### Contents

#### Special Relativity

#### Group Theory

#### The Lagrangian Formalism

*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

- Spacetime symmetries enable us to derive equations that describe free particles.
- Internal symmetries enable us to derive equations that describe interacting particles.

#### Quantum Mechanics

#### Quantum Field Theory

#### Electrodynamics

#### Classical Mechanics

#### Appendices

### What Readers Say

Congratulations on an inspiring book!

#### Paul G Ellis

I felt compelled to write you after reading your “About” section on your webpage. I have similar viewpoints and wanted to express my thanks in writing the Physics from Symmetry book. I am only a first year in my PhD at Michigan State University. My classes (quantum especially) have stressed the importance of symmetry which is accompanied by buzzwords like “group theory.” The problem is that we are not actually taught this stuff and so we just kind of perform the drunkard’s walk on the path to understanding the material. But your text has already been tremendously insightful and I am only on page 52!

#### Nicholas Valverde

Thank you so much for writing this book!

#### Thaddeus Calvert

With real pity, I have just finished reading your wonderful book which I really enjoyed. Great many thanks.

#### Aleksey Levin

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

#### Jonathan Wermelinger

#### 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!

#### Dave Pendleton

#### 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.