Department Staff


Belal E Baaquie

Department of Physics
National University of Singapore
Faculty of Science
Blk S13, 03-03
2 Science Drive 3
Singapore 117542

Tel: (65) 6516-2963
Fax: (65) 6777-6126

  Interview of Belal E Baaquie on "Quantum Finance" by Naoyoshi Kachi on (May 2008)
  • Research Associate, Stanford University, 1976-78
  • Member, Institute for Advanced Study, Princeton 1991
  • Physics Department, Harvard University 1998
  • Physics Department, National University of Singapore, 1984-2000
  • University Scholars Programme, Vice-Dean, 1998-2002
  • Physics Department, National University of Singapore, 2002 to present



  • BS, Physics (1972), California Institute of Technology.
  • PhD, Theoretical Physics, Cornell University, 1976.



  • Exploring the Invisible Universe From Black Holes to Superstrings
    By Belal E. Baaquie (NUS, Singapore), Frederick H Willeboordse (NUS, Singapore)

    World Scientific Publishing Company
    (488pp May 2015, ISBN: 978-981-4618-67-0; ISBN: 978-981-4618-69-4 Ebook)

    This book can be purchased at the website.

    "The new book is a tour de force: the authors have assembled a challenging, comprehensive review of modern physics topics ranging from general relativity to superstring theory and most of the things in between. It could very well be used in an advanced undergraduate physics course intended to cover those topics that many smaller physics departments do not have the time or resources to cover in depth." CHOICE Connect


    "Why"? Why is the world, the Universe the way it is? Is space infinitely large? How small is small? What happens when one continues to divide matter into ever smaller pieces? Indeed, what is matter? Is there anything else besides what can be seen? Pursuing the questions employing the leading notions of physics, one soon finds that the tangible and visible world dissolves - rather unexpectedly -into invisible things and domains that are beyond direct perception. A remarkable feature of our Universe is that most of its constituents turn out to be invisible, and this fact is brought out with great force by this book. Exploring the Invisible Universe covers the gamut of topics in advanced modern physics and provides extensive and well substantiated answers to these questions and many more. Discussed in a non-technical, yet also non-trivial manner, are topics dominated by invisible things - such as Black Holes and Superstrings as well as Fields, Gravitation, the Standard Model, Cosmology, Relativity, the Origin of Elements, Stars and Planetary Evolution, and more. Just giving the answer, as so many books do, is really not telling anything at all. To truly answer the "why" questions of nature, one needs to follow the chain of reasoning that scientists have used to come to the conclusions they have. This book does not shy away from difficult-to-explain topics by reducing them to one-line answers and power phrases suitable for a popular talk show. The explanations are rigorous and straight to the point. This book is rarely mathematical without being afraid, however, to use elementary mathematics when called for. In order to achieve this, a large number of detailed figures, specially developed for this book and found nowhere else, convey insights that otherwise might either be inaccessible or need lengthy and difficult-to-follow explanations. After Exploring the Invisible Universe, a reader will have a deeper insight into our current understanding of the foundations of Nature and be able to answer all the questions above and then some. To understand Nature and the cutting edge ideas of contemporary physics, this is the book to have.

  • Quantum Psyche
    By Belal E. Baaquie, F. Carminati, J. Demongeot, G. Galli Carminati, F. Martin,
    M. Teodorani

    CreateSpace Independent Publishing Platform
    (March 2,
    2015; ISBN-13:
    978-1501024078 ISBN-10: 1501024078)

    This book can be purchased at the website.


    At the end of the 19th century Sigmund Freud discovered that our acts and choices are not only decisions of our consciousness, but that they are also deeply determined by our unconscious (the so-called "Freudian unconscious"). During a long correspondence between them (1932-1958) Wolfgang Pauli and Carl Gustav Jung speculated that the unconscious could be a quantum system. This book is addressed both to all those interested in the new developments of the age-old enquiry in the relations between mind and matter, and also to the experts in quantum physics that are interested in a formalisation of this new approach. The description of the "Bilbao experiment" adds a very interesting experimental inquiry into the synchronicity effect in a group situation, linking theory to a quantifiable verification of these subtle effects.

  • Path Integrals and Hamiltonians: Principles and Methods
    By Belal E. Baaquie

    Cambridge University Press
    March 2014; In stock; ISBN:

    This book can be purchased at the website.

    Reviewed by Michael Berg , on 09/11/2014

    In his Preface, Baaquie says that beyond the traditional approach to QM, that of Schr
    ödinger (via the Schrödinger wave equation), there are two others, "namely the operator approach of Heisenberg and the path integral approach of Dirac-Feynman, that provide a mathematical framework that is independent of the Schrödinger equation." He goes on to say, "[i]n this book, the Schrödinger equation is never directly solved; instead the Hamiltonian [or total energy] operator is analyzed and path integrals for different quantum and classical random systems are studied to gain an understanding of quantum mechanics."

