  A coherent state path integral of anti-commuting fields is considered for a
two-band, semiconductor-related solid which is driven by a ultrashort,
classical laser field. We describe the generation of exciton quasi-particles
from the driving laser field as anomalous pairings of the fundamental,
fermionic fields. This gives rise to Hubbard-Stratonovich transformations from
the quartic, fermionic interaction to various Gaussian terms of self-energy
matrices. We accomplish path integrals of even-valued self-energy matrices with
Euclidean integration measure where three cases of increasing complexity are
classified (scalar self-energy variable, density-related self-energy matrix and
also a self-energy including anomalous-doubled terms). According to the
driving, anomalous-doubled Hamiltonian part, we also specify the case of a SSB
with 'hinge' fields which factorizes the total self-energy matrix by a coset
decomposition into density-related, block diagonal self-energy matrices of a
background functional and into coset matrices with off-diagonal block
generators for the anomalous pairings of fermions. In particular we investigate
the transformation from the coset fields of a curved coset space, as the
independent field degrees of freedom, to locally 'flat' fields with Euclidean
integration measure. This allows to reduce the final path integral to solely
'Nambu'-doubled fields after a saddle point approximaton for the
density-related self-energy matrices and also allows to derive classical field
equations for exciton quasi-particles from various kinds of gradient expansions
of the determinant.
