Journal of Statistical Physics, Vol. 66, Nos. 1/2, 1992. p. 647-659.
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.