Lorentz invariance violation and charge (non--)conservation: A general theoretical frame for extensions of the Maxwell equations

All quantum gravity approaches lead to small modifications in the standard laws of physics which lead to violations of Lorentz invariance. One particular example is the extended standard model (SME). Here, a general phenomenological approach for extensions of the Maxwell equations is presented which turns out to be more general than the SME and which covers charge non--conservation (CNC), too. The new Lorentz invariance violating terms cannot be probed by optical experiments but need, instead, the exploration of the electromagnetic field created by a point charge or a magnetic dipole. Some scalar--tensor theories and higher dimensional brane theories predict CNC in four dimensions and some models violating Special Relativity have been shown to be connected with CNC and its relation to the Einstein Equivalence Principle has been discussed. Due to this upcoming interest, the experimental status of electric charge conservation is reviewed. Up to now there seem to exist no unique tests of charge conservation. CNC is related to the precession of polarization, to a modification of the $1/r$--Coulomb potential, and to a time-dependence of the fine structure constant. This gives the opportunity to describe a dedicated search for CNC.Comment: To appear in Physical Review

Learning to Control in Metric Space with Optimal Regret

We study online reinforcement learning for finite-horizon deterministic control systems with {\it arbitrary} state and action spaces. Suppose that the transition dynamics and reward function is unknown, but the state and action space is endowed with a metric that characterizes the proximity between different states and actions. We provide a surprisingly simple upper-confidence reinforcement learning algorithm that uses a function approximation oracle to estimate optimistic Q functions from experiences. We show that the regret of the algorithm after $K$ episodes is $O(HL(KH)^{\frac{d-1}{d}})$ where $L$ is a smoothness parameter, and $d$ is the doubling dimension of the state-action space with respect to the given metric. We also establish a near-matching regret lower bound. The proposed method can be adapted to work for more structured transition systems, including the finite-state case and the case where value functions are linear combinations of features, where the method also achieve the optimal regret

Direct Detection of the Primordial Inflationary Gravitational Waves

Inflationary cosmology is successful in explaining a number of outstanding cosmological issues including the flatness, the horizon and the relic issues. More spectacular is the experimental confirmation of the structure as arose from the inflationary quantum fluctuations. However, the physics in the inflationary era is unclear. Polarization observations of Cosmic Microwave Background (CMB) missions may detect the tensor mode effects of inflationary gravitational waves (GWs) and give an energy scale of inflation. To probe the inflationary physics, direct observation of gravitational waves generated in the inflationary era is needed. In this essay, we advocate that the direct observation of these GWs with sensitivity Omega-gw down to 10**(-23) is possible using present projected technology development if foreground could be separated.Comment: 6 pages, 1 figure, received an honorable mention in the 2009 Essay Competition of the Gravity Research Foundatio

Largest eigenvalue distribution in the double scaling limit of matrix models: A Coulomb fluid approach

Using thermodynamic arguments we find that the probability that there are no eigenvalues in the interval (-s,\infty) in the double scaling limit of Hermitean matrix models is O(exp(-s^{2m+1})) as s\to+\infty.Here m=1,2,3.. determine the m^{th} multi-critical point of the level density:\sigma(x)\sim b[1-(x/b)^2]^{m-1/2} and b^2\sim N.Furthermore,the size of the transition zone where the eigenvalue density becomes vanishingly small at the tail of the spectrum is \sim N^{(m-3/2)/(2m+1)} in agreement with earlier work based on the string equation.Comment: 10 pages, no figures, to appear in J.Phys. A Lett. 199

Q & A Experiment to Search for Vacuum Dichroism, Pseudoscalar-Photon Interaction and Millicharged Fermions

