7,483 research outputs found

### Inverse problem for Dirac systems with locally square-summable potentials and rectangular Weyl functions

Inverse problem for Dirac systems with locally square summable potentials and
rectangular Weyl functions is solved. For that purpose we use a new result on
the linear similarity between operators from a subclass of triangular integral
operators and the operator of integration.Comment: Some of the main results from [16] (A. Sakhnovich, Inverse Problems
18 (2002), 331--348) and the submitted to ArXiv papers[2] and [5] (see
arXiv:0912.4444 and arXiv:1106.1263) are generalized for the case of the
locally square-summable potentials and rectangular Weyl function

### Lukewarm black holes in quadratic gravity

Perturbative solutions to the fourth-order gravity describing
spherically-symmetric, static and electrically charged black hole in an
asymptotically de Sitter universe is constructed and discussed. Special
emphasis is put on the lukewarm configurations, in which the temperature of the
event horizon equals the temperature of the cosmological horizon

### Implication of Compensator Field and Local Scale Invariance in the Standard Model

We introduce Weyl's scale symmetry into the standard model (SM) as a local
symmetry. This necessarily introduces gravitational interactions in addition to
the local scale invariance group \tilde U(1) and the SM groups SU(3) X SU(2) X
U(1). The only other new ingredients are a new scalar field \sigma and the
gauge field for \tilde U(1) we call the Weylon. A noteworthy feature is that
the system admits the St\" uckelberg-type compensator. The \sigma couples to
the scalar curvature as (-\zeta/2) \sigma^2 R, and is in turn related to a St\"
uckelberg-type compensator \varphi by \sigma \equiv M_P e^{-\varphi/M_P} with
the Planck mass M_P. The particular gauge \varphi = 0 in the St\" uckelberg
formalism corresponds to \sigma = M_P, and the Hilbert action is induced
automatically. In this sense, our model presents yet another mechanism for
breaking scale invariance at the classical level. We show that our model
naturally accommodates the chaotic inflation scenario with no extra field.Comment: This work is to be read in conjunction with our recent comments
hep-th/0702080, arXiv:0704.1836 [hep-ph] and arXiv:0712.2487 [hep-ph]. The
necessary ingredients for describing chaotic inflation in the SM as
entertained by Bezrukov and Shaposhnikov [17] have been provided by our
original model [8]. We regret their omission in citing our original model [8

### The geometry of manifolds and the perception of space

This essay discusses the development of key geometric ideas in the 19th
century which led to the formulation of the concept of an abstract manifold
(which was not necessarily tied to an ambient Euclidean space) by Hermann Weyl
in 1913. This notion of manifold and the geometric ideas which could be
formulated and utilized in such a setting (measuring a distance between points,
curvature and other geometric concepts) was an essential ingredient in
Einstein's gravitational theory of space-time from 1916 and has played
important roles in numerous other theories of nature ever since.Comment: arXiv admin note: substantial text overlap with arXiv:1301.064

### Quantum effects from a purely geometrical relativity theory

A purely geometrical relativity theory results from a construction that
produces from three-dimensional space a happy unification of Kaluza's
five-dimensional theory and Weyl's conformal theory. The theory can provide
geometrical explanations for the following observed phenomena, among others:
(a) lifetimes of elementary particles of lengths inversely proportional to
their rest masses; (b) the equality of charge magnitude among all charged
particles interacting at an event; (c) the propensity of electrons in atoms to
be seen in discretely spaced orbits; and (d) `quantum jumps' between those
orbits. This suggests the possibility that the theory can provide a
deterministic underpinning of quantum mechanics like that provided to
thermodynamics by the molecular theory of gases.Comment: 7 pages, LaTeX jpconf.cls (Institute of Physics Publishing), 6
Encapsulated PostScript figures (Fig. 6 is 1.8M uncompressed); Presented at
VI Mexican School on Gravitation and Mathematical Physics "Approaches to
Quantum Gravity

### Conformal Invariance in Einstein-Cartan-Weyl space

We consider conformally invariant form of the actions in Einstein, Weyl,
Einstein-Cartan and Einstein-Cartan-Weyl space in general dimensions($>2$) and
investigate the relations among them. In Weyl space, the observational
consistency condition for the vector field determining non-metricity of the
connection can be obtained from the equation of motion. In Einstein-Cartan
space a similar role is played by the vector part of the torsion tensor. We
consider the case where the trace part of the torsion is the Kalb-Ramond type
of field. In this case, we express conformally invariant action in terms of two
scalar fields of conformal weight -1, which can be cast into some interesting
form. We discuss some applications of the result.Comment: 10 pages, version to appear MPL

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