  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
non-interacting 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.