A number of experiments are underway to detect vacuum birefringence and dichroism -- PVLAS, Q & A, and BMV. Recently, PVLAS experiment has observed optical rotation in vacuum by a magnetic field (vacuum dichroism). Theoretical interpretations of this result include a possible pseudoscalar-photon interaction and the existence of millicharged fermions. Here, we report the progress and first results of Q & A (QED [quantum electrodynamics] and Axion) experiment proposed and started in 1994. A 3.5-m high-finesse (around 30,000) Fabry-Perot prototype detector extendable to 7-m has been built and tested. We use X-pendulums and automatic control schemes developed by the gravitational-wave detection community for mirror suspension and cavity control. To polarize the vacuum, we use a 2.3-T dipole permanent magnet, with 27-mm-diameter clear borehole and 0.6-m field length,. In the experiment, the magnet is rotated at 5-10 rev/s to generate time-dependent polarization signal with twice the rotation frequency. Our ellipsometer/polarization-rotation-detection-system is formed by a pair of Glan-Taylor type polarizing prisms with extinction ratio lower than 10-8 together with a polarization modulating Faraday Cell with/without a quarter wave plate. We made an independent calibration of our apparatus by performing a measurement of gaseous Cotton-Mouton effect of nitrogen. We present our first experimental results and give a brief discussion of our experimental limit on pseudo-scalar-photon interaction and millicharged fermions.Comment: 21 pages, 13 figures, submitted to Modern Physics Letter

λϕ4\lambda\phi^4 model and Higgs mass in standard model calculated by Gaussian effective potential approach with a new regularization-renormalization method

Basing on new regularization-renormalization method, the $\lambda\phi^4$ model used in standard model is studied both perturbatively and nonperturbatively (by Gaussian effective potential). The invariant property of two mass scales is stressed and the existence of a (Landau) pole is emphasized. Then after coupling with the SU(2)$\times$U(1) gauge fields, the Higgs mass in standard model (SM) can be calculated as $m_H\approx$138GeV. The critical temperature ($T_c$) for restoration of symmetry of Higgs field, the critical energy scale ($\mu_c$, the maximum energy scale under which the lower excitation sector of the GEP is valid) and the maximum energy scale ($\mu_{max}$, at which the symmetry of the Higgs field is restored) in the standard model are $T_c\approx$476 GeV, $\mu_c\approx 0.547\times 10^{15}$GeV and $\mu_{\max}\approx 0.873 \times 10^{15}$ GeVv respectively.Comment: 12 pages, LaTex, no figur

Suspension of the fiber mode-cleaner launcher and measurement of the high extinction-ratio (10^{-9}) ellipsometer for the Q & A experiment

The Q & A experiment, first proposed and started in 1994, provides a feasible way of exploring the quantum vacuum through the detection of vacuum birefringence effect generated by QED loop diagram and the detection of the polarization rotation effect generated by photon-interacting (pseudo-)scalar particles. Three main parts of the experiment are: (1) Optics System (including associated Electronic System) based on a suspended 3.5-m high finesse Fabry-Perot cavity, (2) Ellipsometer using ultra-high extinction-ratio polarizer and analyzer, and (3) Magnetic Field Modulation System for generating the birefringence and the polarization rotation effect. In 2002, the Q & A experiment achieved the Phase I sensitivity goal. During Phase II, we set (i) to improve the control system of the cavity mirrors for suppressing the relative motion noise, (ii) to enhance the birefringence signal by setting-up a 60-cm long 2.3 T transverse permanent magnet rotatable to 10 rev/s, (iii) to reduce geometrical noise by inserting a polarization-maintaining optical fiber (PM fiber) as a mode cleaner, and (iv) to use ultra-high extinction-ratio (10^{-9}) polarizer and analyzer for ellipsometry. Here we report on (iii) & (iv); specifically, we present the properties of the PM-fiber mode-cleaner, the transfer function of its suspension system, and the result of our measurement of high extinction-ratio polarizer and analyzer.Comment: 8 pages, 6 figures, presented in the 6th Edoardo Amaldi Conference on Gravitational Waves, Okinawa, Japan, June 2005, and accepted by "Journal of Physics: Conference Series". Modifications from version 2 were made based on the referees' comments on figures. Ref. [31] were update