Noise Kernel in Stochastic Gravity and Stress Energy Bi-Tensor of Quantum Fields in Curved Spacetimes

The noise kernel is the vacuum expectation value of the (operator-valued) stress-energy bi-tensor which describes the fluctuations of a quantum field in curved spacetimes. It plays the role in stochastic semiclassical gravity based on the Einstein-Langevin equation similar to the expectation value of the stress-energy tensor in semiclassical gravity based on the semiclassical Einstein equation. According to the stochastic gravity program, this two point function (and by extension the higher order correlations in a hierarchy) of the stress energy tensor possesses precious statistical mechanical information of quantum fields in curved spacetime and, by the self-consistency required of Einstein's equation, provides a probe into the coherence properties of the gravity sector (as measured by the higher order correlation functions of gravitons) and the quantum nature of spacetime. It reflects the low and medium energy (referring to Planck energy as high energy) behavior of any viable theory of quantum gravity, including string theory. It is also useful for calculating quantum fluctuations of fields in modern theories of structure formation and for backreaction problems in cosmological and black holes spacetimes. We discuss the properties of this bi-tensor with the method of point-separation, and derive a regularized expression of the noise-kernel for a scalar field in general curved spacetimes. One collorary of our finding is that for a massless conformal field the trace of the noise kernel identically vanishes. We outline how the general framework and results derived here can be used for the calculation of noise kernels for Robertson-Walker and Schwarzschild spacetimes.Comment: 22 Pages, RevTeX; version accepted for publication in PR

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

Testing Anomalous Higgs Couplings in Triple Photon Production at the Tevatron Collider

We derive bounds on Higgs and gauge--boson anomalous interactions using the CDF data for the process $p \bar{p} \to \gamma\gamma\gamma + X$. We use a linearly realized $SU_L(2) \times U_Y(1)$ invariant effective Lagrangian to describe the bosonic sector of the Standard Model, keeping the fermionic couplings unchanged. All dimension--six operators that lead to anomalous Higgs interactions involving $\gamma$ and $Z$ are considered. We also show the sensitivity that can be achieved for these couplings at Fermilab Tevatron upgrades.Comment: 13 pages, RevTeX, 2 figures included using epsfi

Four Poynting Theorems

The Poynting vector is an invaluable tool for analysing electromagnetic problems. However, even a rigorous stress-energy tensor approach can still leave us with the question: is it best defined as \Vec{E} \cross \Vec{H} or as \Vec{D} \cross \Vec{B}? Typical electromagnetic treatments provide yet another perspective: they regard \Vec{E} \cross \Vec{B} as the appropriate definition, because \Vec{E} and \Vec{B} are taken to be the fundamental electromagnetic fields. The astute reader will even notice the fourth possible combination of fields: i.e. \Vec{D} \cross \Vec{H}. Faced with this diverse selection, we have decided to treat each possible flux vector on its merits, deriving its associated energy continuity equation but applying minimal restrictions to the allowed host media. We then discuss each form, and how it represents the response of the medium. Finally, we derive a propagation equation for each flux vector using a directional fields approach; a useful result which enables further interpretation of each flux and its interaction with the medium.Comment: 8 pages. Updated slightly from EJP versio

Ianus: an Adpative FPGA Computer

Dedicated machines designed for specific computational algorithms can outperform conventional computers by several orders of magnitude. In this note we describe {\it Ianus}, a new generation FPGA based machine and its basic features: hardware integration and wide reprogrammability. Our goal is to build a machine that can fully exploit the performance potential of new generation FPGA devices. We also plan a software platform which simplifies its programming, in order to extend its intended range of application to a wide class of interesting and computationally demanding problems. The decision to develop a dedicated processor is a complex one, involving careful assessment of its performance lead, during its expected lifetime, over traditional computers, taking into account their performance increase, as predicted by Moore's law. We discuss this point in detail

Linear Response, Validity of Semi-Classical Gravity, and the Stability of Flat Space

A quantitative test for the validity of the semi-classical approximation in gravity is given. The criterion proposed is that solutions to the semi-classical Einstein equations should be stable to linearized perturbations, in the sense that no gauge invariant perturbation should become unbounded in time. A self-consistent linear response analysis of these perturbations, based upon an invariant effective action principle, necessarily involves metric fluctuations about the mean semi-classical geometry, and brings in the two-point correlation function of the quantum energy-momentum tensor in a natural way. This linear response equation contains no state dependent divergences and requires no new renormalization counterterms beyond those required in the leading order semi-classical approximation. The general linear response criterion is applied to the specific example of a scalar field with arbitrary mass and curvature coupling in the vacuum state of Minkowski spacetime. The spectral representation of the vacuum polarization function is computed in n dimensional Minkowski spacetime, and used to show that the flat space solution to the semi-classical Einstein equations for n=4 is stable to all perturbations on distance scales much larger than the Planck length.Comment: 22 pages: This is a significantly expanded version of gr-qc/0204083, with two additional sections and two new appendices giving a complete, explicit example of the semi-classical stability criterion proposed in the previous pape

