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We present a generalized quasi-particle theory for bosonic lattice systems,which naturally contains all relevant collective modes, including the Higgsamplitude in the strongly correlated superfluid. In contrast to Bogoliubovtheory, this non-perturbative method does not rely on a small condensatedepletion and is valid for any interaction strength in three spatialdimensions. It is based on an expansion around the bosonic Gutzwiller groundstate in terms of appropriately chosen fluctuation operators and lays thefoundation for the description of real-time dynamics in terms of the natural,weakly interacting quasi-particles. Furthermore, it provides a systematicframework for efficiently calculating observables beyond the Gutzwillerapproximation and for including external perturbations, as well as higher orderdecay and interactions in terms of quasi-particle operators. It allows for theconstruction of an alternative path integral approach in terms ofquasi-particle coherent states.

Quasi-Particle Theory for the Higgs Amplitude Mode