Anmerkung: Cover -- Titlepage -- Copyright -- Dedication -- Preface -- Contents -- List of Plates -- 8 Introduction to Volume 2 -- 8.1 Overview -- 8.2 Quantum theory in the early 1920s: deficiencies and discoveries (exclusion principle and spin) -- 8.3 Atomic structure à la Bohr, X-ray spectra, and the discovery of the exclusion principle -- 8.3.1 Important clues from X-ray spectroscopy -- 8.3.2 Electron arrangements and the emergence of the exclusion principle -- 8.3.3 The discovery of electron spin -- 8.4 The dispersion of light: a gateway to a new mechanics -- 8.4.1 The Lorentz-Drude theory of dispersion -- 8.4.2 Dispersion theory and the Bohr model -- 8.4.3 Final steps to a correct quantum dispersion formula -- 8.4.4 A generalized dispersion formula for inelastic light scattering-the Kramers-Heisenberg paper -- 8.5 The genesis of matrix mechanics -- 8.5.1 Intensities, and another look at the hydrogen atom -- 8.5.2 The Umdeutung paper -- 8.5.3 The new mechanics receives an algebraic framing-Born and Jordan's Two-Man-Paper -- 8.5.4 Dirac and the formal connection between classical and quantum mechanics -- 8.5.5 The Three-Man-Paper [Dreimännerarbeit]-completion of the formalism of matrix mechanics -- 8.6 The genesis of wave mechanics -- 8.6.1 The mechanical-optical route to quantum mechanics -- 8.6.2 Schrödinger's wave mechanics -- 8.7 The new theory repairs and extends the old -- 8.8 Statistical aspects of the new quantum formalisms -- 8.9 The Como and Solvay conferences, 1927 -- 8.10 Von Neumann puts quantum mechanics in Hilbert space -- Part III Transition to the New Quantum Theory -- 9 The Exclusion Principle and Electron Spin -- 9.1 The road to the exclusion principle -- 9.1.1 Bohr's second atomic theory -- 9.1.2 Clues from X-ray spectra -- 9.1.3 The filling of electron shells and the emergence of the exclusion principle. , 9.2 The discovery of electron spin -- 10 Dispersion Theory in the Old Quantum Theory -- 10.1 Classical theories of dispersion -- 10.1.1 Damped oscillations of a charged particle -- 10.1.2 Forced oscillations of a charged particle -- 10.1.3 The transmission of light: dispersion and absorption -- 10.1.4 The Faraday effect -- 10.1.5 The empirical situation up to ca. 1920 -- 10.2 Optical dispersion and the Bohr atom -- 10.2.1 The Sommerfeld-Debye theory -- 10.2.2 Dispersion theory in Breslau: Ladenburg and Reiche -- 10.3 The correspondence principle in radiation and dispersion theory: Van Vleck and Kramers -- 10.3.1 Van Vleck and the correspondence principle for emission and absorption of light -- 10.3.2 Dispersion in a classical general multiply periodic system -- 10.3.3 The Kramers dispersion formula -- 10.4 Intermezzo: the BKS theory and the Compton effect -- 10.5 The Kramers-Heisenberg paper and the Thomas-Reiche-Kuhn sum rule: on the verge of Umdeutung -- 11 Heisenberg's Umdeutung Paper -- 11.1 Heisenberg in Copenhagen -- 11.2 A return to the hydrogen atom -- 11.3 From Fourier components to transition amplitudes -- 11.4 A new quantization condition -- 11.5 Heisenberg's Umdeutung paper: a new kinematics -- 11.6 Heisenberg's Umdeutung paper: a new mechanics -- 12 The Consolidation of Matrix Mechanics: Born-Jordan, Dirac and the Three-Man-Paper -- 12.1 The ``Two-Man-Paper'' of Born and Jordan -- 12.2 The new theory derived differently: Dirac's formulation of quantum mechanics -- 12.3 The ``Three-Man-Paper'' of Born, Heisenberg, and Jordan -- 12.3.1 First chapter: systems of a single degree of freedom -- 12.3.2 Second chapter: foundations of the theory of systems of arbitrarily many degrees