Abstract
We present a survey of recent developments in constructive quantum field theory.
Supported in part by the National Science Foundation under Grant MPS 74-13252.
Supported in part by the National Science Foundation under Grant MPS 73-05037.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
D. Brydges, Boundedness below for fermion model theories. Preprint.
C. Burnap, private communication.
J. Dimock, The P(ф)2 Green’s functions: smoothness in the coupling constant.
J.-P. Eckmann, J. Magnon and R. Seneor, Decay properties and Borel summability for Schwinger functions in p(Ń„)2 theories. Commun. Math. Phys. To appear.
P. Federbush, A new approach to the stability of matter I,II. J. Math Phys. to appear.
P. Federbush, The semi-Euclidean approach in statistical mechanics I. Basic expansion steps and estimates II. The Custer expansion, a special example. Preprint.
J. Feldman, On the absence of bound states in the λф 42 quantum field model without symmetry breaking. Canadian J. Phys. 52, 1583–1587 (1974).
J. Feldman, The λфλф 43 field theory in a finite volume, Commun. Math. Phys. 37, 93–120 (1974).
J. Feldman and K. Osterwalder, The Wightman axioms and mass gap for Ń„ 43 , these proceedings.
J. Fröhlich, Schwinger functions and their generating functionals, II. Adv. Math, to appear.
J. Fröhlich, The quantized “Sine-Gordon” equation with a nonvanishing mass term in two space-time dimensions. Preprint.
J. Glimm, The mathematics of quantum field theory. Adv. Math. To appear.
J. Glimm, Analysis over infinite dimensional spaces and applications to quantum field theory. Proceedings Int. Congress Math., 1974.
J. Glimm and A. Jaffe, Quantum field models, in: Statistical mechanics and quantum field theory, ed. by C. de Witt and R. Stora, Gordon and Breach, New York, 1971.
J. Glimm and A. Jaffe, Boson quantum field models, in: Mathematics of contemporary physics, ed. by R. Streater, Academic Press, New York, 1972.
J. Glimm and A. Jaffe, Positivity of the ф 43 Hamiltonian, Fort. d. Physik, 21, 327–376 (1973).
J. Glimm and A. Jaffe, ф4 quantum field model in the single phase region: Differentiability of the mass and bounds on critical exponents, Phys. Rev. D10, 536–539 (1974).
J. Glimm and A. Jaffe, A remark on the existence of ф 44 . Phys. Rev. Lett. 33, 440–442 (1974).
J. Glimm and A. Jaffe, The entropy principle for vertex functions in quantum field models, Ann. l’Inst. H. Poincaré, 21, 1–26 (1974).
J. Glimm and A. Jaffe, Critical point dominance in quantum field models, Ann. l’Inst. H. Poincaré, 21, 27–41 (1974).
J. Glimm and A. Jaffe, Absolute bounds on vertices and couplings, Ann. l’Inst. H. Poincaré, 22, to appear.
J. Glimm and A. Jaffe, On the approach to the critical point, Ann. l’Inst. H. Poincaré, 22, to appear.
J. Glimm and A. Jaffe, Two and three body equations in quantum field models, Preprint.
J. Glimm and A. Jaffe, On three-particle structure of Ń„4 and the infinite scaling limit. Preprint.
J. Glimm, A. Jaffe and T. Spencer, The Wightman axioms and particle structure in the P(ф)2 quantum field model. Ann. Math. 100, p. 585–632 (1974).
J. Glimm, A. Jaffe and T. Spencer, The particle structure of the weakly coupled P(02 model and other applications of high temperature expansions, in: Constructive quantum field theory, Ed. by G. Velo and A. Wightman, Springer-Verlag, Berlin, 1973.
F. Guerra, L. Rosen and B. Simon, Correlation inequalities and the mass gap in P(Ń„)2 III. Mass gap for a class of strongly coupled theories with nonzero external field. Preprint
D. Isaacson, Private communication.
A. Jaffe, States of constructive field theory. Proceedings of 17th International Conference on high energy physics, London, 1974. J.R. Smith, editor, pp. I-243 to I-250.
J. Lebowitz, GHS and other inequalities. Commun. Math. Phys. 35, 87–92 (1974).
B. McCoy and T. Wu, The two dimensional Ising model. Harvard University Press, Cambridge, 1973.
C. Newman, Inequalities for Ising models and field theories which obey the Lee-Yang theorem. Commun. Math. Phys. To appear.
C. Newman, Moment inequalities for ferromagnetic Gibbs distributions. Preprint.
K. Osterwalder and R. Schrader, Axioms for Euclidean Green’s functions, I. Commun. Math. Phys. 31, 83–112 (1973).
K. Osterwalder and R. Schrader, Axioms for Euclidean Green’s functions, II. Preprint.
Y. Park, Lattice approximation of the (λф4-μф)3 field theory in a finite volume. Preprint.
G. Parisi, Field theory approach to second order phase transitions in three and two dimensional systems. Cargése Summer School, 1973.
J. Percus, Correlation inequalities for Ising spin lattices. Preprint.
J. Rosen, Private communication.
J. Rosen and B. Simon, Fluctuations in P(Ń„)1 processes. Preprint.
R. Schrader, Yukawa quantum field theory in two space time dimensions without cutoff. Ann. Phys. 70, 412–457 (1972).
B. Simon, The P(Ń„)2 Euclidean quantum field theory. Princeton University Press, Princeton, 1974.
E. Seiler, Schwinger functions for the Yukawa model in two dimensions with space-time cutoff.
T. Spencer, The absence of even bound states in ф 42 . Commun. Math. Phys., 39, 77–79 (1974).
T. Spencer, The decay of the Bethe Salpeter kernel in P(q)2 quantum field models. Preprint.
T. Spencer and F. Zirilli, private communication.
G. Sylvester, Representations and inequalities for Ising model Ursell functions, Commun. Math. Phys., to appear.
G. Sylvester, private communication.
C. Tracey and B. McCoy, Neutron scattering and the correlation functions of the Ising model near Tc. Phys. Rev. Lett. 31, 1500–1504 (1973).
A. Wightman, Introduction to some aspects of the relativistic dynamics of quantized fields, in: 1964 Cargése Summer School Lectures, Fd. by M. Lévy, Gordon and Breach, New York (1967), p. 171–291.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1985 Birkhäuser Boston Inc.
About this chapter
Cite this chapter
Glimm, J., Jaffe, A. (1985). Particles and Bound States and Progress Toward Unitarity and Scaling. In: Quantum Field Theory and Statistical Mechanics. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-5158-3_9
Download citation
DOI: https://doi.org/10.1007/978-1-4612-5158-3_9
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-3275-5
Online ISBN: 978-1-4612-5158-3
eBook Packages: Springer Book Archive