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

Particle phenomenology on noncommutative spacetime

We introduce particle phenomenology on the noncommutative spacetime called the Groenewold-Moyal plane. The length scale of spcetime noncommutativity is constrained from the CPT violation measurements in $K^{0}-\bar{K}^{0}$ system and $g-2$ difference of $\mu^+ - \mu^-$. The $K^{0}-\bar{K}^{0}$ system provides an upper bound on the length scale of spacetime noncommutativity of the order of $10^{-32} \textrm{m}$, corresponding to a lower energy bound $E$ of the order of $E \gtrsim 10^{16}\textrm{GeV}$. The $g-2$ difference of $\mu^+ - \mu^-$ constrains the noncommutativity length scale to be of the order of $10^{-20} \textrm{m}$, corresponding to a lower energy bound $E$ of the order of $E \gtrsim 10^{3}\textrm{GeV}$. We also present the phenomenology of the electromagnetic interaction of electrons and nucleons at the tree level in the noncommutative spacetime. We show that the distributions of charge and magnetization of nucleons are affected by spacetime noncommutativity. The analytic properties of electromagnetic form factors are also changed and it may give rise to interesting experimental signals.Comment: 10 pages, 3 figures. Published versio

New Models of General Relativistic Static Thick Disks

New families of exact general relativistic thick disks are constructed using the ``displace, cut, fill and reflect'' method. A class of functions used to ``fill'' the disks is derived imposing conditions on the first and second derivatives to generate physically acceptable disks. The analysis of the function's curvature further restrict the ranges of the free parameters that allow phisically acceptable disks. Then this class of functions together with the Schwarzschild metric is employed to construct thick disks in isotropic, Weyl and Schwarzschild canonical coordinates. In these last coordinates an additional function must be added to one of the metric coefficients to generate exact disks. Disks in isotropic and Weyl coordinates satisfy all energy conditions, but those in Schwarzschild canonical coordinates do not satisfy the dominant energy condition.Comment: 27 pages, 14 figure

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 Hawking temperature of expanding cosmological black holes

In the context of a debate on the correct expression of the Hawking temperature of an expanding cosmological black hole, we show that the correct expression in terms of the Hawking-Hayward quasi-local energy m of the hole is T=1/(8\pi m(t)). This expression holds for comoving black holes and agrees with a recent proposal by Saida, Harada, and Maeda.Comment: 5 latex pages, to appear in Phys. Rev. D. Some references adde

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

The fate of the Wilson-Fisher fixed point in non-commutative \phi^4

In this article we study non-commutative vector sigma model with the most general \phi^4 interaction on Moyal-Weyl spaces. We compute the 2- and 4-point functions to all orders in the large N limit and then apply the approximate Wilson renormalization group recursion formula to study the renormalized coupling constants of the theory. The non-commutative Wilson-Fisher fixed point interpolates between the commutative Wilson-Fisher fixed point of the Ising universality class which is found to lie at zero value of the critical coupling constant a_* of the zero dimensional reduction of the theory, and a novel strongly interacting fixed point which lies at infinite value of a_* corresponding to maximal non-commutativity beyond which the two-sheeted structure of a_* as a function of the dilation parameter disappears.Comment: 19 pages, 7 figures, v2:one reference adde

New results for the missing quantum numbers labeling the quadrupole and octupole boson basis

The many $2^k$-pole boson states, $|N_kv_k\alpha_k I_kM_k>$ with $k=2,3$, realize the irreducible representation (IR) for the group reduction chains $SU(2k+1)\supset R_{2k+1}\supset R_3\supset R_2$. They have been analytically studied and widely used for the description of nuclear systems. However, no analytical expression for the degeneracy $d_v(I)$ of the $R_{2k+1}$'s IR, determined by the reduction $R_{2k+1}\supset R_3$, is available. Thus, the number of distinct values taken by $\alpha_k$ has been so far obtained by solving some complex equations. Here we derive analytical expressions for the degeneracy $d_v(I)$ characterizing the octupole and quadrupole boson states, respectively. The merit of this work consists of the fact that it completes the analytical expressions for the $2^k$-pole boson basis.Comment: 10page

A combinatorial formula for homogeneous moments

We establish a combinatorial formula for homogeneous moments and give some examples where it can be put to use. An application to the statistical mechanics of interacting gauged vortices is discussed.Comment: 8 pages, LaTe

Possible way out of the Hawking paradox: Erasing the information at the horizon

We show that small deviations from spherical symmetry, described by means of exact solutions to Einstein equations, provide a mechanism to "bleach" the information about the collapsing body as it falls through the aparent horizon, thereby resolving the information loss paradox. The resulting picture and its implication related to the Landauer's principle in the presence of a gravitational field, is discussed.Comment: 11 pages, Latex. Some comments added to answer to some raised questions. Typos corected. Final version, to appear in Int. J. Modern. Phys.