Lesson plan
Polyakov formula
In differential geometry and mathematical physics (especially string theory), the Polyakov formula expresses the conformal variation of the zeta functional determinant of a Riemannian manifold. Proposed by Alexander Markovich Polyakov, this formula arose in the study of the quantum theory of strings. The corresponding density is local, and therefore is a Riemannian curvature invariant. In particular, whereas the functional determinant itself is prohibitively difficult to work with in general, its conformal variation can be written down explicitly.
Article summary
In differential geometry and mathematical physics (especially string theory), the Polyakov formula expresses the conformal variation of the zeta functional determinant of a Riemannian manifold. Proposed by Alexander Markovich Polyakov, this formula arose in the study of the quantum theory of strings. The corresponding density is local, and therefore is a Riemannian curvature invariant. In particular, whereas the functional determinant itself is prohibitively difficult to work with in general, its conformal variation can be written down explicitly.
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