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

TL;DR

This paper develops a fermionic coherent state path integral framework for ultrashort laser pulse-driven semiconductors, transforming complex coset fields into Euclidean fields to derive classical exciton equations.

Contribution

It introduces a novel transformation from curved coset fields to flat Euclidean fields in a fermionic path integral for laser-driven semiconductors, enabling classical exciton dynamics derivation.

Findings

Path integral formulation for fermionic fields in semiconductors under laser excitation.

Transformation of coset fields to Euclidean fields simplifies the path integral.

Derivation of classical exciton equations from gradient expansions.

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.