Relation Between Einstein And Quantum Field Equations

We show that there exists a choice of scalar field modes, such that the evolution of the quantum field in the zero-mass and large-mass limits is consistent with the Einstein equations for the background geometry. This choice of modes is also consistent with zero production of these particles and thus corresponds to a preferred vacuum state preserved by the evolution. In the zero-mass limit, we find that the quantum field equation implies the Einstein equation for the scale factor of a radiation-dominated universe; in the large-mass case, it implies the corresponding Einstein equation for a matter-dominated universe. Conversely, if the classical radiation-dominated or matter-dominated Einstein equations hold, there is no production of scalar particles in the zero and large mass limits, respectively. The suppression of particle production in the large mass limit is over and above the expected suppression at large mass. Our results hold for a certain class of conformally ultrastatic background geometries and therefore generalize previous results by one of us for spatially flat Robertson-Walker background geometries. In these geometries, we find that the temporal part of the graviton equations reduces to the temporal equation for a massless minimally coupled scalar field, and therefore the results for massless particle production hold also for gravitons. Within the class of modes we study, we also find that the requirement of zero production of massless scalar particles is not consistent with a non-zero cosmological constant. Possible implications are discussed.Comment: Latex, 24 pages. Minor changes in text from original versio

Reply to Comment on "Completely positive quantum dissipation"

This is the reply to a Comment by R. F. O'Connell (Phys. Rev. Lett. 87 (2001) 028901) on a paper written by the author (B. Vacchini, ``Completely positive quantum dissipation'', Phys.Rev.Lett. 84 (2000) 1374, arXiv:quant-ph/0002094).Comment: 2 pages, revtex, no figure

A Search for Hard X-Ray Emission from Globular Clusters - