Ground state of a quantum particle coupled to a scalar Bose field. (English) Zbl 0908.60094
Summary: We use methods from functional integration to prove the existence and uniqueness of the ground state of a confined quantum particle coupled to a scalar massless Bose field. For an external potential growing at infinity, the ground state exists under fairly general conditions while, for a decaying potential, an unphysical condition on the coupling strength is still needed.
MSC:
60K40 | Other physical applications of random processes |
81V45 | Atomic physics |
81S40 | Path integrals in quantum mechanics |