Quantum correlation functions and the classical limit

We study the transition from the full quantum mechanical description of physical systems to an approximate classical stochastic one. Our main tool is the identification of the closed-time-path (CTP) generating functional of Schwinger and Keldysh with the decoherence functional of the consistent histories approach. Given a degree of coarse-graining in which interferences are negligible, we can explicitly write a generating functional for the effective stochastic process in terms of the CTP generating functional. This construction gives particularly simple results for Gaussian processes. The formalism is applied to simple quantum systems, quantum Brownian motion, quantum fields in curved spacetime. Perturbation theory is also explained. We conclude with a discussion on the problem of backreaction of quantum fields in spacetime geometry.Comment: 30 pages, latex; minor changes, added some explanations and refeence

Non-equilibrium dynamics of a thermal plasma in a gravitational field

We introduce functional methods to study the non-equilibrium dynamics of a quantum massless scalar field at finite temperature in a gravitational field. We calculate the Close Time Path (CTP) effective action and, using its formal equivalence with the influence functional, derive the noise and dissipation kernels of the quantum open system in terms of quantities in thermodynamical equilibrium. Using this fact, we formally prove the existence of a Fluctuation-Dissipation Relation (FDR) at all temperatures between the quantum fluctuations of the plasma in thermal equilibrium and the energy dissipated by the external gravitational field. What is new is the identification of a stochastic source (noise) term arising from the quantum and thermal fluctuations in the plasma field, and the derivation of a Langevin-type equation which describes the non-equilibrium dynamics of the gravitational field influenced by the plasma. The back reaction of the plasma on the gravitational field is embodied in the FDR. From the CTP effective action the contribution of the quantum scalar field to the thermal graviton polarization tensor can also be derived and it is shown to agree with other techniques, most notably, Linear Response Theory (LRT). We show the connection between the LRT, which is applicable for near-equilibrium conditions and the functional methods used in this work which are useful for fully non-equilibrium conditions.Comment: Final version published in Phys. Rev.

Monte Carlo studies of the ordering of the one-dimensional Heisenberg spin glass with long-range power-law interactions

The nature of the ordering of the one-dimensional Heisenberg spin-glass model with a long-range power-law interaction is studied by extensive Monte Carlo simulations, with particular attention to the issue of the spin-chirality decoupling/coupling. Large system sizes up to $L=4096$ are studied. With varying the exponent $\sigma$ describing the power-law interaction, we observe three distinct types of ordering regimes. For smaller $\sigma$, the spin and the chirality order at a common finite temperature with a common correlation-length exponent, exhibiting the standard spin-chirality coupling behavior. For intermediate $\sigma$, the chirality orders at a temperature higher than the spin, exhibiting the spin-chirality decoupling behavior. For larger $\sigma$, both the spin and the chirality order at zero temperature. We construct a phase diagram in the $\sigma$ versus the temperature plane, and discuss implications of the results. Critical properties associated with both the chiral-glass and the spin-glass transitions are also determined.Comment: 28 pages, 26 figures, to appear in J. Phys. Soc. Jp

p21(Cip1) plays a critical role in the physiological adaptation to fasting through activation of PPARα.

Fasting is a physiological stress that elicits well-known metabolic adaptations, however, little is known about the role of stress-responsive tumor suppressors in fasting. Here, we have examined the expression of several tumor suppressors upon fasting in mice. Interestingly, p21 mRNA is uniquely induced in all the tissues tested, particularly in liver and muscle (>10 fold), and this upregulation is independent of p53. Remarkably, in contrast to wild-type mice, p21-null mice become severely morbid after prolonged fasting. The defective adaptation to fasting of p21-null mice is associated to elevated energy expenditure, accelerated depletion of fat stores, and premature activation of protein catabolism in the muscle. Analysis of the liver transcriptome and cell-based assays revealed that the absence of p21 partially impairs the transcriptional program of PPARα, a key regulator of fasting metabolism. Finally, treatment of p21-null mice with a PPARα agonist substantially protects them from their accelerated loss of fat upon fasting. We conclude that p21 plays a relevant role in fasting adaptation through the positive regulation of PPARα