QUANTUM-MECHANICS OF SPACETIME SIGNATURE

It is suggested that the Wick rotation angle is a genuine dynamical degree of freedom, rather than just a technical device needed to improve the convergence of functional integrals. The one-loop effective potential V(theta) of the Wick angle theta is calculated, using heat-kernel regularization. It is found that when the number of fermionic degrees of freedom exceeds the number of bosonic degrees of freedom, the real part of V(theta) is minimized, and the imaginary part is stationary, uniquely in D = 4 dimensions, at the value theta = pi, corresponding to Lorentzian signature.