J. M. Jauch

Bio: J. M. Jauch is an academic researcher. The author has contributed to research in topics: Electron & Secondary electrons. The author has an hindex of 8, co-authored 9 publications receiving 3745 citations.

Physical reality and mathematical description

Abstract: I : Art, History and Philosophy.- Science and Art.- Leonard de Vinci et l'hydrodynamique.- Our knowledge of the external world.- Geometrie and Physik.- Quantum physics and process metaphysics.- What happened to our elementary particles? (Variations on a theme of Jauch).- Partons-elementary constituents of the proton?.- Is the zero-point energy real?.- Reflections on "Fundamentality and complexity".- II : Mathematical Physics.- Weights on spaces.- A second look at the essential selfadjointness of the Schrodinger operators.- Some absolutely continuous operators.- A remark on the Kochen-Specker theorem.- Die Heisenberg-Weyl'schen Vertauschungsrelationen: Zum Beweis des von Neumannschen Satzes.- Real versus complex representations and linear-antilinear commutant.- III: Scattering Theory and Field Theory.- Approche algebrique de la theoree non-relativiste de la diffusion a canaux multiples.- Fourier scattering subspaces.- N-Particle scattering rates.- Cross sections in the quantum theory of scattering.- On long-range potentials.- Phenomenological aspects of localizability.- Charge distributions from relativistic form factors.- Charges and currents in the Thirring model.- The nonlocal nature of electromagnetic interactions.- Le modele des champs de jauge unifies.- Is anti-gravitation possible?.- IV : Quantum Theory and Statistical Mechanics.- On a new definition of quantal states.- The minimal K-flow associated to a quantum diffusion process.- Composite particles in many-body theory.- On the quantum analogue of the Levy distribution.- Existence and bounds for critical energies of the Hartree operator.- Long range ordering in one-component Coulomb systems.- A scale group for Bolt zmann-type equations.- Effect of a non-resonant electromagnetic field on the frequencies of a nuclear magnetic moment system.

The Theory of Photons and Electrons: The Relativistic Quantum Field Theory of Charged Particles with Spin One-half

Abstract: 1 General Principles.- 1-1 The natural unit system.- 1-2 Some fundamental notions of the special theory of relativity.- 1-3 Some basic notions of quantum mechanics.- 1-4 Localizability.- 1-5 Observables of a field.- 1-6 Canonical transformations.- 1-7 Lorentz transformations as canonical transformations.- 1-8 The action principle.- 1-9 The equation of motion.- 1-10 Momentum operators.- 1-11 Conservation laws.- 1-12 Commutation rules.- 2 the Radiation Field.- 2-1 The classical field equations.- 2-2 The associated boundary value problem.- 2-3 A Lagrangian for the radiation field.- 2-4 Quantization of the radiation field.- 2-5 Momentum operators for the radiation field.- 2-6 Plane wave decomposition of the radiation field.- 2-7 Explicit representations of the field operators.- 2-8 The spin of the photon.- 2-9 Definition of the vacuum.- 3 Relativistic Theory of Free Electrons.- 3-1 The field equations for the one-particle problem.- 3-2 The associated boundary value problem.- 3-3 Relativistic invariance of the field equations.- 3-4 The bilinear covariants.- 3-5 A Lagrangian for the spinor field.- 3-6 Quantization.- 3-7 Momentum operators.- 3-8 Plane wave decomposition.- 3-9 Explicit representation of the field operators.- 3-10 The definition of the vacuum.- 4 Interaction of Radiation with Electrons.- 4-1 The field equations.- 4-2 Commutation rules for the interacting fields.- 4-3 The interaction picture.- 4-4 Measurability of the fields.- 5 Invariance Properties of the Coupled Fields.- 5-1 Proper Lorentz transformations.- 5-2 Gauge transformations.- 5-3 Space inversion.- 5-4 Time inversion.- 5-5 Charge conjugation.- 5-6 Scale transformations.- 6 Subsidiary Condition and Longitudinal Field.- 6-1 The covariant Coulomb interaction.- 6-2 The subsidiary condition and the construction of the state vector.- 6-3 The Gupta method.- 6-4 Gauge-independent interaction.- 6-5 Radiation fields with finite mass.- 7 the S-Matrix.- 7-1 Preliminary definition of the S-matrix.- 7-2 The wave matrix.- 7-3 The wave operator.- 7-4 Integral representation of the wave operator.- 7-5 Definition of the S-matrix.- 7-6 Invariance properties of the S-matrix.- 8 Evaluation of the S-Matrix.- 8-1 The iteration solution.- 8-2 The Feynman-Dyson diagrams.- 8-3 Diagrams in momentum space.- 8-4 Closed loops.- 8-5 The substitution law.- 8-6 Lifetimes and cross sections.- 8-7 Evaluation of the S-matrix in the Heisenberg picture.- 9 the Divergences in the Iteration Solution.- 9-1 Historical background.- 9-2 Classification of divergences.- 9-3 The vacuum fluctuations.- 9-4 The self-energy of the electron.- 9-5 The self-energy of the photon.- 9-6 The vertex part.- 10 Renormalization.- 10-1 The primitive divergences.- 10-2 Irreducible and proper diagrams.- 10-3 Separation of divergences in irreducible parts.- 10-4 Separation of divergences in reducible parts.- 10-5 Mass renormalization.- 10-6 Charge renormalization.- 10-7 Wave function renormalization.- 10-8 Sufficiency proof.- 10-9 Regulators.- 11 the Photon-Electron System.- 11-1 Compton scattering.- 11-2 Double Compton scattering.- 11-3 Radiative corrections to Compton scattering.- 11-4 Pair production in photon-electron collisions.- 12 the Electron-Electron System.- 12-1 Moller scattering.- 12-2 Bhabha scattering.- 12-3 Bremsstrahlung in electron-electron collisions.- 12-4 Annihilation of free negaton-positon pairs.- 12-5 Positronium selection rules.- 12-6 Positronium annihilation.- 13 the Photon-Photon System.- 13-1 Photon-photon scattering as part of a diagram.- 13-2 Photon-photon scattering cross sections.- 13-3 Pair production in photon-photon collision.- 14 Theory of the External Field.- 14-1 The external field approximation.- 14-2 The bound interaction picture.- 14-3 Commutation rules.- 14-4 The electron propagation function.- 14-5 The S-matrix in the external field approximation.- 14-6 Renormalization.- 14-7 Cross sections and energy levels.- 15 External Field Problems.- 15-1 Coulomb scattering.- 15-2 Radiative corrections to Coulomb scattering.- 15-3 The magnetic moment of the election.- 15-4 Energy levels in hydrogen-like atoms.- 15-5 Radiative transitions between bound states.- 15-6 Bremsstrahlung.- 15-7 Pair production and annihilation.- 15-8 Delbruck and Rayleigh scattering.- 16 Special Problems.- 16-1 The infrared divergences.- 16-2 Radiation damping in collision processes.- 16-3 The natural line width of stationary states.- 16-4 The self-stress of the electron.- 16-5 Outlook.- Mathematical Appendix.- Appendix A1 the Invariant Functions.- A1-1 The homogeneous delta-functions.- A1-2 The inhomogeneous delta-functions.- A1-3 Relations between the ?-functions.- A1-4 Integral representations.- A1-5 Explicit expressions.- A1-6 The S-functions.- Appendix A2 the Gamma-Matrices.- A2-1 Various representations.- A2-3 The amplitudes of the plane wave solutions.- A2-5 Spin sums.- A2-6 Polarization sums.- Appendix A3 a Theorem on the Representation of the Extended.- Lorentz Group by Irreducible Tensors.- Appendix A4 the Ordering Theorem.- A4-1 The ordering theorem for commuting fields.- A4-2 The ordering theorem for anticommuting fields.- A4-3 A generalization of the ordering theorem.- A4-4 The ordering of chronological products.- Appendix A5 on the Evaluation of Certain Integrals.- A5-1 Convergent integrals.- A5-2 Divergent integrals.- A5-3 The integral for the photon self-energy part.- A5-4 The integral for the electron self-energy part.- Appendix A6 a Limiting Relation for the ?-function.- Appendix A7 the Method of Analytic Continuation.- A7-1 The Bohr-Peierls-Placzek relation.- A7-2 The principle of limiting distance.- A7-3 The fundamental theorem on analytic continuation.- A7-4 Applications.- Appendix A8 Notation.- Supplement for the Second Edition.- Supplement S1 Formulations of Quantum Electrodynamics.- S1-1 Lagrangian QFT.- S1-2 Axiomatic QFT.- S1-3 Locality, covariance, and indefinite metric.- S1-4 Lehmann-Symanzik-Zimmermann and related formalisms.- S1-5 Null plane QED.- References.- Supplement S2 Renormalization.- S2-1 Dyson-Salam-Ward renormalization.- S2-2 Bogouubov-Parasiuk-Hepp-Zimmermann renormalization.- S2-3 Analytic renormalization.- References.- Supplement S3 Coherent States.- S3-1 A finite number of degrees of freedom.- S3-2 Coherent states of the radiation field.- S3-3 Application to ordering theorems.- References.- Supplement S4 Infrared Divergences.- S4-1 Dollard's discovery.- S4-2 A new picture.- S4-3 The asymptotically modified fields.- References.- Supplement S5 Predictions and Precision Experiments.- S5-1 The anomalous magnetic moment.- S5-2 The hyperfine structure of the hydrogen ground state.- S5-3 The Lamb-Retherford shift in hydrogen.- S5-4 Energy levels in positronium.- S5-5 Muonium hyperfine structure.- References.- Author Index.

Quantum Mechanics of One- and Two-Electron Atoms

Abstract: One of the simplest, and most completely treated, fields of application of quantum mechanics is the theory of atoms with one or two electrons For hydrogen and the analcgous ions He+, Li++, etc, the calculations can be performed exactly, both in Schrodinger’s nonrelativistic wave mechanics and in Dirac’s relativistic theory of the electron More specifically, the calculations are exact for a single electron in a fixed Coulomb potential Hydrogen-like atoms thus furnish an excellent way of testing the validity of quantum mechanics For such atoms the correction terms due to the motion and structure of atomic nuclei and due to quantum electrodynamic effects are small and can be calculated with high accuracy Since the energy levels of hydrogen and similar atoms can be investigated experimentally to an astounding degree of accuracy, some accurate tests of the validity of quantum electrodynamics are also possible Finally, the theory of such atoms in an external electric or magnetic field has also been developed in detail and compared with experiment

The Cosmological Constant and Dark Energy

Abstract: Physics welcomes the idea that space contains energy whose gravitational effect approximates that of Einstein's cosmological constant, \ensuremath{\Lambda}; today the concept is termed dark energy or quintessence. Physics also suggests that dark energy could be dynamical, allowing for the arguably appealing picture of an evolving dark-energy density approaching its natural value, zero, and small now because the expanding universe is old. This would alleviate the classical problem of the curious energy scale of a millielectron volt associated with a constant \ensuremath{\Lambda}. Dark energy may have been detected by recent cosmological tests. These tests make a good scientific case for the context, in the relativistic Friedmann-Lema\^{\i}tre model, in which the gravitational inverse-square law is applied to the scales of cosmology. We have well-checked evidence that the mean mass density is not much more than one-quarter of the critical Einstein--de Sitter value. The case for detection of dark energy is not yet as convincing but still serious; we await more data, which may be derived from work in progress. Planned observations may detect the evolution of the dark-energy density; a positive result would be a considerable stimulus for attempts at understanding the microphysics of dark energy. This review presents the basic physics and astronomy of the subject, reviews the history of ideas, assesses the state of the observational evidence, and comments on recent developments in the search for a fundamental theory.

The Zeno’s paradox in quantum theory

Abstract: We seek a quantum‐theoretic expression for the probability that an unstable particle prepared initially in a well defined state ρ will be found to decay sometime during a given interval. It is argued that probabilities like this which pertain to continuous monitoring possess operational meaning. A simple natural approach to this problem leads to the conclusion that an unstable particle which is continuously observed to see whether it decays will never be found to decay!. Since recording the track of an unstable particle (which can be distinguished from its decay products) approximately realizes such continuous observations, the above conclusion seems to pose a paradox which we call Zeno’s paradox in quantum theory. The relation of this result to that of some previous works and its implications and possible resolutions are briefly discussed. The mathematical transcription of the above‐mentioned conclusion is a structure theorem concerning semigroups. Although special cases of this theorem are known, the ge...

Quantum Measurement and Control

Abstract: The control of individual quantum systems promises a new technology for the 21st century – quantum technology. This book is the first comprehensive treatment of modern quantum measurement and measurement-based quantum control, which are vital elements for realizing quantum technology. Readers are introduced to key experiments and technologies through dozens of recent experiments in cavity QED, quantum optics, mesoscopic electronics, and trapped particles several of which are analyzed in detail. Nearly 300 exercises help build understanding, and prepare readers for research in these exciting areas. This important book will interest graduate students and researchers in quantum information, quantum metrology, quantum control and related fields. Novel topics covered include adaptive measurement; realistic detector models; mesoscopic current detection; Markovian, state-based and optimal feedback; and applications to quantum information processing.