Providing a pedagogical introduction to the essential principles of path integrals and Hamiltonians, this book describes cutting-edge quantum mathematical techniques applicable to a vast range of fields, from quantum mechanics, solid state physics, statistical mechanics, quantum field theory, and superstring theory to financial modeling, polymers, biology, chemistry, and quantum finance. Eschewing use of the Schroedinger equation, the powerful and flexible combination of Hamiltonian operators and path integrals is used to study a range of different quantum and classical random systems, succinctly demonstrating the interplay between a system's path integral, state space, and Hamiltonian. With a practical emphasis on the methodological and mathematical aspects of each derivation, this is a perfect introduction to these versatile mathematical methods, suitable for researchers and graduate students in physics and engineering.

Why is rubber elastic? Why are leaves green? Why can a gecko climb a wall? Answering these and a myriad of other puzzles of nature, Exploring Integrated Science shows how the simplest questions that arise from our daily experiences can lead us through a chain of reasoning that explains some of the most fascinating principles of science. Written in a non-technical, entertaining style to engage those without a science background while maintaining the academic rigor required by more advanced readers, the book follows a unique format that enhances the learning process. Each chapter begins with a pertinent question that forms the basis for explaining a scientific principle. Step by step, the text then delves into the more sophisticated scientific matter necessary for providing insight into the question presented, elucidating key principles and concepts. Each chapter contains a summary highlighting the salient points, answers the question definitively, and concludes with a series of exercises to test readers' assimilation of the material. Richly illustrated with more than 650 vibrant color images, this work captures the essence of our intuitive appreciation of nature, which is the starting point for the adventure of science. Presenting integrated scientific ideas that seamlessly blend biology, mathematics, chemistry, and physics, this volume brings the most complex and intriguing phenomena to readers in a manner that is both accessible and entertaining. The book has an accompanying website with more information.

The Theoretical Foundations of Quantum Mechanics addresses fundamental issues that are not discussed in most books on quantum mechanics. This book focuses on analyzing the underlying principles of quantum mechanics and explaining the conceptual and theoretical underpinning of quantum mechanics. In particular, the concepts of quantum indeterminacy, quantum measurement and quantum superposition are analyzed to clarify the concepts that are implicit in the formulation of quantum mechanics. The Schrodinger equation is never solved in the book. Rather, the discussion on the fundamentals of quantum mechanics is treated in a rigorous manner based on the mathematics of quantum mechanics. The new concept of the interplay of empirical and trans-empirical constructs in quantum mechanics is introduced to clarify the foundations of quantum mechanics and to explain the counter-intuitive construction of nature in quantum mechanics. The Theoretical Foundations of Quantum Mechanics is aimed at the advanced undergraduate and assumes introductory knowledge of quantum mechanics. Its objective is to provide a solid foundation for the reader to reach a deeper understanding of the principles of quantum mechanics.

The economic crisis of 2008 has shown that the capital markets need new theoretical and mathematical concepts to describe and price financial instruments. Focusing almost exclusively on interest rates and coupon bonds, this book does not employ stochastic calculus the bedrock of the present day mathematical finance for any of the derivations. Instead, it analyzes interest rates and coupon bonds using quantum finance. The Heath-Jarrow-Morton and the Libor Market Model are generalized by realizing the forward and Libor interest rates as an imperfectly correlated quantum field. Theoretical models have been calibrated and tested using bond and interest rates market data. Building on the principles formulated in the author s previous book (Quantum Finance, Cambridge University Press, 2004) this ground-breaking book brings together a diverse collection of theoretical and mathematical interest rate models. It will interest physicists and mathematicians researching in finance, and professionals working in the finance industry.

The Theoretical Foundations of Quantum Mechanics addresses fundamental issues that are not discussed in most books on quantum mechanics. This book focuses on analyzing the underlying principles of quantum mechanics and explaining the conceptual and theoretical underpinning of quantum mechanics. In particular, the concepts of quantum indeterminacy, quantum measurement and quantum superposition are analyzed to clarify the concepts that are implicit in the formulation of quantum mechanics. The Schrodinger equation is never solved in the book. Rather, the discussion on the fundamentals of quantum mechanics is treated in a rigorous manner based on the mathematics of quantum mechanics. The new concept of the interplay of empirical and trans-empirical constructs in quantum mechanics is introduced to clarify the foundations of quantum mechanics and to explain the counter-intuitive construction of nature in quantum mechanics. The Theoretical Foundations of Quantum Mechanics is aimed at the advanced undergraduate and assumes introductory knowledge of quantum mechanics. Its objective is to provide a solid foundation for the reader to reach a deeper understanding of the principles of quantum mechanics.

This book applies the mathematics and concepts of quantum mechanics and quantum field theory to the modelling of interest rates and the theory of options. Particular emphasis is placed on path integrals and Hamiltonians. Financial mathematics is dominated by stochastic calculus. The present book offers a formulation that is completely independent of that approach. As such many results emerge from the ideas developed by the author. This work will be of interest to physicists and mathematicians working in the field of finance, to quantitative analysts in banks and finance firms and to practitioners in the field of fixed income securities and foreign exchange. The book can also be used as a graduate text for courses in financial physics and financial mathematics.

Why is rubber elastic? Why are leaves green? Why can a gecko climb a wall? Answering these and a myriad of other puzzles of nature, Exploring Integrated Science shows how the simplest questions that arise from our daily experiences can lead us through a chain of reasoning that explains some of the most fascinating principles of science.

Written in a non-technical, entertaining style to engage those without a science background while maintaining the academic rigor required by more advanced readers, the book follows a unique format that enhances the learning process. Each chapter begins with a pertinent question that forms the basis for explaining a scientific principle. Step by step, the text then delves into the more sophisticated scientific matter necessary for providing insight into the question presented, elucidating key principles and concepts. Each chapter contains a summary highlighting the salient points, answers the question definitively, and concludes with a series of exercises to test readers assimilation of the material.

Richly illustrated with more than 650 vibrant color images, this work captures the essence of our intuitive appreciation of nature, which is the starting point for the adventure of science. Presenting integrated scientific ideas that seamlessly blend biology, mathematics, chemistry, and physics, this volume brings the most complex and intriguing phenomena to readers in a manner that is both accessible and entertaining.

The book has an accompanying website with more information.