Noise Kernel and Stress Energy Bi-Tensor of Quantum Fields in Hot Flat Space and Gaussian Approximation in the Optical Schwarzschild Metric

Continuing our investigation of the regularization of the noise kernel in curved spacetimes [N. G. Phillips and B. L. Hu, Phys. Rev. D {\bf 63}, 104001 (2001)] we adopt the modified point separation scheme for the class of optical spacetimes using the Gaussian approximation for the Green functions a la Bekenstein-Parker-Page. In the first example we derive the regularized noise kernel for a thermal field in flat space. It is useful for black hole nucleation considerations. In the second example of an optical Schwarzschild spacetime we obtain a finite expression for the noise kernel at the horizon and recover the hot flat space result at infinity. Knowledge of the noise kernel is essential for studying issues related to black hole horizon fluctuations and Hawking radiation backreaction. We show that the Gaussian approximated Green function which works surprisingly well for the stress tensor at the Schwarzschild horizon produces significant error in the noise kernel there. We identify the failure as occurring at the fourth covariant derivative order.Comment: 21 pages, RevTeX

Universal Drinfeld-Sokolov Reduction and Matrices of Complex Size

We construct affinization of the algebra $gl_{\lambda}$ of ``complex size'' matrices, that contains the algebras $\hat{gl_n}$ for integral values of the parameter. The Drinfeld--Sokolov Hamiltonian reduction of the algebra $\hat{gl_{\lambda}}$ results in the quadratic Gelfand--Dickey structure on the Poisson--Lie group of all pseudodifferential operators of fractional order. This construction is extended to the simultaneous deformation of orthogonal and simplectic algebras that produces self-adjoint operators, and it has a counterpart for the Toda lattices with fractional number of particles.Comment: 29 pages, no figure

Phase Transition in Conformally Induced Gravity with Torsion

We have considered the quantum behavior of a conformally induced gravity in the minimal Riemann-Cartan space. The regularized one-loop effective potential considering the quantum fluctuations of the dilaton and the torsion fields in the Coleman-Weinberg sector gives a sensible phase transition for an inflationary phase in De Sitter space. For this effective potential, we have analyzed the semi-classical equation of motion of the dilaton field in the slow-rolling regime.Comment: 7pages, no figur

Chiral Symmetry and Diffractive Neutral Pion Photo- and Electroproduction

We show that diffractive production of a single neutral pion in photon-induced reactions at high energy is dynamically suppressed due to the approximate chiral symmetry of QCD. These reactions have been proposed as a test of the odderon exchange mechanism. We show that the odderon contribution to the amplitude for such reactions vanishes exactly in the chiral limit. This result is obtained in a nonperturbative framework and by using PCAC relations between the amplitudes for neutral pion and axial vector current production.Comment: 22 pages, 7 figure

The intrinsic charm contribution to the proton spin

The charm quark contribution to the first moment of $g_1(x,Q^2)$ is calculated using a heavy mass expansion of the divergence of the singlet axial current. It is shown to be small.Comment: LATEX, 6 page

Axial anomaly and the precise value of the π0→2γ\pi^0 \to 2 \gamma decay width

The anomaly in the vacuum expectation value of the product of axial and two vector currents (AVV) in QCD is investigated. The goal is to determine from its value the $\pi^0 \to 2 \gamma$ decay width with high precision. The sum rule for AVV formfactor is studied. The difference $f_{\pi^0} - f_{\pi^+}$ caused by strong interaction is calculated and appears to be small. The $\pi^0 - \eta$ mixing is accounted. The $\pi^0 \to 2 \gamma$ decay width determined theoretically from the axial anomaly is found to be $\Gamma(\pi^0 \to 2 \gamma) = 7.93 eV$ with an error $\sim 1.5$. The measurement of the $\pi^0 \to 2 \gamma$ decay width at the same level of accuracy would allow one to achieve a high precision test of QCD.Comment: 8 pages, few misprints are correcte

