jack wrote:
What does it mean to say a field has " an infinite degrees of
freedom"?

....

function A^u which are not unique. The free electromagnetic field may
be decribed by several different Lagrangians all with a finite number
of field variables e.g. E and B, or A^u and by a finite number of
field equations. So where does the "infinite number of degrees of
freedom com from? Cann someone deliniate exactly what the difference
is in the definition of "degrees of freedom" as it pertains to the
classical point particles formulation and classical field theory?

"Degrees of freedom" is the information content basically. If you
describe a theory about 3 point particles with position and momentum,
all information is contained in the 3 sets of position/momentum vector
elements, giving a finite amount of degrees of freedom.

If you describe a theory of a continous field, you need information
about the fields value at every point since it is a function defined
over, well, a field

So your finite number of continous field variables each contain an
infinite amount of information (has infinite degrees of freedom).

If you make a spatial quantization of the field definition, you reduce
the information content to finite levels of course.

/Bjorn