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

Abstract

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.