
Period Integrals and Quanta
The fundamental period integrals on space time are:
 Quantized Flux: A 1dimensional period integral on any space.
 The integral of A over a closed 1dimensional domain, or curve.
Alias the CartanHilbert Action integral, or the Kelvin Circuation integral, or
the BohmAharanov integral. Note that dA= 0 over the interior domain, a fact
that corresponds to Meisner expulsion in superconductors.
 Quantized Charge: A 2dimensional period integral on space time.
 The integral of G over a closed N2=2dimensional domain or surface.
Alias the Gauss integral of electromagnetism. Note that this is NOT equivalent
to the integral of F=dA, except in very special circumstances, and then only on
a space of four dimensions. Further note that J = dG = 0 over the interior
domain.
 Quantized Spin: A 3dimensional period integral on space time.
 The integral of A^G over a closed N1=3dimensional domain. Note that
d(A^G) = F^G = 0 over the interior domain. In electromagnetism, this
constraint corresponds to domains where the first Poincare invariant vanishers;
D.EB.H = 0.
 Quantized Torsion: A 3dimensional period integral on any space.
 The integral of A^dA over a closed 3dimensional domain. Alias the
Topological Torsion integral. Note that d(A^dA) = dA^dA = F^F = 0 over the
interior domain. In electromagnetism, this constraint corresponds to domains
where the second Poincare invariant vanishes; E.B=0. The Hopf invariant.
