FundaIrental Aspects of Quantum 'Iheory," held at the Centro di Cultura Scientifica "Alessandro Volta," Villa Olma, Carro, Italy, 2-7 September 1985. The rreeting was dedicated to the rremory of the late pro fessor Piero Caldirola, a prominent member of the Physics Departrrent of the University of r1ilan and a native of Como. The aim of the workshop has been to present several recent experi rrental results and theoretical developrrents concerning the various fa cets of quantum physics. The breadth of scope of the rreeting was in accordance with Professor Caldirola's vast scientific interests, and fostered communication among experirrental physicists, theoretical and mathematical physicists, and nEthematicians, working in different but related fields. Indeed, lectu rers endeavoured to make their contributions understandable to people acquainted with the problem but not necessarily familiar with the tech nical details; and these efforts were successful, as indicated by the frequent private discussions which took place among participants belon ging to different breeds and brands. 1ne rreeting was made up of six one-day sessions, each of them addres sing to a specific aspect of quantum theory: 1. General Problems and Crucial Experinents; with emphasis on sin gle-particle interference eh rirrents of neutrons and of photons, and on the rreasurerrent problem. 2. Quantization and Stochastic Processes; including stochastic quan tization of gauge fields, stochastic description of supersyrnmetric fields, quantum stochastic calculus and stochastic mechanics."