Renormalised fermion vacuum expectation values on anti-de Sitter space-time

The Schwinger–de Witt and Hadamard methods are used to obtain renormalised vacuum expectation values for the fermion condensate, charge current and stress-energy tensor of a quantum fermion field of arbitrary mass on four-dimensional anti-de Sitter space–time. The quantum field is in the global anti-de Sitter vacuum state. The results are compared with those obtained using the Pauli–Villars and zeta-function regularisation methods, respectively.