Selected Papers of Walter E. Thirring with Commentaries".... with the huge success of the quantum theory, starting especially with the Schrödinger equation in 1926, came a feeling among the leading physicists that mathematics should keep in the background or, as one person put it, `elegance is for tailors'. From the other side, mid-twentieth century mathematicians were not much more hospitable about intrusions of physics, as we can see, for instance, in Hardy's well known little essay. Walter was one of the first, in the post-war years, to try to put things back together." -- from the Foreword by Elliott Lieb 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. |
Contents
Commentary 3 | 3 |
Matter 25 | 25 |
A Lower Bound with the Best Possible Constant for Coulomb Hamiltonians | 65 |
Lower Bounds to the Energy Levels of Atomic and Molecular Systems | 73 |
The Use of Exterior Forms in Einsteins Gravitation Theory | 97 |
Asymptotic Neutrality of Large ZIons | 135 |
From Relative Entropy to Entropy | 149 |
Dynamical Entropy of C Algebras and von Neumann Algebras | 159 |
KMS States for the Weyl Algebra | 423 |
Quasi Particles at Finite Temperature | 433 |
Commentary | 457 |
A Covariant Formulation of the BlochNordsieck Method | 463 |
On the Divergence of Perturbation Theory for Quantized Fields | 469 |
Quantum Field Theories with GalileiInvariant Interactions | 489 |
A Soluble Relativistic Field Theory | 509 |
The Taming of the Dipole Ghost | 531 |
Dynamical Entropy and the Third Law of Thermodynamics | 189 |
Quantum KSystems | 203 |
Mixing Properties of Quantum Systems | 217 |
Chaotic Properties of the Noncommutative 2Shift | 233 |
Clustering for Algebraic KSystems | 251 |
Commentary | 297 |
On the Mathematical Structure of the BCSModel | 309 |
On the Mathematical Structure of the BCSModel II | 321 |
Systems with Negative Specific Heat | 331 |
A Soluble Model for a System with Negative Specific Heat | 345 |
Thermodynamic Functions for Fermions with Gravostatic and Electrostatic | 359 |
Dynamics of Unstable Systems | 377 |
Unpredictability of symmetry breaking in a phase transition | 389 |
Bounds on the Entropy in Terms of OneParticle Distributions | 397 |
On the Equivalence of Adiabatic Invariance and the KMSCondition | 415 |
A Model for a DiaElectric | 537 |
Commentary | 559 |
Quantum Field Theory in de Sitter Space | 583 |
How Hot is the de Sitter Space? | 603 |
FiveDimensional Theories and CPViolations | 617 |
Introduction to KaluzaKlein Theory | 633 |
Commentary | 665 |
ThreeField Theory of Strong Interactions | 677 |
The w Toy Decay in the Quark Model | 691 |
Predictions of the Static Quark Model on Boson Decays | 701 |
| 711 | |
Anosov Actions on NonCommutative Algebras 261 | 724 |
Acknowledgments | 725 |
Common terms and phrases
abelian algebra assume automorphism bosons c-number C*-algebra calculate canonical classical cluster commutation consider constant converges corresponding d³x defined denote density derivative dynamical eigenvalues electron entropy equilibrium evolution exists expectation value expression factor fermions field equations finite function gauge gives graphs gravitational Hamiltonian Hilbert space implies infinite integral interaction invariant K-systems Killing vector fields kinetic energy Lagrangian Lemma limit linear lower bound mass Math mathematical matrix element meson metric microcanonical microcanonical ensemble momentum Narnhofer negative obtain operators P₁ particles perturbation theory phase photons Phys physical potential Proof properties quantized quantum field theory relations relativistic renormalization representation result scalar scattering amplitude solution spectrum spin subalgebra temperature tensor Theorem thermodynamic Thirring tion transformation unitary vanish vector fields von Neumann algebra zero