Say we have a real field that satisfies: E^2 = P^2 + m^2 Assume spacetime is 4D. Assume the field is at rest and grab a single point of this field and slowly displace it a distance x. Just as an anchored string (string with an additional sideways restoring force) with fixed end points will have its length change when a point is displaced and just as a two dimensional "anchored" membrane will change its area when a single point is displaced can we say that a 3 dimensional "anchored" membrane will change its volume if a single point is displaced a distance x? When I say "anchored" membrane it is the real relativistic field I am thinking of. For small displacements, x, the change in volume is proportional to what power of x? Thanks for any suggestions on how to solve this.