Quantum Field Theory for Economics and Finance
- What inspired this book?
Quantum field theory (QFT) has been my primary domain of research. I was inspired to look beyond its applications in physics by the work of K. G. Wilson, who applied QFT to the classical phenomenon of phase transitions. I was convinced that uncertainty in the social sciences could also be similarly modeled by QFT. The main purpose of this book is to introduce the mathematics of quantum mechanics and QFT – termed as quantum mathematics — to the field of finance and economics. The topics chosen focus on the mathematical tools of quantum mathematics that can facilitate further studies of finance and economics; hence, the emphasis in the Chapters on QFT is on its diverse mathematical ideas and derivations.
- What do you hope will be the lasting impact of the book?
Mathematical and theoretical finance is currently completely dominated by stochastic calculus; the mathematics of economics is mostly focused on calculus and on (partial) differential equations. My hope is that the book will have a lasting impact by convincing specialists in economics and finance to expand their ‘bag of tricks’ by including models based on quantum mathematics.
The close connection of economics and finance with QFT is reflected in the organization of the Chapters of the book, with topics of the two subjects being interwoven: this interleaving clearly demonstrates and illustrates how ideas from QFT carry over to economics and finance.
- How does the book link your research to real world applications?
The most compelling justification for the application of the mathematics of quantum fields to economics and finance is that the application is supported by empirical evidence. Included in the book are a collection of theoretical models — based on quantum mathematics – that explain empirically grounded areas of economics and finance. It is shown in the book that market data provides strong support for these models.