A theoretical physics FAQ
A theoretical physics FAQ
http://www.mat.univie.ac.at/~neum/physicsfaq.txt
This site contains answers to some more or less frequently asked
questions from theoretical physics. They were edited from my answers
to postings to the moderated newsgroup sci.physics.research
(or, for some, to the unmoderated newsgroup de.sci.physik).
If you like the FAQ and/or found it useful, I'd appreciate if you
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@xxxxxxxxxxxx).
Compared to the version of June 20, 2005, there are only three new
topics (as well as a number of minor improvements to older entries):
S13f. Objective probabilities
S16h. Modeling reality
S16i. What is a system (e.g., an ideal gas)?
(This lack of growth is due to the fact that I currently have almost no
free time for discussing physics. I apologize to those I had left with
halffinished discussions, in particular to Seratend  hope to continue
at some time in the future...)
Happy Reading!
Arnold Neumaier
University of Vienna
http://www.mat.univie.ac.at/~neum/
I like to see people grow

Table of Contents

QM = quantum mechanics, QFT = quantum field theory,
QED = quantum electrodynamics, CCR = canonical commutation relations,
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. Quantumclassical correspondence
S1h. Can all quantum states be realized in nature?
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. Localization and position operators
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 'onshell' and 'offshell'?
S3e. Virtual particles and Coulomb interaction
S3f. Are virtual particles and decaying particles the same?
S4a. Are electrons pointlike/structureless?
S4b. How much information is in a particle?
S4c. How real is the wave function?
S4d. How real are Feynman's paths?
S4e. Can particles go backward in time?
S4f. What about particles faster than light
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
S6a. Nonperturbative computations in QFT
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. The classical limit of relativistic QFT
S6f. What are interpolating fields?
S7a. What is the mass gap?
S7b. Why can a bound state of massless quarks be heavy?
S7c. Bound states in relativistic QFT
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?
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
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 ether?
S10j. What is time?
S11a. A concise formulation of the measurement problem of QM
S11b. The double slit experiment
S11c. The SternGerlach experiment
S11d. The minimal interpretation
S11e. The preferred basis problem
S11f. Master equation and pointer variables
S11g. Does decoherence solve the measurement problem?
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?
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
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?
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
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)?
S17a. How to get information from sci.physics.research
S17b. How to get your work published
S17c. How to sell your revolutionary idea
S17d. Useful background for theoretical physics
S17e. Stories about physicists
S17f. Other physics FAQs
S18a. What is the meaning of 'selfconsistent'?
S18b. What is a vector?
S18c. Learning quantum mechanics at age 14
S19a. Acknowledgments
A theoretical physics FAQ
http://www.mat.univie.ac.at/~neum/physicsfaq.txt
This site contains answers to some more or less frequently asked
questions from theoretical physics. They were edited from my answers
to postings to the moderated newsgroup sci.physics.research
(or, for some, to the unmoderated newsgroup de.sci.physik).
If you like the FAQ and/or found it useful, I'd appreciate if you
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@xxxxxxxxxxxx).
Compared to the version of June 20, 2005, there are only three new
topics (as well as a number of minor improvements to older entries):
S13f. Objective probabilities
S16h. Modeling reality
S16i. What is a system (e.g., an ideal gas)?
(This lack of growth is due to the fact that I currently have almost no
free time for discussing physics. I apologize to those I had left with
halffinished discussions, in particular to Seratend  hope to continue
at some time in the future...)
Happy Reading!
Arnold Neumaier
University of Vienna
http://www.mat.univie.ac.at/~neum/
I like to see people grow

Table of Contents

QM = quantum mechanics, QFT = quantum field theory,
QED = quantum electrodynamics, CCR = canonical commutation relations,
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. Quantumclassical correspondence
S1h. Can all quantum states be realized in nature?
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. Localization and position operators
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 'onshell' and 'offshell'?
S3e. Virtual particles and Coulomb interaction
S3f. Are virtual particles and decaying particles the same?
S4a. Are electrons pointlike/structureless?
S4b. How much information is in a particle?
S4c. How real is the wave function?
S4d. How real are Feynman's paths?
S4e. Can particles go backward in time?
S4f. What about particles faster than light
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
S6a. Nonperturbative computations in QFT
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. The classical limit of relativistic QFT
S6f. What are interpolating fields?
S7a. What is the mass gap?
S7b. Why can a bound state of massless quarks be heavy?
S7c. Bound states in relativistic QFT
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?
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
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 ether?
S10j. What is time?
S11a. A concise formulation of the measurement problem of QM
S11b. The double slit experiment
S11c. The SternGerlach experiment
S11d. The minimal interpretation
S11e. The preferred basis problem
S11f. Master equation and pointer variables
S11g. Does decoherence solve the measurement problem?
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?
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
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?
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
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)?
S17a. How to get information from sci.physics.research
S17b. How to get your work published
S17c. How to sell your revolutionary idea
S17d. Useful background for theoretical physics
S17e. Stories about physicists
S17f. Other physics FAQs
S18a. What is the meaning of 'selfconsistent'?
S18b. What is a vector?
S18c. Learning quantum mechanics at age 14
S19a. Acknowledgments
.
Relevant Pages
 A theoretical physics FAQ
... Of course, the FAQ refers only to a tiny part of theoretical physics, ... Postulates for the formal core of quantum mechanics ... What are 'bare' and 'dressed' particles? ... Is quantum mechanics compatible with general relativity? ... (sci.physics.research)  A theoretical physics FAQ
... A theoretical physics FAQ ... This is the yearly reminder that this FAQ exists and is alive... ... Classical and Quantum Mechanics via Lie algebras, ... Is quantum mechanics compatible with general relativity? ... (sci.physics.research)  A theoretical physics FAQ
... questions from theoretical physics. ... Postulates for the formal core of quantum mechanics ... Why does QFT look so different from QM? ... Is quantum mechanics compatible with general relativity? ... (sci.physics.research)  Re: Renormalization
... and the way Dirac, Pauli, Heisenberg and others tried to unify relativity and quantum mechanics in the 1920's ... If it turned out that some physical system could ... Maybe this is just because the field concept itself has no relationship to physics, and therefore cannot be made rigorous, in principle? ... (sci.physics.research)  A theoretical physics FAQ
... Of course, the FAQ refers only to a tiny part of theoretical physics, ... What are 'bare' and 'dressed' particles? ... Why does QFT look so different from QM? ... Is quantum mechanics compatible with general relativity? ... (sci.physics.research) 
