Ori, Fabio
(2023)
Heat kernel methods in perturbative quantum gravity.
[Laurea magistrale], Università di Bologna, Corso di Studio in
Physics [LMDM270]
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Abstract
The heat kernel method is a powerful technique in mathematical physics, with applications ranging from black hole entropy to mathematical finance. It consists in a variety of perturbation methods applied to elliptic secondorder differential operators on manifolds, which allow to study asymptotic expansions and singularities of Green functions. Perturbative quantum gravity is grounded on the background field method, where the metric tensor is split into a fixed background and quantum perturbations. By moving to euclidean time, the kinetic operators of BRSTquantised gravity become elliptic operators of secondorder in partial derivatives, which can be studied via heat kernel techniques. The heat kernel coefficients obtained in this expansion correspond to the counterterms needed to renormalise the oneloop effective action; once computed onshell, i.e. by using Einstein equations, they become gauge invariant. Up to now, only the first three coefficients for perturbative quantum gravity were known, so the main goal of this thesis is to compute the fourth one, which allows to study renormalisation theory for D=6 gravity at oneloop, behaving similarly to D=4 gravity at twoloops. Both theories are known to be nonrenormalisable, and our calculation shows the precise coefficient of the oneloop term that gives the logarithmic divergences in D=6 extended to arbitrary dimensions (for D>6 the divergences are not anymore logarithmic). Our result is in accordance with the oneloop calculation performed independently through the N=4 spinning particle in the worldline formalism. The computations are then extended to the case of matter fields coupled to the graviton, in the vacuum approximation; a suitable extension of these results to the general matter case might have a role in evaluating quantum corrections to the entropy of KerrNewmann black holes.
Abstract
The heat kernel method is a powerful technique in mathematical physics, with applications ranging from black hole entropy to mathematical finance. It consists in a variety of perturbation methods applied to elliptic secondorder differential operators on manifolds, which allow to study asymptotic expansions and singularities of Green functions. Perturbative quantum gravity is grounded on the background field method, where the metric tensor is split into a fixed background and quantum perturbations. By moving to euclidean time, the kinetic operators of BRSTquantised gravity become elliptic operators of secondorder in partial derivatives, which can be studied via heat kernel techniques. The heat kernel coefficients obtained in this expansion correspond to the counterterms needed to renormalise the oneloop effective action; once computed onshell, i.e. by using Einstein equations, they become gauge invariant. Up to now, only the first three coefficients for perturbative quantum gravity were known, so the main goal of this thesis is to compute the fourth one, which allows to study renormalisation theory for D=6 gravity at oneloop, behaving similarly to D=4 gravity at twoloops. Both theories are known to be nonrenormalisable, and our calculation shows the precise coefficient of the oneloop term that gives the logarithmic divergences in D=6 extended to arbitrary dimensions (for D>6 the divergences are not anymore logarithmic). Our result is in accordance with the oneloop calculation performed independently through the N=4 spinning particle in the worldline formalism. The computations are then extended to the case of matter fields coupled to the graviton, in the vacuum approximation; a suitable extension of these results to the general matter case might have a role in evaluating quantum corrections to the entropy of KerrNewmann black holes.
Tipologia del documento
Tesi di laurea
(Laurea magistrale)
Autore della tesi
Ori, Fabio
Relatore della tesi
Scuola
Corso di studio
Indirizzo
THEORETICAL PHYSICS
Ordinamento Cds
DM270
Parole chiave
Perturbative quantum gravity,Heat kernel,Oneloop effective action,Background field formalism,SeeleyDeWitt coefficients
Data di discussione della Tesi
14 Luglio 2023
URI
Altri metadati
Tipologia del documento
Tesi di laurea
(NON SPECIFICATO)
Autore della tesi
Ori, Fabio
Relatore della tesi
Scuola
Corso di studio
Indirizzo
THEORETICAL PHYSICS
Ordinamento Cds
DM270
Parole chiave
Perturbative quantum gravity,Heat kernel,Oneloop effective action,Background field formalism,SeeleyDeWitt coefficients
Data di discussione della Tesi
14 Luglio 2023
URI
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