of freedom -- 12.3.3 Third chapter: connection with the theory of eigenvalues of Hermitian forms -- 12.3.4 Third chapter (cont'd): continuous spectra. , 12.3.5 Fourth chapter: physical applications of the theory -- 13 De Broglie's Matter Waves and Einstein's Quantum Theory of the Ideal Gas -- 13.1 De Broglie and the introduction of wave-particle duality -- 13.2 Wave interpretation of a particle in uniform motion -- 13.3 Classical extremal principles in optics and mechanics -- 13.4 De Broglie's mechanics of waves -- 13.5 Bose-Einstein statistics and Einstein's quantum theory of the ideal gas -- 14 Schrödinger and Wave Mechanics -- 14.1 Schrödinger: early work in quantum theory -- 14.2 Schrödinger and gas theory -- 14.3 The first (relativistic) wave equation -- 14.4 Four papers on non-relativistic wave mechanics -- 14.4.1 Quantization as an eigenvalue problem. Part I -- 14.4.2 Quantization as an eigenvalue problem. Part II -- 14.4.3 Quantization as an eigenvalue problem. Part III -- 14.4.4 Quantization as an eigenvalue problem. Part IV -- 14.5 The ``equivalence'' paper -- 14.6 Reception of wave mechanics -- 15 Successes and Failures of the Old Quantum Theory Revisited -- 15.1 Fine structure 1925-1927 -- 15.2 Intermezzo: Kuhn losses suffered and recovered -- 15.3 External field problems 1925-1927 -- 15.3.1 The anomalous Zeeman effect: matrix-mechanical treatment -- 15.3.2 The Stark effect: wave-mechanical treatment -- 15.4 The problem of helium -- 15.4.1 Heisenberg and the helium spectrum: degeneracy, resonance, and the exchange force -- 15.4.2 Perturbative attacks on the multi-electron problem -- 15.4.3 The helium ground state: perturbation theory gives way to variational methods -- Part IV The Formalism of Quantum Mechanics and Its Statistical Interpretation -- 16 Statistical Interpretation of Matrix and Wave Mechanics -- 16.1 Evolution of probability concepts from the old to the new quantum theory -- 16.2 The statistical transformation theory of Jordan and Dirac. , 16.2.1 Jordan's and Dirac's versions of the statistical transformation theory -- 16.2.2 Jordan's ``New foundation …'' I -- 16.2.3 Hilbert, von Neumann, and Nordheim on Jordan's ``New foundation …'' I -- 16.2.4 Jordan's ``New foundation …'' II -- 16.3 Heisenberg's uncertainty relations -- 16.4 Como and Solvay, 1927 -- 17 Von Neumann's Hilbert Space Formalism -- 17.1 ``Mathematical foundation …'' -- 17.2 ``Probability-theoretic construction …'' -- 17.3 From canonical transformations to transformations in Hilbert space -- 18 Conclusion: Arch and Scaffold -- 18.1 Continuity and discontinuity in the quantum revolution -- 18.2 Continuity and discontinuity in two early quantum textbooks -- 18.3 The inadequacy of Kuhn's model of a scientific revolution -- 18.4 Evolution of species and evolution of theories -- 18.5 The role of constraints in the quantum revolution -- 18.6 Limitations of the arch-and-scaffold metaphor -- 18.7 Substitution and generalization -- Appendix -- C C. The Mathematics of Quantum Mechanics -- C.1 Matrix algebra -- C.2 Vector spaces (finite dimensional) -- C.3 Inner-product spaces (finite dimensional) -- C.4 A historical digression: integral equations and quadratic forms -- C.5 Infinite-dimensional spaces -- C.5.1 Topology: open and closed sets, limits, continuous functions, compact sets -- C.5.2 The first Hilbert space: l2 -- C.5.3 Function spaces: L2 -- C.5.4 The axiomatization of Hilbert space -- C.5.5 A new notation: Dirac's bras and kets -- C.5.6 Operators in Hilbert space: von Neumann's spectral theory -- Bibliography -- Index.

