Physics Review D
We consider spacetime as having an a priori arbitrary, possibly fractional dimension p>0 and propose a new variational principle for actions defined on p-dimensional spaces. Demanding that the action be stationary with respect to variations in p leads to a constraint equation whose solution yields an explicit determination of the dimension at the classical level. We illustrate these concepts by analyzing a model which reduces to free scalar field theory when p is any positive integer.
Hochberg, D. and Wheeler, J. T., and , Spacetime dimension from a variational principle,Phys. Rev. D43 (1991) 2617 - 2621. http://prola.aps.org/abstract/PRD/v43/i8/p2617_1