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A coherent state path integral of anti-commuting fields is considered for atwo-band, semiconductor-related solid which is driven by a ultrashort,classical laser field. We describe the generation of exciton quasi-particlesfrom the driving laser field as anomalous pairings of the fundamental,fermionic fields. This gives rise to Hubbard-Stratonovich transformations fromthe quartic, fermionic interaction to various Gaussian terms of self-energymatrices. We accomplish path integrals of even-valued self-energy matrices withEuclidean integration measure where three cases of increasing complexity areclassified (scalar self-energy variable, density-related self-energy matrix andalso a self-energy including anomalous-doubled terms). According to thedriving, anomalous-doubled Hamiltonian part, we also specify the case of a SSBwith 'hinge' fields which factorizes the total self-energy matrix by a cosetdecomposition into density-related, block diagonal self-energy matrices of abackground functional and into coset matrices with off-diagonal blockgenerators for the anomalous pairings of fermions. In particular we investigatethe transformation from the coset fields of a curved coset space, as theindependent field degrees of freedom, to locally 'flat' fields with Euclideanintegration measure. This allows to reduce the final path integral to solely'Nambu'-doubled fields after a saddle point approximaton for thedensity-related self-energy matrices and also allows to derive classical fieldequations for exciton quasi-particles from various kinds of gradient expansionsof the determinant.

Fermionic coherent state path integral for ultrashort laser pulses and transformation to a field theory of coset matrices