Poisson-Lie group of pseudodifferential symbols

We introduce a Lie bialgebra structure on the central extension of the Lie algebra of differential operators on the line and the circle (with scalar or matrix coefficients). This defines a Poisson--Lie structure on the dual group of pseudodifferential symbols of an arbitrary real (or complex) order. We show that the usual (second) Benney, KdV (or GL_n--Adler--Gelfand--Dickey) and KP Poisson structures are naturally realized as restrictions of this Poisson structure to submanifolds of this ``universal'' Poisson--Lie group. Moreover, the reduced (=SL_n) versions of these manifolds (W_n-algebras in physical terminology) can be viewed as subspaces of the quotient (or Poisson reduction) of this Poisson--Lie group by the dressing action of the group of functions. Finally, we define an infinite set of functions in involution on the Poisson--Lie group that give the standard families of Hamiltonians when restricted to the submanifolds mentioned above. The Poisson structure and Hamiltonians on the whole group interpolate between the Poisson structures and Hamiltonians of Benney, KP and KdV flows. We also discuss the geometrical meaning of W_\infty as a limit of Poisson algebras W_\epsilon as \epsilon goes to 0.Comment: 64 pages, no figure

Tests of the Equivalence Principle with Neutral Kaons

We test the Principle of Equivalence for particles and antiparticles, using CPLEAR data on tagged K0 and K0bar decays into pi^+ pi^-. For the first time, we search for possible annual, monthly and diurnal modulations of the observables |eta_{+-}| and phi_{+-}, that could be correlated with variations in astrophysical potentials. Within the accuracy of CPLEAR, the measured values of |eta_{+-}| and phi_{+-} are found not to be correlated with changes of the gravitational potential. We analyze data assuming effective scalar, vector and tensor interactions, and we conclude that the Principle of Equivalence between particles and antiparticles holds to a level of 6.5, 4.3 and 1.8 x 10^{-9}, respectively, for scalar, vector and tensor potentials originating from the Sun with a range much greater than the distance Earth-Sun. We also study energy-dependent effects that might arise from vector or tensor interactions. Finally, we compile upper limits on the gravitational coupling difference between K0 and K0bar as a function of the scalar, vector and tensor interaction range.Comment: 15 pages latex 2e, five figures, one style file (cernart.csl) incorporate

Test of CPT Symmetry and Quantum Mechanics with Experimental data from CPLEAR

We use fits to recent published CPLEAR data on neutral kaon decays to $\pi^+\pi^-$ and $\pi e\nu$ to constrain the CPT--violation parameters appearing in a formulation of the neutral kaon system as an open quantum-mechanical system. The obtained upper limits of the CPT--violation parameters are approaching the range suggested by certain ideas concerning quantum gravity.Comment: 9 pages of uuencoded postscript (includes 3 figures

Spectral quark model and low-energy hadron phenomenology

We propose a spectral quark model which can be applied to low energy hadronic physics. The approach is based on a generalization of the Lehmann representation of the quark propagator. We work at the one-quark-loop level. Electromagnetic and chiral invariance are ensured with help of the gauge technique which provides particular solutions to the Ward-Takahashi identities. General conditions on the quark spectral function follow from natural physical requirements. In particular, the function is normalized, its all positive moments must vanish, while the physical observables depend on negative moments and the so-called log-moments. As a consequence, the model is made finite, dispersion relations hold, chiral anomalies are preserved, and the twist expansion is free from logarithmic scaling violations, as requested of a low-energy model. We study a variety of processes and show that the framework is very simple and practical. Finally, incorporating the idea of vector-meson dominance, we present an explicit construction of the quark spectral function which satisfies all the requirements. The corresponding momentum representation of the resulting quark propagator exhibits only cuts on the physical axis, with no poles present anywhere in the complex momentum space. The momentum-dependent quark mass compares very well to recent lattice calculations. A large number of predictions and relations can be deduced from our approach for such quantities as the pion light-cone wave function, non-local quark condensate, pion transition form factor, pion valence parton distribution function, etc.Comment: revtex, 24 pages, 3 figure