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Selected Papers of Walter E. Thirring with Commentaries
Walter E. Thirring, University of Vienna, Austria

Collected Works
1998; 729 pp; hardcover
Volume: 8
ISBN-10: 0-8218-0812-5
ISBN-13: 978-0-8218-0812-2
List Price: US$164
Member Price: US$131.20
Order Code: CWORKS/8
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This book contains Thirring's scientific contributions to mathematical physics, statistical physics, general relativity, quantum field theory and elementary particle theory from 1950 onward. The order of the papers within the various sections is chronological and reflects the development of the fields during the second half of this century. In some cases, Thirring returned to problems decades later when the tools for their solution had ripened. Each section contains introductory comments by Thirring, outlining his motivation for the work at that time.


  • A complete proof of the divergence of the renormalized perturbation theory in a relativistic quantum field theory and a proof of the divergence of a similar theory
  • A proof of the stability of matter
  • An analysis of a dynamical system with negative specific heat
  • A generalization of the dynamical entropy to quantum dynamical systems


Graduate students, mathematicians, physicists and science historians.


"This is a selected collection (51 out of 156) of journal articles of Walter E. Thirring who has made deep contributions in an almost unbelievably broad field joining mathematics and physics. A pleasant feature of this collected work is the commentary for each article by the author himself, placed at the beginning of each chapter ... The Foreword by Elliott Lieb gives a cohesive picture of extensive works of Thirring and their significance in mathematics and physics."

-- Mathematical Reviews

Table of Contents

I. Mathematical Physics
  • Commentary
  • Convexity properties for Coulomb systems
  • Bound for the kinetic energy of Fermions which proves the stability of matter
  • Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities
  • A lower bound with the best possible constant for Coulomb Hamiltonians
  • Lower bounds to the energy levels of atomic and molecular systems
  • The use of exterior forms in Einstein's gravitation theory
  • Asymptotic neutrality of large \(Z\)-ions
  • Approximate neutrality of large \(Z\)-ions
  • From relative entropy to entropy
  • Dynamical entropy of \(C^*\) algebras and von Neumann algebras
  • Dynamical entropy and the third law of thermodynamics
  • Quantum \(K\)-systems
  • Mixing properties of quantum systems
  • Chaotic properties of the noncommutative \(2\)-shift
  • Clustering for algebraic \(K\)-systems
  • Anosov actions on non-commutative algebras
  • \(C^*\)-dynamical systems for which the tensor product fails
  • Universal nature of the van der Waals forces for Coulomb systems
II. Statistical Physics
  • Commentary
  • A simple theory of superconductivity
  • On the mathematical structure of the B.C.S.-model
  • On the mathematical structure of the B.C.S.-model. II
  • Systems with negative specific heat
  • A soluble model for a system with negative specific heat
  • Thermodynamic functions for Fermions with Gravostatic and electrostatic interactions
  • Dynamics of unstable systems
  • Unpredictability of symmetry breaking in a phase transition
  • Bounds on the entropy in terms of one particle distributions
  • Asymptotic exactness of finite temperature Thomas-Fermi theory
  • On the equivalence of adiabatic invariance and the KMS-condition
  • KMS states for the Weyl algebra
  • Quasi-particles at finite temperatures
III. Quantum Field Theory
  • Commentary
  • Radiative corrections in the non-relativistic limit
  • A covariant formulation of the Bloch-Nordsieck method
  • On the divergence of perturbation theory for quantized fields
  • Quantum field theories with Galilei-invariant interactions
  • Use of causality conditions in quantum field theory
  • A soluble relativistic field theory
  • The taming of the dipole ghost
  • A model for a dia-electric
  • Covariant QED without indefinite metric
IV. General Relativity
  • Commentary
  • An alternative approach to the theory of gravitation
  • Quantum field theory in de Sitter space
  • How hot is the de Sitter space?
  • Five-dimensional theories and CP-violations
  • Introduction to Kaluza-Klein theory
V. Elementary Particle Physics
  • Commentary
  • On the number of fundamental fields
  • Three-field theory of strong interactions
  • The \(\omega \rightarrow \pi_0 + \gamma\) decay in the quark model
  • Electromagnetic properties of hadrons in the static \(S U_6\) model
  • Predictions of the static quark model on boson decays
  • Theory of \(p\)-wave pion-nucleon interaction
  • Curriculum vitae
  • List of Publications
  • Acknowledgments
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