Anmerkung: Cover -- Contents -- 1 Origins I: From the arrow of time to the first quantum field -- 1.1 Quantum prehistory: crises in classical physics -- 1.2 Early work on cavity radiation -- 1.3 Planck's route to the quantization of energy -- 1.4 First inklings of field quantization: Einstein and energy fluctuations -- 1.5 The first true quantum field: Jordan and energy fluctuations -- 2 Origins II: Gestation and birth of interacting field theory: from Dirac to Shelter Island -- 2.1 Introducing interactions: Dirac and the beginnings of quantum electrodynamics -- 2.2 Completing the formalism for free fields: Jordan, Klein, Wigner, Pauli, and Heisenberg -- 2.3 Problems with interacting fields: infinite seas, divergent integrals, and renormalization -- 3 Dynamics I: The physical ingredients of quantum field theory: dynamics, symmetries, scales -- 4 Dynamics II: Quantum mechanical preliminaries -- 4.1 The canonical (operator) framework -- 4.2 The functional (path-integral) framework -- 4.3 Scattering theory -- 4.4 Problems -- 5 Dynamics III: Relativistic quantum mechanics -- 5.1 The Lorentz and Poincaré groups -- 5.2 Relativistic multi-particle states (without spin) -- 5.3 Relativistic multi-particle states (general spin) -- 5.4 How not to construct a relativistic quantum theory -- 5.5 A simple condition for Lorentz-invariant scattering -- 5.6 Problems -- 6 Dynamics IV: Aspects of locality: clustering, microcausality, and analyticity -- 6.1 Clustering and the smoothness of scattering amplitudes -- 6.2 Hamiltonians leading to clustering theories -- 6.3 Constructing clustering Hamiltonians: second quantization -- 6.4 Constructing a relativistic, clustering theory -- 6.5 Local fields, non-localizable particles! -- 6.6 From microcausality to analyticity -- 6.7 Problems -- 7 Dynamics V: Construction of local covariant fields. , 7.1 Constructing local, Lorentz-invariant Hamiltonians -- 7.2 Finite-dimensional representations of the homogeneous Lorentz group -- 7.3 Local covariant fields for massive particles of any spin: the Spin-Statistics theorem -- 7.4 Local covariant fields for spin-& -- #189 -- (spinor fields) -- 7.5 Local covariant fields for spin-1 (vector fields) -- 7.6 Some simple theories and processes -- 7.7 Problems -- 8 Dynamics VI: The classical limit of quantum fields -- 8.1 Complementarity issues for quantum fields -- 8.2 When is a quantum field "classical"? -- 8.3 Coherent states of a quantum field -- 8.4 Signs, stability, symmetry-breaking -- 8.5 Problems -- 9 Dynamics VII: Interacting fields: general aspects -- 9.1 Field theory in Heisenberg representation: heuristics -- 9.2 Field theory in Heisenberg representation: axiomatics -- 9.3 Asymptotic formalism I: the Haag-Ruelle scattering theory -- 9.4 Asymptotic formalism II: the Lehmann-Symanzik-Zimmermann (LSZ) theory -- 9.5 Spectral properties of field theory -- 9.6 General aspects of the particle-field connection -- 9.7 Problems -- 10 Dynamics VIII: Interacting fields: perturbative aspects -- 10.1 Perturbation theory in interaction picture and Wick's theorem -- 10.2 Feynman graphs and Feynman rules -- 10.3 Path-integral formulation of field theory -- 10.4 Graphical concepts: N-particle irreducibility -- 10.5 How to stop worrying about Haag's theorem -- 10.6 Problems -- 11 Dynamics IX: Interacting fields: non-perturbative aspects -- 11.1 On the (non-)convergence of perturbation theory -- 11.2 "Perturbatively non-perturbative" processes: threshhold bound states -- 11.3 "Essentially non-perturbative" processes: non-Borel-summability in field theory -- 11.4 Problems -- 12 Symmetries I: Continuous spacetime symmetry: why we need Lagrangians in field theory. , 12.1 The problem with derivatively coupled theories: seagulls, Schwinger terms, and T* products -- 12.2 Canonical formalism in quantum field theory -- 12.3 General condition for Lorentz-invariant field theory -- 12.4 Noether's theorem, the stress-energy tensor, and all that stuff -- 12.5 Applications of Noether's theorem -- 12.6 Beyond Poincaré: supersymmetry and superfields -- 12.7 Problems -- 13 Symmetries II: Discrete spacetime symmetries -- 13.1 Parity properties of a general local covariant field -- 13.2 Charge-conjugation properties of a general local covariant field -- 13.3 Time-reversal properties of a general local covariant field -- 13.4 The TCP and Spin-Statistics theorems -- 13.5 Problems -- 14 Symmetries III: Global symmetries in field theory -- 14.1 Exact global symmetries are rare! -- 14.2 Spontaneous breaking of global symmetries: the Goldstone theorem -- 14.3 Spontaneous breaking of global symmetries: dynamical aspects -- 14.4 Problems -- 15 Symmetries IV: Local symmetries in field theory -- 15.1 Gauge symmetry: an example in particle mechanics -- 15.2 Constrained Hamiltonian systems -- 15.3 Abelian gauge theory as a constrained Hamiltonian system -- 15.4 Non-abelian gauge theory: construction and functional integral formulation -- 15.5 Explicit quantum-breaking of global symmetries: anomalies -- 15.6 Spontaneous symmetry-breaking in theories with a local gauge symmetry -- 15.7 Problems -- 16 Scales I: Scale sensitivity of .eld theory amplitudes and effective field theories -- 16.1 Scale separation as a precondition for theoretical science -- 16.2 General structure of local effective Lagrangians -- 16.3 Scaling properties of effective Lagrangians: relevant, marginal, and irrelevant operators -- 16.4 The renormalization group -- 16.5 Regularization methods in field theory -- 16.6 Effective field theories: a compendium -- 16.7 Problems. , 17 Scales II: Perturbatively renormalizable field theories -- 17.1 Weinberg's power-counting theorem and the divergence structure of Feynman integrals -- 17.2 Counterterms, subtractions, and perturbative renormalizability -- 17.3 Renormalization and symmetry -- 17.4 Renormalization group approach to renormalizability -- 17.5 Problems -- 18 Scales III: Short-distance structure of quantum field theory -- 18.1 Local composite operators in field theory -- 18.2 Factorizable structure of field theory amplitudes: the operator product expansion -- 18.3 Renormalization group equations for renormalized amplitudes -- 18.4 Problems -- 19 Scales IV: Long-distance structure of quantum field theory -- 19.1 The infrared catastrophe in unbroken abelian gauge theory -- 19.2 The Bloch-Nordsieck resolution -- 19.3 Unbroken non-abelian gauge theory: confinement -- 19.4 How confinement works: three-dimensional gauge theory -- 19.5 Problems -- Appendix A: The functional calculus -- Appendix B: Rates and cross-sections -- Appendix C: Majorana spinor algebra -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Y -- Z.

Anmerkung: Cover -- CONSTRUCTING QUANTUM MECHANICS -- Copyright -- Preface -- Contents -- List of plates -- Chapter 1 Introduction to Volume One -- 1.1 Overview -- 1.2 Early developments: Planck, Einstein, and Bohr -- 1.2.1 Planck, the second law, and black-body radiation -- 1.2.2 Planck's first tenuous steps toward energy quantization -- 1.2.3 Einstein, equipartition, and light quanta -- 1.2.4 Einstein, fluctuations, and light quanta -- 1.2.5 Lorentz convinces Planck of energy quantization -- 1.2.6 From Einstein, equipartition, and specific heat to Nernst and the Solvay conference -- 1.2.7 Bohr and Rutherford's model of the atom -- 1.2.8 Bohr and Nicholson's theory -- 1.2.9 The Balmer formula and the birth of the Bohr model of the atom -- 1.2.10 Einstein and the Bohr model -- 1.3 The old quantum theory: principles, successes, and failures -- 1.3.1 Sommerfeld's path to quantum theory -- 1.3.2 Quantum conditions: Planck, Sommerfeld, Ishiwara, Wilson, Schwarzschild, and Epstein -- 1.3.3 Ehrenfest and the adiabatic principle -- 1.3.4 The correspondence principle from Bohr to Kramers, Born, and Van Vleck -- 1.3.5 The old quantum theory's winning streak: fine structure, Stark effect, X-ray spectra -- 1.3.6 The old quantum theory's luck runs out:multiplets, Zeeman effect, helium -- 1.3.7 Born taking stock -- Part I Early Developments -- Chapter 2 Planck, the Second Law of Thermodynamics, and Black-body Radiation -- 2.1 The birthdate of quantum theory? -- 2.2 Early work on black-body radiation (1860-1896) -- 2.3 Planck, the second law of thermodynamics, and