Arnold Neumaier
Jan31-09, 06:34 AM
================================================== ===============
A theoretical physics FAQ
http://www.mat.univie.ac.at/~neum/physics-faq.txt
================================================== ===============
This is the yearly reminder that this FAQ exists and is alive...
Happy Reading!
Arnold Neumaier
University of Vienna
http://www.mat.univie.ac.at/~neum/
I like to see people grow
================================================== ===============
This site (a simple ASCII file) contains answers to some more or less
frequently asked questions from theoretical physics. Starting in 2004,
the topics were edited from my answers to postings to the moderated
newsgroup sci.physics.research (or, for some, translated from postings
to the unmoderated German newsgroup de.sci.physik).
Currently, the FAQ contains 147 topics, grouped into 20 chapters,
and filling over 10000 lines of text (about half a megabyte),
corresponding to a book of about 200 pages.
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 have questions, please post them to the moderated newsgroup
sci.physics.research (http://www.lns.cornell.edu/spr)!
If you found this FAQ useful you are likely to benefit also
from reading the following book:
Arnold Neumaier and Dennis Westra,
Classical and Quantum Mechanics via Lie algebras,
Cambridge University Press, to appear (2009?).
http://www.mat.univie.ac.at/~neum/papers/physpapers.html#QML
arXiv:0810.1019
Of course, the FAQ refers only to a tiny part of theoretical physics,
namely to what I happened to discuss on sci.physics.research.
The answers are only as good as my understanding of the matter.
This doesn't mean that they are poor but probably that they are
not perfect. Many topics are discussed quite in detail, but this is
not a book, so don't expect completeness or comprehensiveness in any
sense.
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 not
always the mainstream view. In any case, I try to be accurate,
consistent, and intelligible.
================================================== ===================
In the following table of contents, the asterisks refer to sections
that have been added or strongly modified since January 2008.
(The asterisks in the document itself will refer to sections added
since today.)
Table of Contents
Chapter 1 (16 sections)
S1a. What are bras and kets?
S1b. Projective geometry and quantum mechanics
S1c. What is the meaning of the entries of a density matrix?
S1d. Postulates for the formal core of quantum mechanics
S1e. Open quantum systems
S1f. Interaction with a heat bath
S1g. Quantum-classical mechanics
S1h. Can all quantum states be realized in nature?
S1i. Modes and wave functions of laser beams
S1j. Classical and quantum tunneling
S1k. Quantization in non-Cartesian coordinates
S1l. Second quantization
S1m. When is an object macroscopic?
S1n. The role of the ergodic hypothesis
*S1o. Does quantum mechanics apply to single systems?
*S1p. Dissipative dynamics and Lagrangians
Chapter 2 (9 sections)
S2a. Lie groups and Lie algebras
S2b. The Galilei group as contraction of the Poincare group
S2c. Representations of the Poincare group, spin and gauge invariance
S2d. Forms of relativistic dynamics
S2e. Is there a multiparticle relativistic quantum mechanics?
S2f. What is a photon?
S2g. Particle positions and the position operator
S2h. Localization and position operators
*S2i. Coherent states of light as ensembles
Chapter 3 (6 sections)
S3a. What are 'bare' and 'dressed' particles?
S3b. How meaningful are single Feynman diagrams?
S3c. How real are 'virtual particles'?
S3d. What is the meaning of 'on-shell' and 'off-shell'?
S3e. Virtual particles and Coulomb interaction
S3f. Are virtual particles and decaying particles the same?
Chapter 4 (10 sections)
S4a. How do atoms and molecules look like?
S4b. Why are observable densities state-dependent?
S4c. Are electrons pointlike/structureless?
S4d. How much information is in a particle?
*S4e. Entropy and missing information
S4f. How real is the wave function?
S4g. How real are Feynman's paths?
S4h. Can particles go backward in time?
S4i. What about particles faster than light (tachyons)?
S4j. Do free particles exist?
Chapter 5 (9 sections)
S5a. QM pictures and representations
S5b. Inequivalent representations of the CCR/CAR
S5c. Why does QFT look so different from QM?
S5d. Why is QFT based on a classical action?
S5e. Why does the action only contain first derivatives?
S5f. Why normal ordering?
S5g. Why locality and causal commutation relations?
S5h. Creation operators and rigged Hilbert space
S5i. Why Feynman diagrams?
Chapter 6 (8 sections)
S6a. Nonperturbative computations in quantum field theory
S6b. The formal functional integral approach to QFT
S6c. Functional integrals, Wightman functions, and rigorous QFT
S6d. Is there a rigorous interacting QFT in 4 dimensions?
