Massless Scalar Field Propagator in a Quantized Space-Time

We consider in detail the analytic behaviour of the non-interacting massless scalar field two-point function in H.S. Snyder's discretized non-commuting spacetime. The propagator we find is purely real on the Euclidean side of the complex $p^2$ plane and goes like $1/p^2$ as $p^2\to 0$ from either the Euclidean or Minkowski side. The real part of the propagator goes smoothly to zero as $p^2$ increases to the discretization scale $1/a^2$ and remains zero for $p^2>1/a^2$. This behaviour is consistent with the termination of single-particle propagation on the ultraviolet side of the discretization scale. The imaginary part of the propagator, consistent with a multiparticle-production branch discontinuity, is finite and continuous on the Minkowski side, slowly falling to zero when $1/a^2<p^2<\infty$. Finally, we argue that the spectral function for the multiparticle states appears to saturate as $p^2$ probes just beyond the $1/a^2$ discretization scale. We speculate on the cosmological consequences of such a spectral function.Comment: 6 pages, 1 eps figure embedded in manuscrip

Contracted Representation of Yang's Space-Time Algebra and Buniy-Hsu-Zee's Discrete Space-Time

Motivated by the recent proposition by Buniy, Hsu and Zee with respect to discrete space-time and finite spatial degrees of freedom of our physical world with a short- and a long-distance scales, $l_P$ and $L,$ we reconsider the Lorentz-covariant Yang's quantized space-time algebra (YSTA), which is intrinsically equipped with such two kinds of scale parameters, $\lambda$ and $R$. In accordance with their proposition, we find the so-called contracted representation of YSTA with finite spatial degrees of freedom associated with the ratio $R/\lambda$, which gives a possibility of the divergence-free noncommutative field theory on YSTA. The canonical commutation relations familiar in the ordinary quantum mechanics appear as the cooperative Inonu-Wigner's contraction limit of YSTA, $\lambda \to 0$ and $R \to \infty.

Sine-Gordon Soliton on a Cnoidal Wave Background

The method of Darboux transformation, which is applied on cnoidal wave solutions of the sine-Gordon equation, gives solitons moving on a cnoidal wave background. Interesting characteristics of the solution, i.e., the velocity of solitons and the shift of crests of cnoidal waves along a soliton, are calculated. Solutions are classified into three types (Type-1A, Type-1B, Type-2) according to their apparent distinct properties.Comment: 11 pages, 5 figures, Contents change

A new approach to the analysis of a noncommutative Chern-Simons theory

A novel approach to the analysis of a noncommutative Chern--Simons gauge theory with matter coupled in the adjoint representation has been discussed. The analysis is based on a recently proposed closed form Seiberg--Witten map which is exact in the noncommutative parameter.Comment: 9 pages latex, some new results added. To be published in Modern Physics Letters

Photon deflection by a Coulomb field in noncommutative QED

In noncommutative QED photons present self-interactions in the form of triple and quartic interactions. The triple interaction implies that, even though the photon is electrically neutral, it will deflect when in the presence of an electromagnetic field. If detected, such deflection would be an undoubted signal of noncommutative space-time. In this work we derive the general expression for the deflection of a photon by any electromagnetic field. As an application we consider the case of the deflection of a photon by an external static Coulomb field.Comment: 07 pages, some typos corrected, accepted for publication in JP

Cortical alpha activity predicts the confidence in an impending action

When we make a decision, we experience a degree of confidence that our choice may lead to a desirable outcome. Recent studies in animals have probed the subjective aspects of the choice confidence using confidence-reporting tasks. These studies showed that estimates of the choice confidence substantially modulate neural activity in multiple regions of the brain. Building on these findings, we investigated the neural representation of the confidence in a choice in humans who explicitly reported the confidence in their choice. Subjects performed a perceptual decision task in which they decided between choosing a button press or a saccade while we recorded EEG activity. Following each choice, subjects indicated whether they were sure or unsure about the choice. We found that alpha activity strongly encodes a subject's confidence level in a forthcoming button press choice. The neural effect of the subjects' confidence was independent of the reaction time and independent of the sensory input modeled as a decision variable. Furthermore, the effect is not due to a general cognitive state, such as reward expectation, because the effect was specifically observed during button press choices and not during saccade choices. The neural effect of the confidence in the ensuing button press choice was strong enough that we could predict, from independent single trial neural signals, whether a subject was going to be sure or unsure of an ensuing button press choice. In sum, alpha activity in human cortex provides a window into the commitment to make a hand movement

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

Noncommutative D-Brane in Non-Constant NS-NS B Field Background

We show that when the field strength H of the NS-NS B field does not vanish, the coordinates X and momenta P of an open string endpoints satisfy a set of mixed commutation relations among themselves. Identifying X and P with the coordinates and derivatives of the D-brane world volume, we find a new type of noncommutative spaces which is very different from those associated with a constant B field background.Comment: 11 pages, Latex, minor modification

Hydrogen Isocyanide in Comet 73P/Schwassmann-Wachmann (Fragment B)

We present a sensitive 3-sigma upper limit of 1.1% for the HNC/HCN abundance ratio in comet 73P/Schwassmann-Wachmann (Fragment B), obtained on May 10-11, 2006 using Caltech Submillimeter Observatory (CSO). This limit is a factor of ~7 lower than the values measured previously in moderately active comets at 1 AU from the Sun. Comet 73P/Schwassmann-Wachmann was depleted in most volatile species, except of HCN. The low HNC/HCN ratio thus argues against HNC production from polymers produced from HCN. However, thermal degradation of macromolecules, or polymers, produced from ammonia and carbon compounds, such as acetylene, methane, or ethane appears a plausible explanation for the observed variations of the HNC/HCN ratio in moderately active comets, including the very low ratio in comet 73P/Schwassmann-Wachmann reported here. Similar polymers have been invoked previously to explain anomalous 14N/15N ratios measured in cometary CN.Comment: 6 pages, 5 figures, 2 table