# One-loop stress-tensor renormalization in curved background: the relation between $\zeta$-function and point-splitting approaches, and an improved point-splitting procedure

@article{Moretti1998OneloopSR,
title={One-loop stress-tensor renormalization in curved background: the relation between \$\zeta\$-function and point-splitting approaches, and an improved point-splitting procedure},
author={Valter Moretti},
journal={arXiv: General Relativity and Quantum Cosmology},
year={1998}
}
• Valter Moretti
• Published 1998
• Mathematics, Physics
• arXiv: General Relativity and Quantum Cosmology
We conclude the rigorous analysis of a previous paper concerning the relation between the (Euclidean) point-splitting approach and the local $\zeta$-function procedure to renormalize physical quantities at one-loop in (Euclidean) QFT in curved spacetime. The stress tensor is now considered in general $D$-dimensional closed manifolds for positive scalar operators $-\Delta + V(x)$. Results obtained in previous works (in the case D=4 and $V(x) =\xi R(x) + m^2$) are rigorously proven and… Expand
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