The Relativistic Particle: Dirac observables and Feynman propagator

We analyze the algebra of Dirac observables of the relativistic particle in four space-time dimensions. We show that the position observables become non-commutative and the commutation relations lead to a structure very similar to the non-commutative geometry of Deformed Special Relativity (DSR). In this framework, it appears natural to consider the 4d relativistic particle as a five dimensional massless particle. We study its quantization in terms of wave functions on the 5d light cone. We introduce the corresponding five-dimensional action principle and analyze how it reproduces the physics of the 4d relativistic particle. The formalism is naturally subject to divergences and we show that DSR arises as a natural regularization: the 5d light cone is regularized as the de Sitter space. We interpret the fifth coordinate as the particle's proper time while the fifth moment can be understood as the mass. Finally, we show how to formulate the Feynman propagator and the Feynman amplitudes of quantum field theory in this context in terms of Dirac observables. This provides new insights for the construction of observables and scattering amplitudes in DSR.Comment: 14 pages, Revtex

The FIRST-2MASS Red Quasar Survey

Combining radio observations with optical and infrared color selection -- demonstrated in our pilot study to be an efficient selection algorithm for finding red quasars -- we have obtained optical and infrared spectroscopy for 120 objects in a complete sample of 156 candidates from a sky area of 2716 square degrees. Consistent with our initial results, we find our selection criteria -- J-K>1.7, R-K>4.0 -- yield a ~50% success rate for discovering quasars substantially redder than those found in optical surveys. Comparison with UVX- and optical color-selected samples shows that >~ 10% of the quasars are missed in a magnitude-limited survey. Simultaneous two-frequency radio observations for part of the sample indicate that a synchrotron continuum component is ruled out as a significant contributor to reddening the quasars' spectra. We go on to estimate extinctions for our objects assuming their red colors are caused by dust. Continuum fits and Balmer decrements suggest E(B-V) values ranging from near zero to 2.5 magnitudes. Correcting the K-band magnitudes for these extinctions, we find that for K <= 14.0, red quasars make up between 25% and 60% of the underlying quasar population; owing to the incompleteness of the 2MASS survey at fainter K-band magnitudes, we can only set a lower limit to the radio-detected red quasar population of >20-30%.Comment: 80 pages (single-column, preprint format) 20 figures, Accepted for publicated in Ap

Doubly Special Relativity and de Sitter space

In this paper we recall the construction of Doubly Special Relativity (DSR) as a theory with energy-momentum space being the four dimensional de Sitter space. Then the bases of the DSR theory can be understood as different coordinate systems on this space. We investigate the emerging geometrical picture of Doubly Special Relativity by presenting the basis independent features of DSR that include the non-commutative structure of space-time and the phase space algebra. Next we investigate the relation between our geometric formulation and the one based on quantum $\kappa$-deformations of the Poincar\'e algebra. Finally we re-derive the five-dimensional differential calculus using the geometric method, and use it to write down the deformed Klein-Gordon equation and to analyze its plane wave solutions.Comment: 26 pages, one formula (67) corrected; some remarks adde

Snyder's Quantized Space-time and De Sitter Special Relativity

There is a one-to-one correspondence between Snyder's model in de Sitter space of momenta and the \dS-invariant special relativity. This indicates that physics at the Planck length $\ell_P$ and the scale $R=3/\Lambda$ should be dual to each other and there is in-between gravity of local \dS-invariance characterized by a dimensionless coupling constant $g=\ell_P/R\sim 10^{-61}$.Comment: 8 page

Signals from the Noise: Image Stacking for Quasars in the FIRST Survey

We present a technique to explore the radio sky into the nanoJansky regime by employing image stacking using the FIRST survey. We first discuss the non-intuitive relationship between the mean and median values of a distribution that is dominated by noise, followed by an analysis of the systematic effects present in FIRST's 20cm VLA snapshot images. Image stacking allows us to recover the properties of source populations with fluxes a factor of 30 or more below the rms noise level. Mean estimates of radio flux density, luminosity, etc., are derivable for any source class having arcsecond positional accuracy. We use this technique to compute the mean radio properties for 41,295 quasars from the SDSS DR3 catalog. There is a tight correlation between optical and radio luminosity, with the radio luminosity increasing as the 0.85 power of optical luminosity. This implies declining radio-loudness with optical luminosity: the most luminous objects (M=-28.5) have average radio-to-optical ratios 3 times lower than the least luminous objects (M=-20). There is also a striking correlation between optical color and radio loudness: quasars that are either redder or bluer than the norm are brighter radio sources, with objects 0.8 magnitudes redder than the SDSS composite spectrum having radio-loudness ratios that are higher by a factor of 10. We explore the longstanding question of whether a radio-loud/radio-quiet dichotomy exists in quasars, finding that optical selection effects probably dominate the distribution function of radio loudness, which has at most a modest (~20%) inflection between the radio-loud and radio-quiet ends of the distribution. We also find, surprisingly, that broad absorption line quasars have higher mean radio flux densities, with the greatest disparity arising in the rare low-ionization BAL subclass.Comment: 17 pages, 19 figures, accepted by ApJ; corrected error in absolute magnitude

