Application of Feynman path integration to the ground state of plasmaron

Abstract

In this thesis, the Frohlich-type electron-plasmon Hamiltonian of the plasmaron which is the dressing of an electron by plasmons has been investigated using Feynman's path integral approach. The full form including the off-diagonal part of the plasmaron propagator and density matrix are derived. Then the ground state energy and the Krivoglaz-Pekar effective mass can be obtained from the diagonal part of the density matrix while the Feynman effective mass is evaluated from the off-diagonal part. The MATHEMATICA program has been used to find these quantities numerically. They are compared with those from the generalized path integral method in the weak coupling and strong coupling limits. Furthermore, the behaviour of the effective mass shows an interesting characteristic which may be connected to the phenomenon known as Wigner crystallization.