arXiv subjects
Publications and source records attributed to P. G. Castro.
In this work we investigate the $q$-deformation of the $so(4)$ dynamical symmetry of the hydrogen atom using the theory of the quantum group $su_q(2)$. We derive the energy spectrum in a physically consistent manner and find a degeneracy breaking as well as a smaller Hilbert space. We point out that using the deformed Casimir as was done before leads to inconsistencies in the physical interpretation of the theory.
Nonrelativistic quantum mechanics and conformal quantum mechanics are deformed through a Jordanian twist. The deformed space coordinates satisfy the Snyder noncommutativity. The resulting deformed Hamiltonians are pseudo-Hermitian Hamiltonians of the type discussed by Mostafazadeh. The quantization scheme makes use of the so-called "unfolded formalism" discussed in previous works. A Hopf algebra structure, compatible with the physical interpretation of the coproduct, is introduced for the Universal Enveloping Algebra of a suitably chosen dynamical Lie algebra (the Hamiltonian is contained among its generators). The multi-particle sector, uniquely determined by the deformed 2-particle Hamiltonian, is composed of bosonic particles.
Noncommutative oscillators are first-quantized through an abelian Drinfel'd twist deformation of a Hopf algebra and its action on a module. Several important and subtle issues making possible the quantization are solved. The spectrum of the single-particle Hamiltonians is computed. The multi-particle Hamiltonians are fixed, unambiguously, by the Hopf algebra coproduct. The symmetry under particle exchange is guaranteed. In d=2 dimensions the rotational invariance is preserved, while in d=3 the so(3) rotational invariance is broken down to an so(2) invariance.
We present a survey of ~800 square degrees of the galactic plane observed with the QUaD telescope. The primary product of the survey are maps of Stokes I, Q and U parameters at 100 and 150 GHz, with spatial resolution 5 and 3.5 arcminutes respectively. Two regions are covered, spanning approximately 245-295 and 315-5 degrees in galactic longitude l, and -4<b<+4 degrees in galactic latitude b. At 0.02 degree square pixel size, the median sensitivity is 74 and 107 kJy/sr at 100 GHz and 150 GHz respectively in I, and 98 and 120 kJy/sr for Q and U. In total intensity, we find an average spectral index of 2.35+/-0.01 (stat) +/- 0.02 (sys) for |b|<1 degree, indicative of emission components other than thermal dust. A comparison to published dust, synchrotron and free-free models implies an excess of emission in the 100 GHz QUaD band, while better agreement is found at 150 GHz. A smaller excess is observed when comparing QUaD 100 GHz data to WMAP 5-year W band; in this case the excess is likely due to the wider bandwidth of QUaD. Combining the QUaD and WMAP data, a two-component spectral fit to the inner galactic plane (|b|<1 degree) yields mean spectral indices of -0.32 +/- 0.03 and 2.84 +/- 0.03; the former is interpreted as a combination of the spectral indices of synchrotron, free-free and dust, while the second is attributed largely to the thermal dust continuum. In the same galactic latitude range, the polarization data show a high degree of alignment perpendicular to the expected galactic magnetic field direction, and exhibit mean polarization fraction 1.38+/-0.08 (stat) +/-0.1 (sys) % at 100 GHz and 1.70 +/- 0.06 (stat) +/- 0.1 (sys) % at 150GHz. We find agreement in polarization fraction between QUaD 100 GHz and WMAP W band, the latter giving 1.1 +/- 0.4 %.
