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Given a gauge field theory, the various fields involved have (pointwise) degrees of freedom.

For instance, if I consider the gauge theory of gravity in four dimensions, I have a set of tetrads $\{ e_\mu \}$ (16 DoF), which, from the gauge freedom of the Lorentz group (6 dimensions) drop down to 10 (the appropriate number for a metric tensor), and furthermore, after gauge-fixing the coordinates (4 dimensions), drop down to a total of 6 physical degrees of freedom, for a total of 10 gauge degrees of freedom.

People seem to mention propagating degrees of freedom a fair bit, but their definition seems a bit murky. The most I could find out is that they are the degrees of freedom that do not depend on the field's source, and therefore can freely propagate (hence related to the two degrees of freedom in gravitational waves/gravitons I suppose, which can indeed be sourceless), but that's about all I could find.

Is there a field-theoretic definition of propagating degrees of freedom that does not depend on specific solutions?

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$$ \text{Propagating DOF} = \text{on-shell DOF} = \#\text{(initial conditions)}/2,$$

cf. e.g. Refs. 1-2 and this, this & this Phys.SE posts.

References:

  1. D.Z. Freedman & A. Van Proeyen, SUGRA, 2012.

  2. H. Nastase, Intro to SUGRA, arXiv:1112.3502; chapter 5.

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