Why This Book?

In the course of studjakobbwcopyying physics I became, like any student of physics, familiar with many fundamental equations and their solutions, but I was never really able to see their connection.

I was thrilled when I understood that most of them have a common origin: Symmetry. To me, the most beautiful thing in physics is when something incomprehensible, suddenly becomes comprehensible, because of a deep explanation. That’s why I fell in love with symmetries.

For example, for quite some time I couldn’t really understand spin, which is some kind of curious internal angular momentum that almost all fundamental particles carry. Then I learned that spin is a direct consequence of a symmetry, called Lorentz symmetry, and everything started to make sense.

Experiences like this were the motivation for this book and in some sense, I wrote the book I wished had existed when I started my journey in physics. Symmetries are beautiful explanations for many otherwise incomprehensible physical phenomena and this book is based on the idea that we can derive the fundamental theories of physics from symmetry.

One could say that this book’s approach to physics starts at the end: Before we even talk about classical mechanics or non-relativistic quantum mechanics, we will use the (as far as we know) exact symmetries of nature to derive the fundamental equations of quantum field theory. Despite its unconventional approach, this book is about standard physics. We will not talk about speculative, experimentally unverified theories. We are going to use standard assumptions and develop standard theories.

I hope you enjoy reading this book as much as I have enjoyed writing it.

Jakob Schwichtenberg, January 2015


Special Relativity

The book starts with a short chapter about special relativity, which is the foundation for everything that follows. We derive the most important concepts like the Minkowski metric and the famous Lorentz transformations. In addition, we discuss why there is an upper speed limit for everything in physics.

Group Theory

The second part of the books develops the mathematics required to utilize symmetry ideas in a physical context. Most of these mathematical tools come from a branch of mathematics called group theory.  A completely self-contained introduction is included and all concepts that are needed to understand the modern theories of physics are explained.

The Lagrangian Formalism

The introduction starts with the basic idea that we get the correct equations of nature by minimizing something, which is commonly called Lagrangian. Demanding that physics is the same in all frames of reference enables us then to derive the fundamental equations of Quantum Field Theory, Quantum Mechanics, Special Relativity, Electrodynamics and Classical Mechanics.

Gauge Theory

In addition to spacetime symmetries, we can have internal symmetries.
  • Spacetime symmetries enable us to derive equations that describe free particles.
  • Internal symmetries enable us to derive equations that describe interacting particles.
The framework that we use to derive these equations from internal symmetries is called Gauge Theory.

Quantum Mechanics

The quantum formalism and the probabilistic interpretation of Quantum Mechanics are explained and motivated.  Afterwards, we take the non-relativistic limit of the Klein-Gordon equation, which yields the Schrödinger equation. Finally, we discuss first applications, like the particle in a box example, and Heisenberg's famous uncertainity principle.

Quantum Field Theory

The fundamental equations that are derived in the second part of the book are used most naturally in Quantum Field Theory. The basic idea how quantum fields can describe particles and particle interactions is described in great detail. Afterwards an outline is presented how this idea can be used to calculate numbers that can be compared with experiments


We derive the inhomogeneous and homogeneous Maxwell equations and discuss how the notions electric and magnetic field come about. In addition, the Lorentz force law and Coulomb's potential are derived.

Classical Mechanics

We derive the Ehrenfest theorem which establishes a connection between Quantum Mechanics and Classical Mechanics. Then, we derive the Lagrangian of  non-relativistic mechanics and Newton's second law, which are the starting points for classical mechanics.


The appendices contain many explanations of important mathematical concepts that may be unfamiliar to beginner students. For example, the Taylor series, the Kronecker Symbol and the matrix exponential function are explained.
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What Readers Say

The main purpose of this book is to present an updated modern approach to physical theories thorough symmetry methods. It shall not be understood as a pure academical approach like many other monographs on the subject, but as an intuitive approach that tries to introduce and justify the concepts and notions in a natural and physically motivated way, deprived from the formal machinery that usually is at the source of difficulties for the beginner. As a first contact text it is remarkably well written and motivated, and constitutes a very good preparation for the study of the hard formalism of more advanced books.

The complete zbMATH review can be read here.

