arXiv subjects

A. Mikovic

Publications and source records attributed to A. Mikovic.

At least 37 records · Page 2Linked to original sources

arXiv2002

Quantum Field Theory of Open Spin Networks and New Spin Foam Models

We describe how a spin-foam state sum model can be reformulated as a quantum field theory of spin networks, such that the Feynman diagrams of that field theory are the spin-foam amplitudes. In the case of open spin networks, we obtain a new type of state-sum models, which we call the matter spin foam models. In this type of state-sum models, one labels both the faces and the edges of the dual two-complex for a manifold triangulation with the simple objects from a tensor category. In the case of Lie groups, such a model corresponds to a quantization of a theory whose fields are the principal bundle connection and the sections of the associated vector bundles. We briefly discuss the relevance of the matter spin foam models for quantum gravity and for topological quantum field theories.

gr-qc↗

arXiv2001

Quantum Field Theory of Spin Networks

We study the transition amplitudes in state-sum models of quantum gravity in D=2,3,4 spacetime dimensions by using the field theory over a Lie group formulation. By promoting the group theory Fourier modes into creation and annihilation operators we construct a Fock space for the quantum field theory whose Feynman diagrams give the transition amplitudes. By making products of the Fourier modes we construct operators and states representing the spin networks associated to triangulations of spatial boundaries of a triangulated spacetime manifold. The corresponding spin network amplitudes give the state-sum amplitudes for triangulated manifolds with boundaries. We also show that one can introduce a discrete time evolution operator, where the time is given by the number of D-simplices in the triangulation, or equivalently by the number of the vertices in the Feynman diagram. The corresponding transition amplitude is a finite sum of Feynman diagrams, and in this way one avoids the problem of infinite amplitudes caused by summing over all possible triangulations.

gr-qc↗

arXiv2000

Super Chern Simons Theory and Flat Super Connections on a Torus

We study the moduli space of a super Chern-Simons theory on a manifold with the topology ${\bf R}\times §$, where $§$ is a compact surface. The moduli space is that of flat super connections modulo gauge transformations on $§$, and we study in detail the case when $§$ is atorus and the supergroup is $OSp(m|2n)$. The bosonic moduli space is determined by the flat connections for the maximal bosonic subgroup $O(m)\times Sp(2n)$, while the fermionic moduli appear only for special parts of the bosonic moduli space, which are determined by a vanishing determinant of a matrix associated to the bosonic part of the holonomy. If the CS supergroup is the exponential of a super Lie algebra, the fermionic moduli appear only for the bosonic holonomies whose generators have zero determinant in the fermion-fermion block of the super-adjoint representation. A natural symplectic structure on the moduli space is induced by the super Chern-Simons theory and it is determined by the Poisson bracket algebra of the holonomies. We show that the symplectic structure of homogenous connections is useful for understanding the properties of the moduli space and the holonomy algebra, and we illustrate this on the example of the $OSp(1|2)$ supergroup.

math-ph↗

arXiv2000

Painleve III Equation and Bianchi VII_0 Model

We examine the reduced phase space of the Bianchi VII_0 cosmological model, including the moduli sector. We show that the dynamics of the relevant sector of local degrees of freedom is given by a Painleve III equation. We then obtain a zero-curvature representation of this Painleve III equation by applying the Belinskii-Zakharov method to the Bianchi VII_0 model.

gr-qc↗

arXiv1999

Free-Field Realization of D-dimensional Cylindrical Gravitational Waves

We find two-dimensional free-field variables for D-dimensional general relativity on spacetimes with D-2 commuting spacelike Killing vector fields and non-compact spatial sections for D>4. We show that there is a canonical transformation which maps the corresponding two-dimensional dilaton gravity theory into a two-dimensional diffeomorphism invariant theory of the free-field variables. We also show that the spacetime metric components can be expressed as asymptotic series in negative powers of the dilaton, with coefficients which can be determined in terms of the free fields.

gr-qc↗

arXiv1998

Free Field Realization of Cylindrically Symmetric Einstein Gravity

Cylindrically reduced Einstein gravity can be regarded as an $SL(2,R)/SO(2)$ sigma model coupled to 2D dilaton gravity. By using the corresponding 2D diffeomorphism algebra of constraints and the asymptotic behaviour of the Ernst equation we show that the theory can be mapped by a canonical transformation into a set of free fields with a Minkowskian target space. We briefly discuss the quantization in terms of these free-field variables, which is considerably simpler than in the other approaches.

