We explore potential uses of physics formulated in Kleinian (i.e., 2+2)
signature spacetimes as a tool for understanding properties of physics in
Lorentzian (i.e., 3+1) signature. Much as Euclidean (i.e., 4+0) signature
quantities can be used to formally construct the ground state wavefunction of a
Lorentzian signature quantum field theory, a similar analytic continuation to
Kleinian signature constructs a state of low particle flux in the direction of
analytic continuation. There is also a natural supersymmetry algebra available
in 2+2 signature, which serves to constrain the structure of correlation
functions. Spontaneous breaking of Lorentz symmetry can produce various
N=1/2 supersymmetry algebras that in 3+1 signature correspond
to non-supersymmetric systems. We speculate on the possible role of these
structures in addressing the cosmological constant problem.Comment: 22 pages, 1 figur