Inclusion of Chemical Potential for Scalar Fields

Abstract: There are two possible methods for the inclusion of the chemical potential in a relativistic bosonic field theory. The most popular method has recently been criticised by some authors, so much so as to require a re-analysis of the entire problem. I here present a new approach to the inclusion of the chemical potential that uses the second method and zeta-function regularisation techniques. I first apply it to the non-interacting field, obtaining an expression for the effective potential which is formally coincident with the well-known one from the first method. My approach, however, seems here mathematically more rigorous since it excludes the presence of the multiplicative anomaly. I then obtain a new expression for the one loop effective potential for the interacting field. This is regularised, presents less cryptic excitation energies, shows Goldstone excitations, and in the noninteracting limit gives the expected expression. The high-temperature expansion is calculated easily and with clarity, and confirms the results of the first method for the critical temperature.