A theoretical physics FAQ

This theoretical physics FAQ contains my answers to questions on theoretical physics discussed over a number of years in various physics discussion groups (see the Acknowledgments at the end of this page).

Most topics are related to quantum mechanics, quantum field theory, renormalization, the measurement problem, randomness, and philosophical issues in physics. Since different sections were written at different times (some date back to the last century), there is some overlap in the treatment of topics, and a few are a bit outdated.

The FAQ is located at http://www.mat.univie.ac.at/~neum/physfaq/physics-faq.html

Please ask questions related to the FAQ at Physics Overflow.

If you spot errors or have suggestions for improvements, please write me (at Arnold.Neumaier@univie.ac.at).

If you like the FAQ and/or found it useful, please link to it from your home page to make it more widely known.

If you found this FAQ useful you are likely to benefit also from reading the free online book

If you want to know my (practically useful and mathematically elegant, but highly nontraditional) views on the interpretation of quantum mechanics, please look at my Thermal Interpretation FAQ.

Happy Reading!

Arnold Neumaier (University of Vienna)

On January 1, 2016, the FAQ contained 240 topical sections, grouped into three parts with 22 chapters and over 120.000 words, corresponding to a book of about 350 pages with 50 lines per page.
The 21 topics in the initial version from April 28, 2004 have grown
to 88 by January 1, 2005,
to 116 by January 4, 2006,
to 128 by January 3, 2007,
to 140 by January 3, 2008,
to 147 by January 30, 2009,
to 154 by January 10, 2010,
to 178 by January 1, 2011,
to 218 by February 29, 2012,
to 231 by January 1, 2013,
to 236 by January 22, 2014,
to 237 by January 1, 2015,
to 240 by January 1, 2016,
and are likely to grow further.
In this FAQ, I try to be accurate, consistent, and intelligible. Many topics are discussed quite in detail; but though of book size, the FAQ is not a book - more like a specialized encyclopedia. But don't expect completeness or comprehensiveness in any sense. Also, the sections within each chapter were created almost independently over a period of many years, and therefore don't tell a continuous story. Within a section, the organization is usually coherent, but in long sections, the material accumulated over the years and may be repetitive or in need of a better arrangement. (This is all done in my spare time, hence has some limitations....)

Very little is said about the more speculative sides of theoretical physics, such as string theory, quantum gravity, and other physics beyond the standard model.

On topics where the physics community has not yet reached a consensus my point of view is of course only one of the possibilities, and usually (but not always) the mainstream view. But I tend to discuss also important alternative views. In particular, I broadly discuss various approaches to the foundations of quantum mechanics.

QM = quantum mechanics,
QFT = quantum field theory,
QED = quantum electrodynamics,
CCR = canonical commutation relations,
s.p.r. = sci.physics.research (newsgroup).
Strings like quant-ph/0303047 or arXiv:0810.1019 refer to electronic documents in the e-Print archive.
p_0 and \p (the backslash indicates a boldface font) denote the time and space part of a 4-vector p.
The Minkowski inner product is always taken to be p^2=p_0^2-\p^2.

A * indicates a new topic added (or an old one significantly expanded) since January 1, 2016.
Minor changes or additions to old topics are not indicated.

``Consider everything, and keep the good.''
(St. Paul, 1 Thess. 5:21)

Table of Contents

The various topics of this FAQ are arranged into chapters of loosely related topics. But the individual topics can usually be read independently of each other.

Labels and arrangement of the topics changed with time, and may change again as answers to further questions will be added and old answers regrouped. So, to cite part of the FAQ, refer to the title of a chapter or section and not only to its label.

Originally, all contributions to the FAQ were written in a simple text format. I am gradually converting the entries into html format. But converting an entry takes time, since the conversion must be done manually to be more legible than the original. If you'd like to have just one or two entries converted, please write me (at Arnold.Neumaier@univie.ac.at), indicating the wanted entries. This will change my editing priorities. Or, even better, do the conversion for me and send me the corresponding html file. I'll then insert it here in place of the text file, possibly after further editing to polish it a bit.

Part A: Quantum mechanics and its interpretation
(9 chapters with 115 sections [116 titles, two repeated in several chapters])

Part B: Relativistic quantum mechanics and quantum field theory
(8 chapters with 84 sections)

Part C: Various topics

(6 chapters with 41 sections)

Since March 1, 2005, there is also a related FAQ in German language,

containing further topics that I have not translated.

Arnold Neumaier (Arnold.Neumaier@univie.ac.at)