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Sergio Zerbini

Publications and source records attributed to Sergio Zerbini.

88 records · Page 5Linked to original sources
arXiv1999

One-loop Quantum Holography for Higher Dimensional Black Holes

The one-loop quantum corrections to the free energy associated with scalar field in a higher dimensional static curved space-time is investigated making use of the conformal transformation method. For a space-time with bifurcate horizon, horizon divergences are accounted for choosing the Planck length as natural cutoff. The leading term in the high temperature quantum correction satifies holographically the "area law", like the tree level Bekenstein-Hawking term. Furthermore it is stressed that only for the asymptotically AdS black holes one may have a microscopic interpretation of the entropy also at quantum level.

hep-th↗
arXiv1999

Quantum scalar field in D-dimensional static black hole space-times

An Euclidean approach for investigating quantum aspects of a scalar field living on a class of D-dimensional static black hole space-times, including the extremal ones, is reviewed. The method makes use of a near horizon approximation of the metric and $ζ$-function formalism for evaluating the partition function and the expectation value of the field fluctuations $<ϕ^2(x)>$. After a review of the non-extreme black hole case, the extreme one is considered in some details. In this case, there is no conical singularity, but the finite imaginary time compactification introduces a cusp singularity. It is found that the $ζ$-function regularized partition function can be defined, and the quantum fluctuations are finite on the horizon, as soon as the cusp singularity is absent, and the corresponding temperature is T=0.

gr-qc↗
arXiv1998

Applications in physics of the multiplicative anomaly formula involving some basic differential operators

In the framework leading to the multiplicative anomaly formula ---which is here proven to be valid even in cases of known spectrum but non-compact manifold (very important in Physics)--- zeta-function regularisation techniques are shown to be extremely efficient. Dirac like operators and harmonic oscillators are investigated in detail, in any number of space dimensions. They yield a non-zero anomaly which, on the other hand, can always be expressed by means of a simple analytical formula. These results are used in several physical examples, where the determinant of a product of differential operators is not equal to the product of the corresponding functional determinants. The simplicity of the Hamiltonian operators chosen is aimed at showing that such situation may be quite widespread in mathematical physics. However, the consequences of the existence of the determinant anomaly have often been overlooked.

hep-th↗
arXiv1998

Is the multiplicative anomaly dependent on the regularization ?

In a recent work, T.S. Evans has claimed that the multiplicative anomaly associated with the zeta-function regularization of functional determinants is regularization dependent. We show that, if one makes use of consistent definitions, this is not the case and clarify some points in Evans' argument.

hep-th↗
arXiv1998

Is the multiplicative anomaly relevant ?

In a recent work, S. Dowker has shed doubt on a recipe used in computing the partition function for a matrix valued operator. This recipe, advocated by Benson, Bernstein and Dodelson, leads naturally to the so called multiplicative anomaly for the zeta-function regularized functional determinants. In this letter we present arguments in favour of the mentioned prescription, showing that it is the valid one in calculations involving the relativistic charged bosonic ideal gas in the framework of functional analysis.

hep-th↗
arXiv1998

One-loop Effective Potential for a Fixed Charged Self-interacting Bosonic Model at Finite Temperature with its Related Multiplicative Anomaly

The one-loop partition function for a charged self-interacting Bose gas at finite temperature in D-dimensional spacetime is evaluated within a path integral approach making use of zeta-function regularization. For D even, a new additional vacuum term ---overlooked in all previous treatments and coming from the multiplicative anomaly related to functional determinants-- is found and its dependence on the mass and chemical potential is obtained. The presence of the new term is shown to be crucial for having the factorization invariance of the regularized partition function. In the non interacting case, the relativistic Bose-Einstein condensation is revisited. By means of a suitable charge renormalization, for D=4 the symmetry breaking phase is shown to be unaffected by the new term, which, however, gives actually rise to a non vanishing new contribution in the unbroken phase.

hep-th↗
arXiv1997

Ray-Singer Torsion for a Hyperbolic 3-Manifold and Asymptotics of Chern-Simons-Witten Invariant

The Ray-Singer torsion for a compact smooth hyperbolic 3-dimensional manifold ${\cal H}^3$ is expressed in terms of Selberg zeta-functions, making use of the associated Selberg trace formulae. Applications to the evaluation of the semiclassical asymptotics of the Witten's invariant for the Chern-Simons theory with gauge group SU(2) as well as to the sum over topologies in 3-dimensional quantum gravity are presented.

hep-th↗
arXiv1996

Zeta-function on the generalised cone

The analytic properties of the zeta-function for a Laplace operator on a generalised cone are studied in some detail using the Cheeger's approach and explicit expressions are given. In the compact case, the zeta-function of the Laplace operator turns out to be singular at the origin. As a result, strictly speaking, the zeta-function regularisation does not ``regularise'' and a further subtraction is required for the related one-loop effective potential.