We present a catalog of compact sources derived from the QUaD Galactic Plane Survey. The survey covers ~800 square degrees of the inner galaxy (|b|<4 degrees) in Stokes I, Q and U parameters at 100 and 150 GHz, with angular resolution 5 and 3.5 arcminutes. 505 unique sources are identified in I, of which 239 are spatially matched between frequency bands, with 50 (216) detected at 100 (150) GHz alone; 182 sources are identified as ultracompact HII (UCHII) regions. Approximating the distribution of total intensity source fluxes as a power-law, we find a slope of $γ_{S,100}=-1.8\pm0.4$ at 100 GHz, and $γ_{S,150}=-2.2\pm0.4$ at 150 GHz. Similarly, the power-law index of the source two-point angular correlation function is $γ_{θ,100}=-1.21\pm0.04$ and $γ_{θ,150}=-1.25\pm0.04$. The total intensity spectral index distribution peaks at $α_{I}\sim0.25$, indicating that dust emission is not the only source of radiation produced by these objects between 100 and 150 GHz; free-free radiation is likely significant in the 100 GHz band. Four sources are detected in polarized intensity P, of which three have matching counterparts in I. Three of the polarized sources lie close to the galactic center, Sagittarius A*, Sagittarius B2 and the Galactic Radio Arc, while the fourth is RCW 49, a bright HII region. An extended polarized source, undetected by the source extraction algorithm on account of its $\sim0.5^{\circ}$ size, is identified visually, and is an isolated example of large-scale polarized emission oriented distinctly from the bulk galactic dust polarization.
In this work we apply the Drinfel'd twist of Hopf algebras to the study of deformed quantum theories. We prove that, by carefully considering the role of the central extension, it is indeed possible to construct the universal enveloping algebra of the Heisenberg algebra and deform it by means of a Drinfel'd twist, which yields a noncommutative theory. Furthermore, we show that in the second-quantization formalism the Hopf algebra structure of the Heisenberg algebra (both undeformed and deformed) can be obtained from the Hopf algebra of the Schrodinger fields and oscillators, as long as they are taken to be odd generators of the osp(1|2) superalgebra. We study the deformation of the fermionic Heisenberg algebra and present an identification with the algebra of the one-dimensional N-extended supersymmetric quantum mechanics, possible for even N. A second construction for the deformation of the one-dimensional N-extended supersymmetric quantum mechanics is presented in the superspace representation, where the supersymmetry generators are realized in terms of operators belonging to the universal enveloping superalgebra of one bosonic and several fermionic oscillators. In both constructions we recover, in a more general setting, some Cliffordization results of the literature.
Centaurus (Cen) A represents one of the best candidates for an isolated, compact, highly polarized source that is bright at typical cosmic microwave background (CMB) experiment frequencies. We present measurements of the 4 degree by 2 degree region centered on Cen A with QUaD, a CMB polarimeter whose absolute polarization angle is known to 0.5 degrees. Simulations are performed to assess the effect of misestimation of the instrumental parameters on the final measurement and systematic errors due to the field's background structure and temporal variability from Cen A's nuclear region are determined. The total (Q, U) of the inner lobe region is (1.00 +/- 0.07 (stat.) +/- 0.04 (sys.), -1.72 +/- 0.06 +/- 0.05) Jy at 100 GHz and (0.80 +/- 0.06 +/- 0.06, -1.40 +/- 0.07 +/- 0.08) Jy at 150 GHz, leading to polarization angles and total errors of -30.0 +/- 1.1 degrees and -29.1 +/- 1.7 degrees. These measurements will allow the use of Cen A as a polarized calibration source for future millimeter experiments.
We evaluate the contribution of cosmic microwave background (CMB) polarization spectra to cosmological parameter constraints. We produce cosmological parameters using high-quality CMB polarization data from the ground-based QUaD experiment and demonstrate for the majority of parameters that there is significant improvement on the constraints obtained from satellite CMB polarization data. We split a multi-experiment CMB dataset into temperature and polarization subsets and show that the best-fit confidence regions for the LCDM 6-parameter cosmological model are consistent with each other, and that polarization data reduces the confidence regions on all parameters. We provide the best limits on parameters from QUaD EE/BB polarization data and we find best-fit parameters from the multi-experiment CMB dataset using the optimal pivot scale of k_p=0.013 Mpc-1 to be {omch2, ombh2, H_0, A_s, n_s, tau}= {0.113, 0.0224, 70.6, 2.29 times 10^-9, 0.960, 0.086}.