S6e. Constructive field theory
S6f. The classical limit of relativistic QFT
S6g. What are interpolating fields?
*S6h. Hilbert space and Hamiltonian in relativistic quantum field theory
Chapter 7 (3 sections)
S7a. What is the mass gap?
S7b. Why can a bound state of massless quarks be heavy?
S7c. Bound states in relativistic quantum field theory
Chapter 8 (9 sections)
S8a. Why renormalization?
S8b. Renormalization without infinities I
S8c. Renormalization without infinities II
S8d. Renormalization and coarse graining
S8e. Renormalization scale and experimental energy scale
S8f. Dimensional regularization
S8g. Nonrelativistic quantum field theory
S8h. Nonrenormalizable theories as effective theories
S8i. What about infrared divergences?
Chapter 9 (6 sections)
S9a. Summing divergent series
S9b. Is QED consistent?
S9c. What about relativistic QFT at finite times?
S9d. Perturbation theory and instantaneous forces
S9e. QED and relativistic quantum chemistry
S9f. Are protons described by QED?
Chapter 10 (13 sections)
S10a. How are matrices and tensors related?
S10b. Is quantum mechanics compatible with general relativity?
S10c. Difficulties in quantizing gravity
S10d. Renormalization in quantum gravity
S10e. Hadamard states and their Hilbert spaces
S10f. Why do gravitons have spin 2?
S10g. What is the tetrad formalism?
S10h. Energy in general relativity
S10i. What happened to the aether?
S10j. What is time?
S10k. Time in quantum mechanics
*S10l. Diffeomorphism invariant classical mechanics
*S10m. The concept of ''Now''
Chapter 11 (7 sections)
S11a. A concise formulation of the measurement problem of QM
S11b. The double slit experiment
S11c. The Stern-Gerlach experiment
S11d. The minimal interpretation
S11e. The preferred basis problem
S11f. Master equation and pointer variables
S11g. Does decoherence solve the measurement problem?
Chapter 12 (6 sections)
S12a. Which interpretation of quantum mechanics is most consistent?
S12b. Which textbook of quantum mechanics is best for foundations?
S12c. What is the role of quantum logic?
S12d. Stochastic quantum mechanics
S12e. Is there a relativistic measurement theory?
S12f. Quantum mechanics and dice
Chapter 13 (10 sections)
S13a. Random numbers and other random objects
S13b. What is the meaning of probabilities?
S13c. What about the subjective interpretation of probabilities?
S13d. Are probabilities limits of relative frequencies?
S13e. How meaningful are probabilities of single events?
S13f. Objective probabilities
S13g. How probable are realizations of stochastic processes?
S13h. How do probabilities apply in practice?
S13i. Incomplete knowledge and statistics
S13j. Priors and entropy in probability theory
Chapter 14 (4 sections)
S14a. Theoretical challenges close to experimental data
S14b. Does the standard model predict chemistry?
S14c. Is the result of a measurement a real number?
S14d. Why use complex numbers in physics?
Chapter 15 (5 sections)
S15a. How precise can physical language be?
*S15b. Why bother about rigor in physics?
S15c. Justifying the foundations of a theory
S15d. Foundations, theory and experiment
S15e. Theoretical physics as a formal model of reality
Chapter 16 (12 sections)
S16a. On progress in science
S16b. How different are physical sciences and social sciences
S16c. Can good theories be falsified?
S16d. What, then, distinguishes a good theory?
S16e. When is a theory preferred to another one?
S16f. What is a fact?
S16g. Physics and experience
S16h. Modeling reality
S16i. What is a system (e.g., an ideal gas)?
S16j. When is a theory confirmed?
S16k. What is real?
*S16l. How many angels fit onto the tip of a needle?
Chapter 17 (7 sections)
S17a. How to get information from sci.physics.research
S17b. How to get your work published
S17c. How to respond to critical referee's reports
S17d. How to sell your revolutionary idea
S17e. Useful background, online lecture notes, etc.
S17f. Stories about physicists
S17g. Other physics FAQs
Chapter 18 (5 sections)
S18a. What is the meaning of 'self-consistent'?
S18b. What is a vector?
S18c. Learning quantum mechanics at age 14
S18d. Research at age 16
S18e. Are there indefinite Hilbert spaces?
