# A theoretical physics FAQ

*From*: Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>*Date*: Fri, 6 Jan 2006 16:40:58 +0000 (UTC)

A theoretical physics FAQ

http://www.mat.univie.ac.at/~neum/physics-faq.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 half-finished 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. Quantum-classical 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 'on-shell' and 'off-shell'? 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 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?

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 'self-consistent'? 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/physics-faq.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 half-finished 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. Quantum-classical 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 'on-shell' and 'off-shell'? 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 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?

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 'self-consistent'? S18b. What is a vector? S18c. Learning quantum mechanics at age 14

S19a. Acknowledgments

.

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