A theoretical physics FAQ

containing 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.

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

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

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


Happy Reading!

Arnold Neumaier
(University of Vienna)
I like to see people grow

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 continuuos story. Within a section, the organization is usually coherent, but in very 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.

On February 29, 2012, the FAQ contained 218 topics, grouped into three parts with 22 chapters and nearly 120.000 words, corresponding to a book of about 340 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,
and are likely to grow further.

Abbreviations:
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, 2013.
Minor changes/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.

Part A: Quantum mechanics and its interpretation
(9 chapters with 107 sections [108 titles, one repeated in two chapters])

Part B: Relativistic quantum mechanics and quantum field theory
(8 chapters with 80 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)