DYNAMIC ORIGIN OF THE LORENTZIAN SIGNATURE OF SPACETIME

It is suggested that not only the curvature, but also the signature of spacetime is subject to quantum fluctuations. A generalized D-dimensional spacetime metric of the form g(munu) = e(mu)(a)eta(ab)e(nu)b is introduced, where eta(ab) = diag{e(itheta), 1, ..., 1}. The corresponding functional integral for quantized fields then interpolates from a euclidian path integral in euclidean space, at theta = 0, to a Feynman path integral in Minkowski space, at theta = pi. Treating the phase e(itheta) as just another quantized field, the signature of spacetime is determined dynamically by its expectation value. The complex-valued effective potential V(theta) for the phase field, induced by massless fields at one-loop, is considered. It is argued that Re[V(theta)] is minimized and Im[V(theta)] is stationary, uniquely in D = 4 dimensions, at theta = pi, which suggests a dynamical origin for the lorentzian signature of spacetime.