Pavlov, Yu. V. Dimensional regularization and the \(n\)-wave procedure for scalar fields in many-dimensional quasi-Euclidean spaces. (English. Russian original) Zbl 1144.81492 Theor. Math. Phys. 128, No. 2, 1034-1045 (2001); translation from Teor. Mat. Fiz. 128, No. 2, 236-248 (2001). Summary: We obtain the vacuum expectation values of the energy-momentum tensor for a scalar field arbitrarily coupled to a curvature in the case of an \(N\)-dimensional quasi-Euclidean space-time; the vacuum is defined in accordance with the Hamiltonian diagonalization method. We extend the \(n\)-wave procedure to the many-dimensional case. We find all the counterterms in the case \(N=5\) and the counterterms for the conformal scalar field in the cases \(N=6,7\). We determine the geometric structure of the first three counterterms in the \(N\)-dimensional case. We show that all the subtractions in the four-dimensional case and the first three subtractions in the many-dimensional case correspond to the renormalization of the parameters in the bare gravitational Lagrangian. We discuss the geometric structure of the other counterterms in the many-dimensional case and the problem of eliminating the conformal anomaly in the four-dimensional case. MSC: 81T20 Quantum field theory on curved space or space-time backgrounds 83E15 Kaluza-Klein and other higher-dimensional theories 81V17 Gravitational interaction in quantum theory PDFBibTeX XMLCite \textit{Yu. V. Pavlov}, Theor. Math. Phys. 128, No. 2, 1034--1045 (2001; Zbl 1144.81492); translation from Teor. Mat. Fiz. 128, No. 2, 236--248 (2001) Full Text: DOI