black-body radiation (1895-1899) -- 2.4 From the Wien law to the Planck law: changing the expression for the entropy of a resonator -- 2.5 Justifying the new expression for the entropy of a resonator -- 2.6 Energy parcels or energy bins? -- Chapter 3 Einstein, Equipartition, Fluctuations, and Quanta. , 3.1 Einstein's annus mirabilis -- 3.2 The statistical trilogy (1902-1904) -- 3.3 The light-quantum paper (1905) -- 3.3.1 Classical theory leads to the Rayleigh-Jeans law -- 3.3.2 Einstein's argument for light quanta: fluctuations in black-body radiation at high frequencies -- 3.3.3 Evidence for light quanta: the photoelectric effect -- 3.4 Black-body radiation and the necessity of quantization -- 3.4.1 The quantization of Planck's resonators -- 3.4.2 Lorentz's 1908 Rome lecture: Planck versus Rayleigh-Jeans -- 3.4.3 Einstein's 1909 Salzburg lecture: fluctuations and wave-particle duality -- 3.5 The breakdown of equipartition and the specific heat of solids at low temperatures (1907-1911) -- 3.6 Einstein's quantum theory of radiation (1916) -- 3.6.1 New derivation of the Planck law -- 3.6.2 Momentum fluctuations and the directed nature of radiation -- Chapter 4 The Birth of the Bohr Model -- 4.1 Introduction -- 4.2 The dissertation: recognition of problems of classical theory -- 4.3 The Rutherford Memorandum: atomic models and quantum theory -- 4.3.1 Prelude: classical atomic models (Thomson, Nagaoka, Schott) -- 4.3.2 Scattering of α particles and Rutherford's nuclear atom -- 4.3.3 Bohr's first encounter with Rutherford's nuclear atom: energy loss of α particles traveling through matter -- 4.3.4 Interlude: Planck's constant enters atomic modeling (Haas, Nicholson) -- 4.3.5 Planck's constant enters Bohr's atomic modeling -- 4.4 From the Rutherford Memorandum to the Trilogy -- 4.4.1 Bohr comparing his results to Nicholson's -- 4.4.2 Enter the Balmer formula -- 4.5 The Trilogy: quantum atomic models and spectra -- 4.5.1 Part One: the hydrogen atom -- 4.5.2 Parts Two and Three: multi-electron atoms and multi-atom molecules -- 4.6 Early evidence for the Bohr model: spectral lines in hydrogen and helium -- Part II The Old Quantum Theory. , Chapter 5 Guiding Principles -- 5.1 Quantization conditions -- 5.1.1 Planck -- 5.1.2 Wilson and Ishiwara -- 5.1.3 Sommerfeld -- 5.1.4 Schwarzschild, Epstein, and (once again) Sommerfeld -- 5.1.5 Einstein -- 5.2 The adiabatic principle -- 5.2.1 Ehrenfest's early work on adiabatic invariants -- 5.2.2 Ehrenfest's 1916 paper on the adiabatic principle -- 5.2.3 The adiabatic principle in Bohr's 1918 paper -- 5.2.4 Sommerfeld's attitude to the adiabatic principle -- 5.3 The correspondence principle -- Chapter 6 Successes -- 6.1 Fine structure -- 6.2 X-ray spectra -- 6.3 The Stark effect -- Chapter 7 Failures -- 7.1 The complex structure of spectral multiplets -- 7.1.1 Sommerfeld on multiplets -- 7.1.2 Heisenberg's core model and multiplets -- 7.2 The anomalous Zeeman effect -- 7.2.1 The Lorentz theory of the normal Zeeman effect -- 7.2.2 Anomalous Zeeman effect: experimental results and pre-Bohr theoretical interpretations -- 7.2.3 The Paschen-Back transmutation of Zeeman lines -- 7.3 The Zeeman effect in the old quantum theory -- 7.3.1 First steps (1913-1919) -- 7.3.2 Empirical regularities and number mysticism (1919-1921) -- 7.3.3 Core models, unmechanical forces, and double-valuedness -- 7.4 The problem of helium -- Appendices -- A Classical Mechanics -- A.1 The physicist's mechanical toolbox (ca 1915) -- A.1.1 Newtonian mechanics -- A.1.2 Lagrangian mechanics -- A.1.3 Hamiltonian mechanics -- A.1.4 The adiabatic principle -- A.2 The astronomer's mechanical toolbox (ca 1915) -- A.2.1 Hamilton-Jacobi theory -- A.2.2 Poisson brackets -- A.2.3 Action-angle variables -- A.2.4 Canonical perturbation theory -- B Spectroscopy -- B.1 Early quantitative spectroscopy -- B.2 Kirchhoff's Laws -- B.3 Technological advances and the emergence of analytic spectroscopy -- B.4 The numerology of spectra: Balmer and Rydberg -- B.5 The Zeeman effect. , B.6 A troublesome red herring -- B.7 Ritz and the combination principle -- Bibliography -- Index.