Rutwig Campoamor-Stursberg

I have just finished your great book, and stand by my glowing Amazon review. […] I also very much enjoyed the bonus chapter, as it contained a little speculative look ahead, answering questions that naturally come up after reading a text such as this. Introducing physics from an analysis of symmetries has given me a new appreciation of the surpassing beauty of the standard model. It motivates so much of what had seemed to me before to be a mass of unrelated formulae, and I also see now more clearly the process of developing a GUT. You hit the balance exactly right for a mathematically trained yet physics novice like me. I will close by saying thank you again, and please write another book! I would like to see a sequel, perhaps expanding on the topic of the bonus chapter.

Jandro Kirkish

So it was with great anticipation that I read Physics from Symmetry, where the author attempts, as the title indicates, to derive much of physics from symmetry. I had heard of Noether’s theorem that says each symmetry is related to a conservation law, but had not seen it worked out in detail until I looked at this book. Nor had I any idea of how far one could go from just these ideas and a willingness to forge ahead with calculations and see where they lead.

This is not a mathematics book. There are no theorems or proofs. What there are is plenty of ideas, clear explanations, detailed calculations and tons of footnotes.

The complete MAA review can be read here.

Peter Rabinovitch – MAA Review

Thank you for writing this wonderful book. By way of background I am not a physicist by training but a EE trying to learn more about QFT for no other purpose than the love of the subject.

Joey Ooi

GREAT book!

Peter Freed

First let me tell you that I liked your book a lot . It is the best introduction to physics I have read in a long time . I don’t know whether the university you are affiliated with has any contacts with Coursera ? I do believe that your book would be an excellent basis for a course at Coursera . It is just the right level to be able to interest a broad group of people .

This book should be a must for every science and math undergraduate . It is the right way to introduce physics to young students and a significant improvement on the way in which undergraduate courses started with classical physics . The beauty of the subject is made obvious and the built up of the field of physics is clearly illustrated ; without compromising on the maths . The structure of the book is well thought through and the student is helped a lot by the diagrams and the summaries at the start of each part . The math required is explained in the appendices just at the right level and with the same clarity as we find in the bulk of the book .

Rudy Blyweert

I think this is a superb book. For a long time it has fascinated me, how much physics that can be derived from symmetry. Somehow I have had the intuition that almost all physics is the result of symmetry, but I did never have the time to dive into the advanced textbooks of quantum field theory, since it is not my field of speciality (I am a physicist, but in my field of research those things are considered “irrelevant”. Therefore, I have to study the physics that interests me most in my spare time, a common problem for researchers). I really love this book, since I at last have found a lucid text that I can read on the train, sitting in a park etc. Symmetry is really the core of physics, and I hope future teachers will adopt Jakob Schwichtenbergs approach in teaching physics with symmetry as its foundation.

G. Ullman

Really helped me understand what was going on in my undergraduate degree. Really recommended for everyone to read, whether a future Feynman or just an interested bystander wishing to peruse the plethora of mechanical machinery which turns the handle of the standard model.

Naim Hussain

I am a student in the elite master course in theoretical and mathematical physics at LMU and I recently started to study your book. Needless to say, it is a masterpiece. I fully agree with everything you wrote in it. This is exactly the book the a physics student need.

Federico Roccati

I recently purchased your book „Physics from Symmetry“, for which I cannot thank you enough! I’ve had a hard time finding a clear and pedagogical description of Lie Group Theory and also of Noether’s Theorem. Thank you so much!

Jonathan Wermelinger

I must say that you have done the current and future generations of undergraduates, as well as interested self-studying amateurs such as myself, a tremendous service by applying the logical structure and clarity of your writing to this often difficult topic.
Indeed, I wish this book had been available many years ago when I was an undergraduate, it would have alleviated years of confusion.