Scalar field propagation in the phi^4 kappa-Minkowski model

In this article we use the noncommutative (NC) kappa-Minkowski phi^4 model based on the kappa-deformed star product, ({*}_h). The action is modified by expanding up to linear order in the kappa-deformation parameter a, producing an effective model on commutative spacetime. For the computation of the tadpole diagram contributions to the scalar field propagation/self-energy, we anticipate that statistics on the kappa-Minkowski is specifically kappa-deformed. Thus our prescription in fact represents hybrid approach between standard quantum field theory (QFT) and NCQFT on the kappa-deformed Minkowski spacetime, resulting in a kappa-effective model. The propagation is analyzed in the framework of the two-point Green's function for low, intermediate, and for the Planckian propagation energies, respectively. Semiclassical/hybrid behavior of the first order quantum correction do show up due to the kappa-deformed momentum conservation law. For low energies, the dependence of the tadpole contribution on the deformation parameter a drops out completely, while for Planckian energies, it tends to a fixed finite value. The mass term of the scalar field is shifted and these shifts are very different at different propagation energies. At the Planckian energies we obtain the direction dependent kappa-modified dispersion relations. Thus our kappa-effective model for the massive scalar field shows a birefringence effect.Comment: 23 pages, 2 figures; To be published in JHEP. Minor typos corrected. Shorter version of the paper arXiv:1107.236

Kinematics of a relativistic particle with de Sitter momentum space

We discuss kinematical properties of a free relativistic particle with deformed phase space in which momentum space is given by (a submanifold of) de Sitter space. We provide a detailed derivation of the action, Hamiltonian structure and equations of motion for such free particle. We study the action of deformed relativistic symmetries on the phase space and derive explicit formulas for the action of the deformed Poincare' group. Finally we provide a discussion on parametrization of the particle worldlines stressing analogies and differences with ordinary relativistic kinematics.Comment: RevTeX, 12 pages, no figure

1-D Harmonic Oscillator in Snyder Space, the Classic and the Quantum

The 1-D dimension harmonic oscillator in Snyder space is investigated in its classical and quantum versions. The classical trajectory is obtained and the semiclassical quantization from the phase space trajectories is discussed. In the meanwhile, an effective cutoff to high frequencies is found. The quantum version is developed and an equivalent usual harmonic oscillator is obtained through an effective mass and an effective frequency introduced in the model. This modified parameters give us an also modified energy spectra.Comment: 8 pages, 2 figure

Linearly-realised Worldsheet Supersymmetry in pp-wave Background

We study the linearly-realised worldsheet supersymmetries in the ``massive'' type II light-cone actions for pp-wave backgrounds. The pp-waves have have 16+N_sup Killing spinors, comprising 16 ``standard'' Killing spinors that occur in any wave background, plus N_sup ``supernumerary'' Killing spinors (0\le N_sup \le 16) that occur only for special backgrounds. We show that only the supernumerary Killing spinors give rise to linearly-realised worldsheet supersymmetries after light-cone gauge fixing, while the 16 standard Killing spinors describe only non-linearly realised inhomogeneous symmetries. We also study the type II actions in the physical gauge, and we show that although in this case the actions are not free, there are now linearly-realised supersymmetries coming both from the standard and the supernumerary Killing spinors. In the physical gauge, there are no mass terms for any worldsheet degrees of freedom, so the masses appearing in the light-cone gauge may be viewed as gauge artefacts. We obtain type IIA and IIB supergravity solutions describing solitonic strings in pp-wave backgrounds, and show how these are related to the physical-gauge fundamental string actions. We study the supersymmetries of these solutions, and find examples with various numbers of Killing spinors, including total numbers that are odd.Comment: Latex, 35 page

Scalar field in the Bianchi I: Non commutative classical and Quantum Cosmology

Using the ADM formalism in the minisuperspace, we obtain the commutative and noncommutative exact classical solutions and exact wave function to the Wheeler-DeWitt equation with an arbitrary factor ordering, for the anisotropic Bianchi type I cosmological model, coupled to a scalar field, cosmological term and barotropic perfect fluid. We introduce noncommutative scale factors, considering that all minisuperspace variables $\rm q^i$ do not commute, so the symplectic structure was modified. In the classical regime, it is shown that the anisotropic parameter $\rm \beta_{\pm nc}$ and the field $\phi$, for some value in the $\lambda_{eff}$ cosmological term and noncommutative $\theta$ parameter, present a dynamical isotropization up to a critical cosmic time $t_{c}$; after this time, the effects of isotropization in the noncommutative minisuperspace seems to disappear. In the quantum regimen, the probability density presents a new structure that corresponds to the value of the noncommutativity parameter.Comment: 17 pages, 6 figures, Acepted in IJT