超短laser脉冲的费米相干态路径积分及陪集矩阵的场论变换
Fermionic coherent state path integral for ultrashort laser pulses and transformation to a field theory of coset matrices
摘要：
本文研究了在超短经典激光场驱动下，两带超导体中反对易场的相干态路径积分。我们描述的激子准粒子的产生从驱动激光场的基本，费米子场的异常配对。这就产生了从四次费米子相互作用到自能矩阵的各种高斯项的哈伯德-斯特拉托诺维奇变换。我们完成了路径积分的偶数值自能矩阵的欧氏积分措施，其中三种情况下，增加的复杂性进行了分类（标量自能变量，密度相关的自能矩阵，也包括自能双倍项）。根据驱动，双重哈密顿部分，我们还指定的情况下，SSB与“铰链”字段分解成密度相关的陪集分解，块对角自能矩阵的背景功能和陪集矩阵的非对角块发电机的费米子的异常配对的总自能矩阵。特别是，我们调查的变换从一个弯曲的陪集空间的陪集领域，作为独立的领域自由度，局部“平坦”的领域与欧几里德积分措施。这允许减少最终的路径积分，以单独的“Nambu”-加倍字段后的鞍点近似的密度相关的自能矩阵，也允许导出经典的场方程激子准粒子从各种梯度展开的行列式。
英文摘要：
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.
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