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Spinnor

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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.

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.

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