  Strong light-matter coupling provides a versatile and novel means to
manipulate chemical processes. Here we develop a theoretical framework to
investigate the spectroscopy and dynamics of a molecular ensemble embedded in
an optical cavity under the collective strong coupling regime. This theory is
constructed by a pseudoparticle representation of the molecular Hamiltonians,
mapping the polaritonic Hamiltonian into a coupled fermion-boson model under
particle number constraints. The mapped model is then analyzed using the
non-equilibrium Green function theory with the important self-energy diagrams
identified through power counting. Numerical demonstrations are shown for the
driven Tavis-Cummings model, which shows an excellent agreement with exact
results.
