Selected Papers from Fifty Years of Mathematical Physics
The papers included in this collection were chosen by the editors as examples of highly cited and important work representing the field of mathematical physics over the last fifty years. As a preface, please read the editorial: Journal of Mathematical Physics turns fifty J. Math. Phys. 50, 050401 (2009).
Look out for a JMP special anniversary issue in Volume 51, Issue 1 in January 2010 for up-to-date reviews of developments stemming from some of this early groundbreaking work.
We invite you to share your reflections with us, as JMP celebrates its 50th consecutive year of publication; address them to the editors at jmp@math.ucdavis.edu.
Table of Contents
These manuscripts were categorized using the current topical sections of the Journal, with papers ordered chronologically within each section.
QUANTUM MECHANICS (GENERAL AND NONRELATIVISTIC) | RELATIVISTIC QUANTUM MECHANICS, FIELD THEORY, BRANE THEORY (INCLUDING STRINGS) | STATISTICAL PHYSICS | METHODS OF MATHEMATICAL PHYSICS | CLASSICAL MECHANICS AND CLASSICAL FIELDS | GENERAL RELATIVITY AND GRAVITATION | DYNAMICAL SYSTEMS
QUANTUM MECHANICS (GENERAL AND NONRELATIVISTIC)
Brownian Motion of a Quantum Oscillator
Julian Schwinger
J. Math. Phys. 2, 407 (1961)
The Inverse Problem in
the Quantum Theory of Scattering
L. D. Faddeyev
and B. Seckler
J. Math. Phys. 4, 72 (1963)
Hydrodynamics of a Superfluid Condensate
Eugene P. Gross
J. Math. Phys. 4, 195 (1963)
Feynman Integrals and the Schrödinger Equation
Edward Nelson
J. Math. Phys. 5, 332 (1964)
Stability
of Matter. I
Freeman J. Dyson and A.
Lenard
J. Math. Phys. 8, 423 (1967)
Stability
of Matter. II
A. Lenard and Freeman J.
Dyson
J. Math. Phys. 9, 698 (1968)
An Exact Quantum Theory
of the Time-Dependent Harmonic Oscillator and of a Charged Particle in a Time-Dependent
Electromagnetic Field
H. R. Lewis, Jr. and W. B.
Riesenfeld
J. Math. Phys. 10, 1458 (1969)
Solution of a Three-Body Problem
in One Dimension
F. Calogero
J. Math. Phys. 10, 2191 (1969)
Solution of the One-Dimensional N-Body Problems with Quadratic and/or
Inversely Quadratic Pair Potentials
F. Calogero
J. Math. Phys. 12, 419 (1971)
The Zeno's paradox in quantum
theory
B. Misra
and E. C. G. Sandarshan
J. Math. Phys. 18, 756 (1977)
Inverse
scattering.
II. Three dimensions
Roger G. Newton
J. Math. Phys. 21, 1698 (1980)
RELATIVISTIC QUANTUM MECHANICS, FIELD THEORY, BRANE THEORY (INCLUDING STRINGS)
On the Many-Particle Structure
of Green's Functions in Quantum Field Theory
K. Symanzik
J. Math. Phys. 1, 249 (1960)
On
the Connection of Spin and Commutation Relations between Different Fields (1961)
Huzihiro Araki
J. Math. Phys. 2, 267 (1961)
Postulates
of Quantum Field Theory
R.
Haag and B. Schroer
J. Math. Phys. 3, 248 (1962)
A Lattice
of Von Neumann Algebras Associated with the Quantum Theory of a Free Bose Field
Huzihiro Araki
J. Math. Phys. 4, 1343 (1963)
Von
Neumann Algebras of Local Observables for Free Scalar Field
Huzihiro Araki
J. Math. Phys. 5, 1 (1964)
An Algebraic
Approach to Quantum Field Theory
Rudolf
Haag and Daniel Kastler
J. Math. Phys. 5, 848 (1964)
Connection between Spin, Statistics,
and Kinks
David Finkelstein and
Julio Rubinstein
J. Math. Phys. 9, 1762 (1968)
Existence
theorem for gauge algebra
I.
A. Batalin and G. A. Vilkovisky
J. Math. Phys. 26, 172 (1985)
Supersymmetric
Yang–Mills theory on a four-manifold
Edward
Witten
J. Math. Phys. 35, 5101 (1994)
STATISTICAL PHYSICS
Determination
of Thermodynamic Green's Functions
Gordon
Baym and N. David Mermin
J. Math. Phys. 2, 232 (1961)
Statistical
Theory of the Energy Levels of Complex Systems. I
Freeman J.
