Abstract
The chessboard model is reviewed and reformulated as a four-state process. In this formulation both the Dirac propagator of the chessboard model and the partition function of the associated Ising chain are observed to be projections of a single matrix of partition functions onto two orthogonal eigenspaces. This helps clarify the role played by the phase associated with Feynman paths in this model.
This is a preview of subscription content, log in via an institution to check access.
References
J. K. Percus,J. Stat. Phys. 16:299 (1977).
J. K. Percus,J. Math. Phys. 23:1162 (1982).
J. K. Percus and M. Q. Zhang,Phys. Rev. B 38:11737 (1988).
J. K. Percus,J. Stat. Phys. 33:1263 (1989).
M. Q. Zhang and J. K. Percus, Inhomogeneous Ising model on a multi-connected network,J. Stat. Phys 56(5/6):695 (1989).
C. Borzi, G. Ord, and J. K. Percus,J. Stat. Phys. 46:51 (1987).
G. Ord, J. K. Percus, and M. Q. Zhang,Nucl. Phys. B 305[FS23]:271 (1988).
H. A. Gersch,Int. J. Theor. Phys. 20:491 (1981).
R. P. Feynman and A. R. Hibbs,Quantum Mechanics and Path Integrals (McGraw-Hill, 1965).
T. Jacobson and L. S. Schulman,J. Phys. A 17:375 (1984).
E. C. G. Stuckelberg,Helv. Phys. Acta 15:23 (1942).
R. P. Feynman,Phys. Rev. 74:939 (1948).
A. L. Kholodenko,Ann. Phys. 202:186 (1990).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ord, G.N. A reformulation of the Feynman chessboard model. J Stat Phys 66, 647–659 (1992). https://doi.org/10.1007/BF01060086
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01060086