Chapter 19 (1 section)
*S19a. God and physics
Chapter 20 (1 section)
S20a. Acknowledgments
================================================== ======================
A theoretical physics FAQ
http://www.mat.univie.ac.at/~neum/physics-faq.txt
================================================== ===============
This is the yearly reminder that this FAQ exists and is alive...
Happy Reading!
Arnold Neumaier
University of Vienna
http://www.mat.univie.ac.at/~neum/
I like to see people grow
================================================== ===============
This site (a simple ASCII file) contains answers to some more or less
frequently asked questions from theoretical physics. Starting in 2004,
the topics were edited from my answers to postings to the moderated
newsgroup sci.physics.research (or, for some, translated from postings
to the unmoderated German newsgroup de.sci.physik).
Currently, the FAQ contains 147 topics, grouped into 20 chapters,
and filling over 10000 lines of text (about half a megabyte),
corresponding to a book of about 200 pages.
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 have questions, please post them to the moderated newsgroup
sci.physics.research (http://www.lns.cornell.edu/spr)!
If you found this FAQ useful you are likely to benefit also
from reading the following book:
Arnold Neumaier and Dennis Westra,
Classical and Quantum Mechanics via Lie algebras,
Cambridge University Press, to appear (2009?).
http://www.mat.univie.ac.at/~neum/papers/physpapers.html#QML
arXiv:0810.1019
Of course, the FAQ refers only to a tiny part of theoretical physics,
namely to what I happened to discuss on sci.physics.research.
The answers are only as good as my understanding of the matter.
This doesn't mean that they are poor but probably that they are
not perfect. Many topics are discussed quite in detail, but this is
not a book, so don't expect completeness or comprehensiveness in any
sense.
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 not
always the mainstream view. In any case, I try to be accurate,
consistent, and intelligible.
================================================== ===================
In the following table of contents, the asterisks refer to sections
that have been added or strongly modified since January 2008.
(The asterisks in the document itself will refer to sections added
since today.)
Table of Contents
Chapter 1 (16 sections)
S1a. What are bras and kets?
S1b. Projective geometry and quantum mechanics
S1c. What is the meaning of the entries of a density matrix?
S1d. Postulates for the formal core of quantum mechanics
S1e. Open quantum systems
S1f. Interaction with a heat bath
S1g. Quantum-classical mechanics
S1h. Can all quantum states be realized in nature?
S1i. Modes and wave functions of laser beams
S1j. Classical and quantum tunneling
S1k. Quantization in non-Cartesian coordinates
S1l. Second quantization
S1m. When is an object macroscopic?
S1n. The role of the ergodic hypothesis
*S1o. Does quantum mechanics apply to single systems?
*S1p. Dissipative dynamics and Lagrangians
Chapter 2 (9 sections)
S2a. Lie groups and Lie algebras
S2b. The Galilei group as contraction of the Poincare group
S2c. Representations of the Poincare group, spin and gauge invariance
S2d. Forms of relativistic dynamics
S2e. Is there a multiparticle relativistic quantum mechanics?
S2f. What is a photon?
S2g. Particle positions and the position operator
S2h. Localization and position operators
*S2i. Coherent states of light as ensembles
Chapter 3 (6 sections)
S3a. What are 'bare' and 'dressed' particles?
S3b. How meaningful are single Feynman diagrams?
S3c. How real are 'virtual particles'?
S3d. What is the meaning of 'on-shell' and 'off-shell'?
S3e. Virtual particles and Coulomb interaction
S3f. Are virtual particles and decaying particles the same?
Chapter 4 (10 sections)
S4a. How do atoms and molecules look like?
S4b. Why are observable densities state-dependent?
S4c. Are electrons pointlike/structureless?
S4d. How much information is in a particle?
*S4e. Entropy and missing information
S4f. How real is the wave function?
S4g. How real are Feynman's paths?
S4h. Can particles go backward in time?
S4i. What about particles faster than light (tachyons)?
S4j. Do free particles exist?
Chapter 5 (9 sections)
S5a. QM pictures and representations
S5b. Inequivalent representations of the CCR/CAR
S5c. Why does QFT look so different from QM?
S5d. Why is QFT based on a classical action?
S5e. Why does the action only contain first derivatives?
S5f. Why normal ordering?
S5g. Why locality and causal commutation relations?
S5h. Creation operators and rigged Hilbert space
S5i. Why Feynman diagrams?
Chapter 6 (8 sections)
S6a. Nonperturbative computations in quantum field theory
S6b. The formal functional integral approach to QFT
S6c. Functional integrals, Wightman functions, and rigorous QFT
S6d. Is there a rigorous interacting QFT in 4 dimensions?