Paul Wakefield

This is the book I’ve been looking for all these years – a clear, concise, well-written summary, from an introductory level, of advanced (for me, at least) physics topics connected by the common thread of symmetry. More specifically, the introductory presentation of symmetry and Lie Groups makes this ordinarily complex topic clear and understandable! I also appreciate the level of presentation – no boring topics such as ropes and pulleys, inclined planes with sliding boxes, etc., no historical fluff and filler (that made me change from physics to chemistry); the chapters start with the really interesting stuff: Special Relativity; Symmetry Tools; Lagrangian Formalism; Classical Mechanics; Electrodynamics; Noether’s Theorem; QM Operators; Klein-Gordon & Dirac Equations; Symmetry of Spin Fields; Schrodinger Eq; and Quantum Field Theory. Plus an Appendix reviewing Calculus and Linear Algebra. The book contains much more than these topics, but this gives an indication of the level and scope involved. Overall, an excellent, almost magical,mtext covering all the major areas of physics in an accessible manner. Highly recommended!

As a retirement project, I’ve been determined to self-teach and update myself on the Physics topics I missed starting 50 years ago when, being bored with the books and courses as taught at the time, I dropped Physics for other pursuits.
However, I’ve never lost my interest and your book is clarifying and helping greatly to rekindle my efforts to complete this item on my bucket list.  If only I’d had you as a teacher years ago!

Dave Pendleton

Most books you can find about physics are explaining things in the same way by following the historical path to develop their theories. In this book the results are not based on historical riddles that need to be solved by doing assumptions that prove to be correct. Here the results are founded on a common principle and the physical equations drop out when symmetries are studied. Due to the common nature of this approach the connection between the physical topics is emphasized.
This approach gave me a new and illuminating view on  many topics and I learned more about the mathematical principles behind physical theories than I did by reading the standard textbooks.

Daniel Hilpert

Most books, as well as lectures, introduce Quantum Physics from Classical Physics, deriving microscopical from macroscopical laws. Didactically this may be correct (although sometimes certain rules and formulae pop up out from nowhere), but in fact the macroscopic exists through certain limits of the microscopic.

This is a book in which this way was chosen, deriving physics from only a few assumptions.
For the interested reader with prior knowledge about modern physics I can strongly recommend this book to further deepen your understanding of the matter.

Arne Becker

I read this book in preparation for my final theoretical physics exam (Bachelor’s degree), mainly because I had no clue concerning Lie-Theory and most other books were overly formal and complicated.

This book gives very easy and intuitive access to the main ideas of group theory with very little assumptions made and foreknowledge required.
I enjoyed the way this book was written, so I kept reading the following chapters, even if they weren’t necessarily relevant for my exam or I’ve already learnt those topics (Quantum Mechanics) and it was worth it, because the book offers nice connections between the Lagrangian formalism and Quantum Physics.


If you have an exam exclusively about Quantum Physics next week and only time to read one book, you probably should better read a standard textbook. But if you are looking for a deeper understanding and the link between things, or if you just started your studies and want an intuitive introduction into the world of physics using symmetry – this is the perfect book for you.

Fritz Waitz

I’m a M.Sc. student in Delft, currently doing a research project of only 6 weeks. I have to do two of these for my rather strange M.Sc. program. The research project is at the Lorentz Instute in Leiden, and contrary to delft they do deal with theoretical physics, specifically quantum field theory, group theory and general relativity. Delft mostly focuses on nano-devices in the master program, so sadly these topics are missing.

The Leiden group I’m working with/at/for gave me a text on group theory, but it seems to be written for mathematicians rather than physicists. I was rather bored with it, and couldn’t make much progress. I decided to hit the library for an e-book that was better fit for me. Group theory, as keywords, didn’t bring up much; but physics symmetry immediately yielded your book. Looking into it, I found a very modern website, an interesting preface and decided to download the book.

I’m now at page 60, after a day. I’m enjoying the writing style – it is indeed very well suited to somebody that hasn’t got much introduction into it. I particularly like going from simple definition to abstract mathematical definition and back.

Josko Daimonie

Excellent book!!!

Enric Arcadia

Latest news


The digital version of Physics from Symmetry has been released

Today Springer released the digital version of Physics from Symmetry. The print version should be available soon. The book can be bought and downloaded as a PDF document at the […]


The Manuscript is Finished!

All corrections and change request have been incorporated. Now the production can begin and the digital and print versions should be available soon.


Physics from Symmetry will be published by Springer

The book will be part of the Undergraduate Lecture Notes in Physics series and be published next year.

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