The N-extended Supersymmetric Quantum Mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its Universal Enveloping Superalgebra. Two constructions are possible. For even N one can identify the 1D N-extended superalgebra with the fermionic Heisenberg algebra. Alternatively, supersymmetry generators can be realized as operators belonging to the Universal Enveloping Superalgebra of one bosonic and several fermionic oscillators. The deformed system is described in terms of twisted operators satisfying twist-deformed (anti)commutators. The main differences between an abelian twist defined in terms of fermionic operators and an abelian twist defined in terms of bosonic operators are discussed.
We present an improved analysis of the final dataset from the QUaD experiment. Using an improved technique to remove ground contamination, we double the effective sky area and hence increase the precision of our CMB power spectrum measurements by ~30% versus that previously reported. In addition, we have improved our modeling of the instrument beams and have reduced our absolute calibration uncertainty from 5% to 3.5% in temperature. The robustness of our results is confirmed through extensive jackknife tests and by way of the agreement we find between our two fully independent analysis pipelines. For the standard 6-parameter LCDM model, the addition of QUaD data marginally improves the constraints on a number of cosmological parameters over those obtained from the WMAP experiment alone. The impact of QUaD data is significantly greater for a model extended to include either a running in the scalar spectral index, or a possible tensor component, or both. Adding both the QUaD data and the results from the ACBAR experiment, the uncertainty in the spectral index running is reduced by ~25% compared to WMAP alone, while the upper limit on the tensor-to-scalar ratio is reduced from r < 0.48 to r < 0.33 (95% c.l). This is the strongest limit on tensors to date from the CMB alone. We also use our polarization measurements to place constraints on parity violating interactions to the surface of last scattering, constraining the energy scale of Lorentz violating interactions to < 1.5 x 10^{-43} GeV (68% c.l.). Finally, we place a robust upper limit on the strength of the lensing B-mode signal. Assuming a single flat band power between l = 200 and l = 2000, we constrain the amplitude of B-modes to be < 0.57 micro-K^2 (95% c.l.).
We present measurements of the cosmic microwave background (CMB) radiation temperature anisotropy in the multipole range 2000<ell<3000 from the QUaD telescope's second and third observing seasons. After masking the brightest point sources our results are consistent with the primary LCDM expectation alone. We estimate the contribution of residual (un-masked) radio point sources using a model calibrated to our own bright source observations, and a full simulation of the source finding and masking procedure. Including this contribution slightly improves the chi^2. We also fit a standard SZ template to the bandpowers and see no strong evidence of an SZ contribution, which is as expected for sigma_8 approx 0.8.
We describe the QUaD experiment, a millimeter-wavelength polarimeter designed to observe the Cosmic Microwave Background (CMB) from a site at the South Pole. The experiment comprises a 2.64 m Cassegrain telescope equipped with a cryogenically cooled receiver containing an array of 62 polarization-sensitive bolometers. The focal plane contains pixels at two different frequency bands, 100 GHz and 150 GHz, with angular resolutions of 5 arcmin and 3.5 arcmin, respectively. The high angular resolution allows observation of CMB temperature and polarization anisotropies over a wide range of scales. The instrument commenced operation in early 2005 and collected science data during three successive Austral winter seasons of observation.
We constrain parity-violating interactions to the surface of last scattering using spectra from the QUaD experiment's second and third seasons of observations by searching for a possible systematic rotation of the polarization directions of CMB photons. We measure the rotation angle due to such a possible "cosmological birefringence" to be 0.55 deg. +/- 0.82 deg. (random) +/- 0.5 deg. (systematic) using QUaD's 100 and 150 GHz TB and EB spectra over the multipole range 200 < l < 2000, consistent with null, and constrain Lorentz violating interactions to < 2^-43 GeV (68% confidence limit). This is the best constraint to date on electrodynamic parity violation on cosmological scales.
