What does this equation mean?

None of this history would be describable in ordinary language without one conceptual device: the quasiparticle. A solid contains on the order of 10^{23} interacting electrons per cubic centimeter, and no exact solution to that many-body problem exists or is expected. Lev Landau’s Fermi-liquid theory showed that in many metals, the low-energy excitations of this impossibly complex system behave, to good approximation, like a gas of weakly interacting particles carrying renormalized properties — an effective mass different from the bare electron mass, a finite lifetime, sometimes a fractional charge. A Cooper pair is a quasiparticle composite; the flat plateaus of the quantum Hall effect are best understood through quasiparticles carrying a fraction of the electron’s charge in the fractional quantum Hall regime; the surface states of a topological insulator are quasiparticles that behave like massless relativistic Dirac fermions despite being made of ordinary, decidedly non-relativistic electrons. The quasiparticle is not a claim that something new has been discovered in every case — it is a bookkeeping device that lets physicists say what a many-body ground state’s excitations look like without solving the underlying problem exactly. Where the device breaks down — in some strongly correlated cuprates and heavy-fermion compounds, where no consistent single quasiparticle description reproduces the observed behavior — is itself one of the most active open problems in the field, sometimes described as “non-Fermi liquid” or “strange metal” behavior.