gr-qc↗

arXiv1998

Remarks on the Reduced Phase Space of (2+1)-Dimensional Gravity on a Torus in the Ashtekar Formulation

We examine the reduced phase space of the Barbero-Varadarajan solutions of the Ashtekar formulation of (2+1)-dimensional general relativity on a torus. We show that it is a finite-dimensional space due to existence of an infinite dimensional residual gauge invariance which reduces the infinite-dimensional space of solutions to a finite-dimensional space of gauge-inequivalent solutions. This is in agreement with general arguments which imply that the number of physical degrees of freedom for (2+1)-dimensional Ashtekar gravity on a torus is finite.

gr-qc↗

arXiv1998

One-Loop Effective Action for Spherical Scalar Field Collapse

We calculate the complete one-loop effective action for a spherical scalar field collapse in the large radius approximation. This action gives the complete trace anomaly, which beside the matter loop contributions, receives a contribution from the graviton loops. Our result opens a possibility for a systematic study of the back-reaction effects for a real black hole.

hep-th↗

arXiv1997

Loop Corrections for 2D Hawking Radiation

We describe how the reduced phase space quantization of the CGHS model of 2d black hole formation allows one to calculate the backreaction up to any finite order in matter loops. We then analyze the backreaction in the Hawking radiation up to two loops. At one-loop order the Hawking temperature does not change, while at two-loop order the temperature increases three times with respect to the classical value. We argue that such a behavior is consistent with the behaviour of the operator quantization Hawking flux for times which are not too late. For very late times the two-loop flux goes to zero which indicates that the backreaction can stop the black hole evaporation.

gr-qc↗

arXiv1997

General Solution for Self-Gravitating Spherical Null Dust

We find the general solution of equations of motion for self-gravitating spherical null dust as a perturbative series in powers of the outgoing matter energy-momentum tensor, with the lowest order term being the Vaidya solution for the ingoing matter. This is done by representing the null-dust model as a 2d dilaton gravity theory, and by using a symmetry of a pure 2d dilaton gravity to fix the gauge. Quantization of this solution would provide an effective metric which includes the back-reaction for a more realistic black hole evaporation model than the evaporation models studied previously.

gr-qc↗

arXiv1997

One-loop Effective Action for a Generic 2D Dilaton Gravity Theory

We study the one-loop effective action for a generic two-dimensional dilaton gravity theory conformally coupled to $N$ matter fields. We obtain an explicit expression for the effective action in the weak-coupling limit under a suitable restriction of the dilaton potential asymptotics. Our result applies to the CGHS model as well as to the spherically symmetric general relativity. The effective action is obtained by using the background-field method, and we take into account the loop contributions from all the fields in the classical action and from the ghosts. In the large-$N$ limit, and after an appropriate field redefinition, the one-loop correction takes the form of the Polyakov-Liouville action.

hep-th↗

arXiv1997

Loop Corrections in the Spectrum of 2D Hawking Radiation

We determine the one-loop and the two-loop back-reaction corrections in the spectrum of the Hawking radiation for the CGHS model of 2d dilaton gravity by evaluating the Bogoliubov coefficients for a massless scalar field propagating on the corresponding backgrounds. Since the back-reaction can induce a small shift in the position of the classical horizon, we find that a positive shift leads to a non-Planckian late-time spectrum, while a null or a negative shift leads to a Planckian late-time spectrum in the leading-order stationary-point approximation. In the one-loop case there are no corrections to the classical Hawking temperature, while in the two-loop case the temperature is three times greater than the classical value. We argue that these results are consistent with the behaviour of the Hawking flux obtained from the operator quantization only for the times which are not too late, in accordance with the limits of validity of the semiclassical approximation.

gr-qc↗

arXiv1996

W-Strings on Curved Backgrounds

We discuss a canonical formalism method for constructing actions describing propagation of W-strings on curved backgrounds. The method is based on the construction of a representation of the W-algebra in terms of currents made from the string coordinates and the canonically conjugate momenta. We construct such a representation for a W_3-string propagating in the background metric with one flat direction by using a simple ansatz for the W-generators where each generator is a polynomial of the canonical currents and the veilbeins. In the case of a general background we show that the simple polynomial ansatz fails, and terms containing the veilbein derivatives must be added.