Dyson
J. Math. Phys. 3, 140 (1962)
Ordering
Energy Levels of Interacting Spin Systems
Elliott
Lieb and Daniel Mattis
J. Math. Phys. 3, 749 (1962)
Stochastic Liouville Equations
Ryogo
Kubo
J. Math. Phys. 4, 174 (1963)
On
the van der Waals Theory of the Vapor-Liquid
Equilibrium. I. Discussion of a One-Dimensional Model
M. Kac, G. E. Uhlenbeck, and P. C.
Hemmer
J. Math. Phys. 4, 216 (1963)
Dimer
Statistics and Phase Transitions
P. W. Kasteleyn
J. Math. Phys. 4, 287 (1963)
Time-Dependent
Statistics of the Ising Model
Roy J. Glauber
J. Math. 4, 294 (1963)
Representations
of the Canonical Commutation Relations Describing a Nonrelativistic
Infinite Free Bose Gas
H. Araki and E.
J. Woods
J. Math. Phys. 4, 637 (1963)
An Exactly Soluble
Model of a Many-Fermion System
J. M. Luttinger
J. Math. Phys. 4, 1154 (1963)
Correlation Functions
and the Critical Region of Simple Fluids
Michael E.
Fisher
J. Math. Phys. 5, 944 (1964)
Random
Walks on Lattices. II
Elliott W. Montroll and George H. Weiss
J. Math. Phys. 6, 167 (1965)
Exact Solution
of a Many-Fermion System and Its Associated Boson
Field
Daniel C. Mattis and Elliott H. Lieb
J. Math. Phys. 6, 304 (1965)
Statistical
Ensembles of Complex, Quaternion, and Real Matrices
Jean Ginibre
J. Math. Phys. 6, 440 (1965)
Statistical
Mechanics of Assemblies of Coupled Oscillators
G. W. Ford, M. Kac, and P. Mazur
J. Math. Phys. 6, 504 (1965)
Rigorous
Treatment of the Van Der Waals-Maxwell Theory of the
Liquid-Vapor Transition
J. L. Lebowitz and O. Penrose
J. Math. Phys. 7, 98 (1966)
Correlations
in Ising Ferromagnets. I
Robert B.
Griffiths
J. Math. Phys. 8, 478 (1967)
Absence of
Ordering in Certain Classical Systems
N. D. Mermin
J. Math. Phys. 8, 1061 (1967)
Solution of the
Dimer Problem by the Transfer Matrix Method
Elliott H. Lieb
J. Math. Phys. 8, 2339 (1967)
Thermodynamics
of a One-Dimensional System of Bosons with Repulsive Delta-Function Interaction
C. N. Yang and
C. P. Yang
J. Math. Phys. 10, 1115 (1969)
On Next-Nearest-Neighbor
Interaction in Linear Chain. I
Chanchal K.
Majumdar and Dipan K. Ghosh
J. Math. Phys. 10, 1388 (1969)
Colorings of a
Hexagonal Lattice
R. J. Baxter
J. Math. Phys. 11, 784 (1970)
A Class of
Matrix Ensembles
Freeman J.
Dyson
J. Math. Phys. 13, 90 (1972)
Completely
positive dynamical semigroups of N-level systems
Vittorio Gorini, Andrzej Kossakowski, and E. C. G. Sudarshan
J. Math Phys. 17, 821 (1976)
Equilibrium
states for mean field models
M. Fannes, H. Spohn, and A. Verbeure
J. Math. Phys. 21, 355 (1980)
METHODS OF MATHEMATICAL PHYSICS
On
the Representations of the Semisimple Lie Groups. II
G. E. Baird and
L. C. Biedenharn
J. Math. Phys. 4, 1449 (1963)
Proof of the
strong subadditivity of quantum-mechanical entropy
Elliott H. Lieb and Mary Beth Ruskai
J. Math. Phys. 14, 1938 (1973)
Painlevé
functions of the third kind
Barry M. McCoy,
Craig A. Tracy, and Tai Tsun Wu
J. Math. Phys. 18, 1058 (1977)
The
planar approximation. II
C. Itzykson and J.-B. Zuber
J. Math. Phys. 21, 411 (1980)
On the
self-linking of knots
Raoul Bott and Clifford Taubes
J. Math. Phys. 35, 5247 (1994)
CLASSICAL MECHANICS AND CLASSICAL FIELDS
Korteweg-deVries
Equation and Generalizations. V. Uniqueness and Nonexistence of
Polynomial Conservation Laws
Martin D. Kruskal, Robert M. Miura, Clifford S. Gardner, and Norman
J. Zabusky
J. Math. Phys. 11, 952 (1970)
New similarity
reductions of the Boussinesq equation
Peter A.
Clarkson and Martin D. Kruskal
J. Math. Phys. 30, 2201 (1989)
GENERAL RELATIVITY AND GRAVITATION
Lorentz
Invariance and the Gravitational Field
T. W. B. Kibble
J. Math. Phys. 2, 212 (1961)
An Approach to
Gravitational Radiation by a Method of Spin Coefficients
Ezra Newman and
Roger Penrose
J. Math. Phys. 3, 566 (1962)
Twistor
Algebra
R. Penrose
J. Math. Phys. 8, 345 (1967)
A
Method for Generating New Solutions of Einstein's Equation. II
Robert Geroch
J. Math. Phys. 13, 394 (1972)
DYNAMICAL SYSTEMS
Periodic Orbits
and Classical Quantization Conditions
Martin C. Gutzwiller
J. Math. Phys. 12, 343 (1971)
Visit the JMP booth at the XVIth International Congress on Mathematical Physics in Prague this Summer to pick up a USB drive loaded with this selection of high-impact papers.
