Polyakov formula
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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.
References
- {{citation|first=Alexander|last=Polyakov|title=Quantum geometry of bosonic strings|journal= Physics Letters B|volume= 103|year=1981|issue=3 |pages=207–210 |doi=10.1016/0370-2693(81)90743-7|bibcode=1981PhLB..103..207P }}
- {{citation|first=Thomas|last=Branson|title=Q-curvature, spectral invariants, and representation theory|journal=Symmetry, Integrability and Geometry: Methods and Applications|volume=3|year=2007|page=090 |doi=10.3842/SIGMA.2007.090 |arxiv=0709.2471 |bibcode=2007SIGMA...3..090B |s2cid=14629173 |url=http://www.emis.de/journals/SIGMA/2007/090/sigma07-090.pdf}}
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