Spacetime dimension from a variational principle

We consider spacetime as having an a priori arbitrary, possibly fractional dimension $p>\mathrm{}0\mathrm{}$ 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.