561 research outputs found
Integrable Discrete Linear Systems and One-Matrix Model
In this paper we analyze one-matrix models by means of the associated
discrete linear systems. We see that the consistency conditions of the discrete
linear system lead to the Virasoro constraints. The linear system is endowed
with gauge invariances. We show that invariance under time-independent gauge
transformations entails the integrability of the model, while the double
scaling limit is connected with a time-dependent gauge transformation. We
derive the continuum version of the discrete linear system, we prove that the
partition function is actually the -function of the KdV hierarchy and
that the linear system completely determines the Virasoro constraints.Comment: 31page
Comment about UV regularization of basic commutators in string theories
Recently proposed by Hwang, Marnelius and Saltsidis zeta regularization of
basic commutators in string theories is generalized to the string models with
non-trivial vacuums. It is shown that implementation of this regularization
implies the cancellation of dangerous terms in the commutators between Virasoro
generators, which break Jacobi identity.Comment: LaTeX, 9 pages, no figures, submitted to Physics Letters
Local Anomalies, Local Equivariant Cohomology and the Variational Bicomplex
The locality conditions for the vanishing of local anomalies in field theory
are shown to admit a geometrical interpretation in terms of local equivariant
cohomology, thus providing a method to deal with the problem of locality in the
geometrical approaches to the study of local anomalies based on the
Atiyah-Singer index theorem. The local cohomology is shown to be related to the
cohomology of jet bundles by means of the variational bicomplex theory. Using
these results and the techniques for the computation of the cohomology of
invariant variational bicomplexes in terms of relative Gel'fand-Fuks cohomology
introduced in [6], we obtain necessary and sufficient conditions for the
cancellation of local gravitational and mixed anomalies.Comment: 36 pages. The paper is divided in two part
Quantization of Two-Dimensional Gravity with Dynamical Torsion
We consider two-dimensional gravity with dynamical torsion in the Batalin -
Vilkovisky and Batalin - Lavrov - Tyutin formalisms of gauge theories
quantization as well as in the background field method.Comment: 12 pages, LaTe
Gravitation, electromagnetism and cosmological constant in purely affine gravity
The Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field,
that has the form of the Maxwell Lagrangian with the metric tensor replaced by
the symmetrized Ricci tensor, is dynamically equivalent to the metric
Einstein-Maxwell Lagrangian, except the zero-field limit, for which the metric
tensor is not well-defined. This feature indicates that, for the
Ferraris-Kijowski model to be physical, there must exist a background field
that depends on the Ricci tensor. The simplest possibility, supported by recent
astronomical observations, is the cosmological constant, generated in the
purely affine formulation of gravity by the Eddington Lagrangian. In this paper
we combine the electromagnetic field and the cosmological constant in the
purely affine formulation. We show that the sum of the two affine (Eddington
and Ferraris-Kijowski) Lagrangians is dynamically inequivalent to the sum of
the analogous (CDM and Einstein-Maxwell) Lagrangians in the
metric-affine/metric formulation. We also show that such a construction is
valid, like the affine Einstein-Born-Infeld formulation, only for weak
electromagnetic fields, on the order of the magnetic field in outer space of
the Solar System. Therefore the purely affine formulation that combines
gravity, electromagnetism and cosmological constant cannot be a simple sum of
affine terms corresponding separately to these fields. A quite complicated form
of the affine equivalent of the metric Einstein-Maxwell- Lagrangian
suggests that Nature can be described by a simpler affine Lagrangian, leading
to modifications of the Einstein-Maxwell-CDM theory for
electromagnetic fields that contribute to the spacetime curvature on the same
order as the cosmological constant.Comment: 17 pages, extended and combined with gr-qc/0612193; published versio
Three-Dimensional Integrable Models and Associated Tangle Invariants
In this paper we show that the Boltzmann weights of the three-dimensional
Baxter-Bazhanov model give representations of the braid group, if some suitable
spectral limits are taken. In the trigonometric case we classify all possible
spectral limits which produce braid group representations. Furthermore we prove
that for some of them we get cyclotomic invariants of links and for others we
obtain tangle invariants generalizing the cyclotomic ones.Comment: Number of pages: 21, Latex fil
Vacuum structure for expanding geometry
We consider gravitational wave modes in the FRW metrics in a de Sitter phase
and show that the state space splits into many unitarily inequivalent
representations of the canonical commutation relations. Non-unitary time
evolution is described as a trajectory in the space of the representations. The
generator of time evolution is related to the entropy operator. The
thermodynamic arrow of time is shown to point in the same direction of the
cosmological arrow of time. The vacuum is a two-mode SU(1,1) squeezed state of
thermo field dynamics. The link between expanding geometry, squeezing and
thermal properties is exhibited.Comment: Latex file, epsfig, 1 figure, 21 page
Hawking Radiation Entropy and Horizon Divergences
We review the problem of divergences in one--loop thermodynamical quantities
for matter fields in thermal equilibrium on a black hole background. We discuss
a number of results obtained for various thermodynamical quantities. Then we
discuss the ansatz called ``literal interpretation" of zeroth law of black hole
mechanics and try to explain the diseases of the conical defect procedure in
light of this ansatz. Finally, an analysis of the consequences implied by our
ansatz on the calculation of the partition function is made.Comment: 32 pages, uses Phyzz
A Conformal Affine Toda Model of 2D-Black Holes the End-Point State and the S-Matrix
In this paper we investigate in more detail our previous formulation of the
dilaton-gravity theory by Bilal--Callan--de~Alwis as a -conformal affine
Toda (CAT) theory. Our main results are: i) a field redefinition of the
CAT-basis in terms of which it is possible to get the black hole solutions
already known in the literature; ii) an investigation the scattering matrix
problem for the quantum black hole states. It turns out that there is a range
of values of the free-falling shock matter fields forming the black hole
solution, in which the end-point state of the black hole evaporation is a zero
temperature regular remnant geometry. It seems that the quantum evolution to
this final state is non-unitary, in agreement with Hawking's scenario for the
black hole evaporation.Comment: ROM2F-93-03, 27 pages, phyzz
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