hep-th↗

arXiv1996

A Quantum Model of Schwarzschild Black Hole Evaporation

We construct a one-loop effective metric describing the evaporation phase of a Schwarzschild black hole in a spherically symmetric null-dust model. This is achieved by quantising the Vaidya solution and by chosing a time dependent quantum state. This state describes a black hole which is initially in thermal equilibrium and then the equilibrium is switched off, so that the black hole starts to evaporate, shrinking to a zero radius in a finite proper time. The naked singularity appears, and the Hawking flux diverges at the end-point. However, a static metric can be imposed in the future of the end-point. Although this end-state metric cannot be determined within our construction, we show that it cannot be a flat metric.

hep-th↗

arXiv1996

Two-loop Back-reaction in 2D Dilaton Gravity

We calculate the two-loop quantum corrections, including the back-reaction of the Hawking radiation, to the one-loop effective metric in a unitary gauge quantization of the CGHS model of 2d dilaton gravity. The corresponding evaporating black hole solutions are analysed, and consistent semi-classical geometries appear in the weak-coupling region of the spacetime when the width of the matter pulse is larger then the short-distance cutoff. A consistent semi-classical geometry also appears in the limit of a shock-wave matter. The Hawking radiation flux receives non-thermal corrections such that it vanishes for late times and the total radiated mass is finite. There are no static remnants for matter pulses of finite width, although a BPP type static remnant appears in the shock-wave limit. Semi-classical geometries without curvature singularities can be obtained as well. Our results indicate that higher-order loop corrections can remove the singularities encountered in the one-loop solutions.

hep-th↗

arXiv1995

Unitary Theory of Evaporating 2D Black Holes

We study a manifestly unitary formulation of 2d dilaton quantum gravity based on the reduced phase space quantization. The spacetime metric can be expanded in a formal power series of the matter energy-momentum tensor operator. This expansion can be used for calculating the quantum corrections to the classical black hole metric by evaluating the expectation value of the metric operator in an appropriate class of the physical states. When the normal ordering in the metric operator is chosen to be with respect to Kruskal vacuum, the lowest order semiclassical metric is exactly the one-loop effective action metric discovered by Bose, Parker and Peleg. The corresponding semiclassical geometry describes an evaporating black hole which ends up as a remnant. The calculation of higher order corrections and implications for the black hole fate are discussed.

gr-qc↗

arXiv1994

Hawking Radiation and Back-Reaction in a Unitary Theory of 2D Quantum Gravity

We investigate the semiclassical limit and quantum corrections to the metric in a unitary quantum gravity formulation of the CGHS 2d dilaton gravity model. A new method for calculating the back-reaction effects has been introduced, as an expansion of the effective metric in powers of the matter energy-momentum tensor. In the semiclassical limit the quantum corrections can be neglected, and we show that physical states exists which contain the Hawking radiation. The first order back-reaction effect is entirely due to the Hawking radiation. It causes the black-hole mass to monotonically decrease, and it makes it unbounded from bellow as the horizon is approched. The second order quantum corrections have been estimated. Since the matter is propagating freely in this unitary theory, we expect that the higher order corrections will stabilize the mass, and the black hole will completely evaporate leaving a nearly flat space.

hep-th↗

arXiv1994

Black Holes and Nonperturbative Canonical 2D Dilaton Gravity

We investigate nonperturbative canonical quantization of two dimensional dilaton gravity theories with an emphasis on the CGHS model. We use an approach where a canonical transformation is constructed such that the constraints take a quadratic form. The required canonical transformation is obtained by using a method based on the Bäcklund transformation from the Liouville theory. We quantize dilaton gravity in terms of the new variables, where it takes a form of a bosonic string theory with background charges. Unitarity is then established by going into a light-cone gauge. As a direct consequence, black holes in this theory do not violate unitarity, and there is no information loss. We argue that the information escapes during the evaporation process. We also discuss the implications of this quantization scheme for the quantum fate of real black holes. The main conclusion is that black holes do not have to violate quantum mechanics.

hep-th↗