We report results from the second and third seasons of observation with the QUaD experiment. Angular power spectra of the Cosmic Microwave Background are derived for both temperature and polarization at both 100 GHz and 150 GHz, and as cross frequency spectra. All spectra are subjected to an extensive set of jackknife tests to probe for possible systematic contamination. For the implemented data cuts and processing technique such contamination is undetectable. We analyze the difference map formed between the 100 and 150 GHz bands and find no evidence of foreground contamination in polarization. The spectra are then combined to form a single set of results which are shown to be consistent with the prevailing LCDM model. The sensitivity of the polarization results is considerably better than that of any previous experiment -- for the first time multiple acoustic peaks are detected in the E-mode power spectrum at high significance.
In this paper we present a parameter estimation analysis of the polarization and temperature power spectra from the second and third season of observations with the QUaD experiment. QUaD has for the first time detected multiple acoustic peaks in the E-mode polarization spectrum with high significance. Although QUaD-only parameter constraints are not competitive with previous results for the standard 6-parameter LCDM cosmology, they do allow meaningful polarization-only parameter analyses for the first time. In a standard 6-parameter LCDM analysis we find the QUaD TT power spectrum to be in good agreement with previous results. However, the QUaD polarization data shows some tension with LCDM. The origin of this 1 to 2 sigma tension remains unclear, and may point to new physics, residual systematics or simple random chance. We also combine QUaD with the five-year WMAP data set and the SDSS Luminous Red Galaxies 4th data release power spectrum, and extend our analysis to constrain individual isocurvature mode fractions, constraining cold dark matter density, alpha(cdmi)<0.11 (95 % CL), neutrino density, alpha(ndi)<0.26 (95 % CL), and neutrino velocity, alpha(nvi)<0.23 (95 % CL), modes. Our analysis sets a benchmark for future polarization experiments.
By correctly identifying the role of central extension in the centrally extended Heisenberg algebra h, we show that it is indeed possible to construct a Hopf algebraic structure on the corresponding enveloping algebra U(h) and eventually deform it through Drinfeld twist. This Hopf algebraic structure and its deformed version U^F(h) are shown to be induced from a more fundamental Hopf algebra obtained from the Schroedinger field/oscillator algebra and its deformed version, provided that the fields/oscillators are regarded as odd-elements of the super-algebra osp(1|2n). We also discuss the possible implications in the context of quantum statistics.
QUaD is a bolometric CMB polarimeter sited at the South Pole, operating at frequencies of 100 and 150 GHz. In this paper we report preliminary results from the first season of operation (austral winter 2005). All six CMB power spectra are presented derived as cross spectra between the 100 and 150 GHz maps using 67 days of observation in a low foreground region of approximately 60 square degrees. This data is a small fraction of the data acquired to date. The measured spectra are consistent with the LCDM cosmological model. We perform jackknife tests which indicate that the observed signal has negligible contamination from instrumental systematics. In addition by using a frequency jackknife we find no evidence for foreground contamination.
We present a search for non-Gaussianity in the WMAP first-year data using the two-point correlation function of maxima and minima in the temperature map. We find evidence for non-Gaussianity on large scales, whose origin appears to be associated with unsubstracted foregrounds, but which is not entirely clear. The signal appears to be associated most strongly with cold spots, and is more pronounced in the Southern galactic hemisphere. Removal of the region of sky near the galactic plane, or filtering out large-scale modes removes the signal. Analysis of individual frequency maps shows strongest signal in the 41GHz Q band. A study of difference maps tests the hypothesis that the non-Gaussianity is due to residual foregrounds and noise, but shows no significant detection. We suggest that the detection is due to large-scale residual foregrounds affecting more than one frequency band, but a primordial contribution from the Cosmic Microwave Background cannot be excluded.