S6e. Constructive field theory
S6f. The classical limit of relativistic QFT
S6g. What are interpolating fields?
*S6h. Hilbert space and Hamiltonian in relativistic quantum field theory
Chapter 7 (3 sections)
S7a. What is the mass gap?
S7b. Why can a bound state of massless quarks be heavy?
S7c. Bound states in relativistic quantum field theory
Chapter 8 (9 sections)
S8a. Why renormalization?
S8b. Renormalization without infinities I
S8c. Renormalization without infinities II
S8d. Renormalization and coarse graining
S8e. Renormalization scale and experimental energy scale
S8f. Dimensional regularization
S8g. Nonrelativistic quantum field theory
S8h. Nonrenormalizable theories as effective theories
S8i. What about infrared divergences?
Chapter 9 (6 sections)
S9a. Summing divergent series
S9b. Is QED consistent?
S9c. What about relativistic QFT at finite times?
S9d. Perturbation theory and instantaneous forces
S9e. QED and relativistic quantum chemistry
S9f. Are protons described by QED?
Chapter 10 (13 sections)
S10a. How are matrices and tensors related?
S10b. Is quantum mechanics compatible with general relativity?
S10c. Difficulties in quantizing gravity
S10d. Renormalization in quantum gravity
S10e. Hadamard states and their Hilbert spaces
S10f. Why do gravitons have spin 2?
S10g. What is the tetrad formalism?
S10h. Energy in general relativity
S10i. What happened to the aether?
S10j. What is time?
S10k. Time in quantum mechanics
*S10l. Diffeomorphism invariant classical mechanics
*S10m. The concept of ''Now''
Chapter 11 (7 sections)
S11a. A concise formulation of the measurement problem of QM
S11b. The double slit experiment
S11c. The Stern-Gerlach experiment
S11d. The minimal interpretation
S11e. The preferred basis problem
S11f. Master equation and pointer variables
S11g. Does decoherence solve the measurement problem?
Chapter 12 (6 sections)
S12a. Which interpretation of quantum mechanics is most consistent?
S12b. Which textbook of quantum mechanics is best for foundations?
S12c. What is the role of quantum logic?
S12d. Stochastic quantum mechanics
S12e. Is there a relativistic measurement theory?
S12f. Quantum mechanics and dice
Chapter 13 (10 sections)
S13a. Random numbers and other random objects
S13b. What is the meaning of probabilities?
S13c. What about the subjective interpretation of probabilities?
S13d. Are probabilities limits of relative frequencies?
S13e. How meaningful are probabilities of single events?
S13f. Objective probabilities
S13g. How probable are realizations of stochastic processes?
S13h. How do probabilities apply in practice?
S13i. Incomplete knowledge and statistics
S13j. Priors and entropy in probability theory
Chapter 14 (4 sections)
S14a. Theoretical challenges close to experimental data
S14b. Does the standard model predict chemistry?
S14c. Is the result of a measurement a real number?
S14d. Why use complex numbers in physics?
Chapter 15 (5 sections)
S15a. How precise can physical language be?
*S15b. Why bother about rigor in physics?
S15c. Justifying the foundations of a theory
S15d. Foundations, theory and experiment
S15e. Theoretical physics as a formal model of reality
Chapter 16 (12 sections)
S16a. On progress in science
S16b. How different are physical sciences and social sciences
S16c. Can good theories be falsified?
S16d. What, then, distinguishes a good theory?
S16e. When is a theory preferred to another one?
S16f. What is a fact?
S16g. Physics and experience
S16h. Modeling reality
S16i. What is a system (e.g., an ideal gas)?
S16j. When is a theory confirmed?
S16k. What is real?
*S16l. How many angels fit onto the tip of a needle?
Chapter 17 (7 sections)
S17a. How to get information from sci.physics.research
S17b. How to get your work published
S17c. How to respond to critical referee's reports
S17d. How to sell your revolutionary idea
S17e. Useful background, online lecture notes, etc.
S17f. Stories about physicists
S17g. Other physics FAQs
Chapter 18 (5 sections)
S18a. What is the meaning of 'self-consistent'?
S18b. What is a vector?
S18c. Learning quantum mechanics at age 14
S18d. Research at age 16
S18e. Are there indefinite Hilbert spaces?
Chapter 19 (1 section)
*S19a. God and physics
Chapter 20 (1 section)
S20a. Acknowledgments
================================================== ======================