hep-th↗
arXiv1996

Quantum Fields in Hyperbolic Space-Times with Finite Spatial Volume

The one-loop effective action for a massive self-interacting scalar field is investigated in $4$-dimensional ultrastatic space-time $ R \times H^3/Γ$, $H^3/Γ$ being a non-compact hyperbolic manifold with finite volume. Making use of the Selberg trace formula, the $ζ$-function related to the small disturbance operator is constructed. For an arbitrary gravitational coupling, it is found that $ζ(s)$ has a simple pole at $s=0$. The one-loop effective action is analysed by means of proper-time regularisations and the one-loop divergences are explicitly found. It is pointed out that, in this special case, also $ζ$-function regularisation requires a divergent counterterm, which however is not necessary in the free massless conformal invariant coupling case. Finite temperature effects are studied and the high-temperature expansion is presented. A possible application to the problem of the divergences of the entanglement entropy for a free massless scalar field in a Rindler-like space-time is briefly discussed.

hep-th↗
arXiv1996

Euclidean Approach to the Entropy for a Scalar Field in Rindler-like Space-Times

The off-shell entropy for a massless scalar field in a D-dimensional Rindler-like space-time is investigated within the conical Euclidean approach in the manifold $C_\be\times\M^N$, $C_\be$ being the 2-dimensional cone, making use of the zeta-function regularisation. Due to the presence of conical singularities, it is shown that the relation between the zeta-function and the heat kernel is non trivial and, as first pointed out by Cheeger, requires a separation between small and large eigenvalues of the Laplace operator. As a consequence, in the massless case, the (naive) non existence of the Mellin transform is by-passed by the Cheeger's analytical continuation of the zeta-function on manifold with conical singularities. Furthermore, the continuous spectrum leads to the introduction of smeared traces. In general, it is pointed out that the presence of the divergences may depend on the smearing function and they arise in removing the smearing cutoff. With a simple choice of the smearing function, horizon divergences in the thermodynamical quantities are recovered and these are similar to the divergences found by means of off-shell methods like the brick wall model, the optical conformal transformation techniques or the canonical path integral method.

hep-th↗
arXiv1995

Finite Temperature Effects for Massive Fields in D-dimensional Rindler-like Spaces

The first quantum corrections to the free energy for massive fields in $D$-dimensional space-times of the form $\R\times\R^+\times\M^{N-1}$, where $D=N+1$ and $\M^{N-1}$ is a constant curvature manifold, is investigated by means of the $ζ$-function regularization. It is suggested that the nature of the divergences, which are present in the thermodynamical quantities, might be better understood making use of the conformal related optical metric and associated techniques. The general form of the horizon divercences of the free energy is obtained as a function of free energy densities of fields having negative square masses (absence of the gap in the Laplace operator spectrum) on ultrastatic manifolds with hyperbolic spatial section $H^{N-2n}$ and of the Seeley-DeWitt coefficients of the Laplace operator on the manifold $\M^{N-1}$. Furthermore, recurrence relations are found relating higher and lower dimensions. The cases of Rindler space, where $\M^{N-1}=\R^{N-1}$ and very massive $D$-dimensional black holes, where $\M^{N-1}=S^{N-1}$ are treated as examples. The renormalization of the internal energy is also discussed.

hep-th↗
arXiv1995

ONE-LOOP QUANTUM CORRECTIONS TO THE ENTROPY FOR A 4-DIMENSIONAL ETERNAL BLACK HOLE

The first quantum corrections to the free energy for an eternal 4-dimensional black hole is investigated at one-loop level, in the large mass limit of the black hole, making use of the conformal techniques related to the optical metric. The quadratic and logarithmic divergences as well as a finite part associated with the first quantum correction to the entropy are obtained at a generic temperature. It is argued that, at the Hawking temperature, the horizon divergences of the internal energy should cancel. Some comments on the divergences of the entropy are also presented.

hep-th↗
arXiv1994

Are p-Branes Asymptotically Black Holes?

An attempt is made to compare the asymptotic state density of twisted $p$-branes and the related state density of mass level $M$ of a $D$-dimensional neutral black hole. To this aim, the explicit form of the twisted $p$-brane total level degeneracy is calculated. The prefactor of the degeneracy, in contrast to the leading behaviour, is found to depend on the winding number of the $p$-brane.

hep-th↗
arXiv1993

Finite temperature effective potential on hyperbolic spacetimes

The finite temperature one-loop effective potential for a scalar field defined on an ultrastatic spacetime, whose spatial part is a compact hyperbolic manifold, is studied. Different analytic expressions, especially valuable at low and high temperature are derived. Based on these results, the symmetry breaking and the topological mass generation are discussed.

hep-th↗
arXiv1993

One-loop effective potential on hyperbolic manifolds

The one-loop effective potential for a scalar field defined on an ultrastatic space-time whose spatial part is a compact hyperbolic manifold, is studied using zeta-function regularization for the one-loop effective action. Other possible regularizations are discussed in detail. The renormalization group equations are derived and their connection with the conformal anomaly is pointed out. The symmetry breaking and the topological mass generation are also discussed.

hep-th↗