The stress-energy tensors are computed for scalar and spinor fields with arbitrary mass in anti-de Sitter spacetime using the $\zeta$-function technique. The results are compared with those obtained by Pauli-Villars regularization. It is found that they agree with one another. The trace anomaly for the Wess-Zumino model (the scalar supermultiplet) in anti-de Sitter spacetime is studied. It is concluded that the trace anomaly must take the "conventional" value in this model although the physical significance of the stress-energy tensor is not clear in anti-de Sitter spacetime. The relation between the $\zeta$-function and Pauli-Villars methods in an arbitrary space is also clarified.

• Received 16 December 1991

DOI:https://doi.org/10.1103/PhysRevD.45.3591