The underlying template running through all the chapters of this book is the application of the concepts of quantum field theory to the description of indeterminate and random phenomena, be they classical or quantum in origin. Quantum field theory was initially developed to explain the phenomena of high energy physics and soon spread to condensed matter and solid state physics. The common thread of these applications was that of a quantum system with a large number of degrees of freedom (independent variables). The pioneering work of Wilson (1983) and Witten (1989) showed that quantum field theory is not tied to quantum physics but, instead, has a wide range of applications in many other fields. These groundbreaking developments brought to the forefront what can be called quantum mathematics, mentioned earlier in the Preface. Quantum mathematics refers to the system of mathematical concepts that arise in quantum systems-with some of the leading concepts being that of quantum fields, vacuum expectation values, Hamiltonians, state spaces, operators, correlation functions, Feynman path integrals and Lagrangians. 1 The interpretation of quantum mathematics, in general, does not have any relation to physics and, instead, needs to reflect the specificity of the domain of inquiry to which quantum mathematics is being applied. Many of the standard books on quantum field theory are written primarily for a readership that is drawn from theoretical physics. There are voluminous and encyclopedic books on quantum field theory-such as the three-volume opus by Weinberg (2010) which runs for more than 1,500 pages-that are meant for professional theorists and researchers, being inaccessible to nonspecialists and beginners. 1 There is a clash of terminology regarding the term "Lagrangian." In economics, the term is used for the auxiliary function-for which there is no special term in physics-required when using a Lagrange multiplier for constrained optimization. In physics, the term "Lagrangian" encodes the fundamental model describing a quantum phenomenon, and has an ontological status equal to that of the Hamiltonian. In this book, physics terminology is used.
