Fractal Cartan Forms are Anyons
e = eu^adx^u&a
is contracted over both the GCT indices u and the tangent space indices a.
Therefore it's locally frame invariant both under GCT Diff(4) for COINCIDENT non-geodesic LNIFs at fixed physical event E as well as for O(1,3) COINCIDENT LIF transformations at same E.
Cartan's whole idea of differential forms is that they are local frame invariants - local coordinate independent.
A general 1 form is
1 = 1udx^u
that's scalar invariant
1 = 1udx^u = 1u'dx^u'
A general 2-form is
2 = 2uvdx^u/\dx^v
2uv = - 2vu
d(p/\q) = dp/\q + (-1)^|p|p/\dq
d^2 = 0
If p is a zero form scalar O
d(O/\q) = dO/\g + O/\dq is a q + 1 form
If p is a 1-form
d(1/\q) = d1/\q - 1/\dq
p/\q = (-1)^|pq|q/\p
If p & q are both 1-forms then they anti-commute sort of like fermion operators.
ckck' + ck'ck = 0
when k = k' that's the Pauli exclusion principle.
If p & q are both 0-forms then they commute like bosons.
bkbk' - bk'bk = 0
You get Heisenberg uncertainty principle by taking canonical conjugates
e.g. c*k = d/dck is conjugate to ck, one must assume c*K is also a 1-form?
c*kck + ckc*k = 1
So now let p & q be rational numbers, i.e. fractal forms.
This gives fractional quantum statistics & fractional charges!