    After the Preface, Baaquie presents a Synopsis of the book, the thrust of which is that it is divided into six parts. We get, in sequence, fundamental principles and the mathematical structure of QM, stochastic processes, discrete degrees of freedom, quadratic path integrals, acceleration action, and finally nonlinear path integrals. The last mentioned material includes, e.g., coverage of a nonlinear quartic Lagrangian. It should be noted that Feynman's presentation of his path integral formalism is fundamentally based on a Lagrangian formalism.

    The book is well written, in a compact style, but not stinting on clear explanations. I don't know whether it is because after a good deal of exposure to quantum physics through the services of Proguvecki and others I am more comfortable with this material, and that explains it, but I think the book is accessible even to us mathematicians. Well, let me hedge my bets and add a caveat: I don't think this book is indicated for raw recruits - you should know some quantum mechanics already, perhaps at the level of Faddeev-Yakubovskii, Lectures on Quantum Mechanics. After this it's the right time for "a pedagogical introduction to the essential principles of path integrals and Hamiltonians," as the present book's back cover advertises.

    However, Path Integrals and Hamiltonians looks like a very useful book, and I, for one, am very happy to have a copy.

    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 Schrodinger 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, mathematical finance and engineering.

  • The Theoretical Foundations of Quantum Mechanics
    By Belal E. Baaquie

    Springer Publications
    2013, XII, 268 p. 75 illus., 43 in color. ISBN 978-1-4614-6224-8)

    You may purchase this new book at the Springer website.

    "The material ... is resented in a detailed and coherent fashion, leading from basic concepts to modern developments, including, e.g., quantum entropies, Bell inequalities, the Mach-Zehnder interferometer, quantum eraser, the process of measurement, and others. ... serve as an introduction for advanced undergraduate students of physics who have already been exposed to a quantum mechanics course, or for more advanced students and researchers from other fields who are interested in learning about these matters." (Hans-Thomas Elze, Mathematical Reviews, March, 2014)

    "The book under present review is an extremely interesting, informative and inspiring, unique addition to the existing wealth of monographs and texts on QM and related areas of Physics literature. ... This is a remarkable creation of a brilliant expert, experienced brain brought in a very fascinating style where by the fundamental foundations of QM, the basis of the building blocks of matter and radiation can and will hopefully be better understood and appreciated." (Paninjukunnath Achuthan, zbMATH, Vol. 1272, 2013)

    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 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.

  • Exploring Integrated Science
    By Belal E. Baaquie and Frederick H. Willeboordse
    CRC Press
    2009 pp: 594, ISBN: 9781420087932 (hc).)
    You may purchase this new book at the Taylor and Francis website.

    Exploring integrated science
    Belal Baaquie and Frederick Willeboordse
    Boca Raton, US: CRC Press 2010 | 594pp | £43.99 (HB)
    ISBN 9781420087932
    Reviewed by Lucy Mitton

    This is a beautifully illustrated and well-written general science textbook which integrates biology, chemistry, physics and basic mathematics in one easy to read volume. The authors, both from the National University of Singapore, seek to show how science is best understood as multidisciplinary, interdisciplinary and transdisciplinary.

    The individual chapters are in the form of questions which the authors seek to answer while introducing a host of scientific principles along the way. There are many fact and biography boxes and summary road maps. Examples of the questions are: Why can sunlight power the world? Why are the elements so different from each other? How does water flow? How do atoms bond? What is electricity? Why can we hear music? Why can we smell perfume? Is RNA jack of all trades, but master of none? Why can a gecko climb a wall?

    Through such basic questions the authors seek to show the wonders of science and establish fundamental principles.

    This book deserves a wide readership amongst upper school pupils and undergraduates whose courses require a broad scientific understanding rather than a specialized textbook.

    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.

  • Interest Rates and Coupon Bonds in Quantum Finance
    By Belal E. Baaquie
    Cambridge University Press
    2009 pp: 508, ISBN-13: 9780521889285 (hc).)
    You may purchase this new book at the CUP's website.

    The economic crisis of 2008 has shown that the capital markets need new theoretical and mathematical concepts to describe and price financial instruments. Focusing 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.




  • Taught a whole range of undergraduate and graduate courses in Physics and Mathematics. Thesis advisor for MSc and PhD degrees. Written many articles on general topics such as finance, education, history, economics and philosophy. Developed many modules for teaching science to a broad based non-specialist audience.


  Research Interest    
  • Quantum field theory
  • Financial modeling based on techniques of quantum theory


  Selected Publications    
The copyright of my published papers have mostly been transferred to the publisher of the journal/book. The files are provided for individual use only. Please obtain legal permission from the publisher for reproduction, if it is necessary.