The first two terms correspond to the Hamiltonian of a quantum particle of mass M and momentum P , in a potential V at position X . The third term describes the bath as an infinite sum of harmonic oscillators with masses m i and momentum p i , at positions q i . ω ω i are the frequencies of the harmonic oscillators. The next term describes the way system and bath are coupled. In the Caldeira–Leggett model, the bath is coupled to the position of the particle. C i are coefficients which depend on the details of the coupling. The last term is a counter-term which must be included to ensure that dissipation is homogeneous in all space. As the bath couples to the position, if this term is not included the model is not translationally invariant, in the sense that the coupling is different wherever the quantum particle is located. This gives rise to an unphysical renormalization of the potential, which can be shown to be suppressed by employing real potentials.