  We develop a squeezed-field path-integral representation for BCS
superconductors utilizing a generalized completeness relation of
squeezed-fermionic coherent states. We derive a Grassmann path integral of
fermionic quasiparticles that explicitly includes the collective degrees of
freedom of the order-parameter dynamics governed by the classical Anderson
pseudospin model. Based on this method, we analyze the spectral function of the
single-particle excitations, and show that the squeezed-field path integral for
the BCS Hamiltonian describes a bosonic sideband branch that corresponds to the
Higgs amplitude mode of BCS superconductors, in addition to reproducing the
quasiparticle and quasihole excitation branches described by the BCS mean-field
approximation.
