Abstract
The cluster expansion [Glimm, Jaffe and Spencer, 1973, 1974] allows a detailed study of the properties of quantum fields. Consequences of the cluster expansion, in addition to the proof of existence of the infinite volume limit, are the detailed properties of the spectrum: the multiplicity of the ground state, the existence of isolated particle spectrum, the existence or absence of bound states, the completeness of scattering states at low energies, analyticity in the coupling constants, Borel summability, etc. Applications have been indicated in Chapter 14 to the study of particles and in Chapters 5 and 16 to the study of phase transitions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Glimm, J., Jaffe, A. and Spencer, T. (1974). The Wightman axioms and particle structure in the P(φ)2 quantum field model, Ann. Math. 100, 585–632.
Spencer, T. (1974b). The mass gap for the P(φ)2 quantum field model with a strong external field, Comm. Math. Phys. 39, 63–76.
Glimm, J., Jaffe, A. and Spencer, T. (1976a). A convergent expansion about mean field theory. Parts I, II, Ann. Phys. 101, 610–630; 631–669.
Spencer, T. (1975). The decay of the Bethe-Salpeter kernel in P(φ)2 quantum field models, Comm. Math. Phys. 44, 143–164.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1981 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Glimm, J., Jaffe, A. (1981). The Cluster Expansion. In: Quantum Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0121-9_18
Download citation
DOI: https://doi.org/10.1007/978-1-4684-0121-9_18
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90562-4
Online ISBN: 978-1-4684-0121-9
eBook Packages: Springer Book Archive