Functional Integral Approach to the Transition Temperature of Attractive Interacting Bose Gas in Traps

The functional integral approach (FIA) is introduced to study the transition temperature of an imperfect Bose gas in traps. An interacting model in quantum statistical mechanics is presented. With the model we study a Bose gas with attractive interaction trapped in an external potential. We obtain the result that the transition temperature of a trapped Bose gas will slightly shift upwards owing to the attractive interacting force. Successful application of the FIA to Bose systems is demonstrated.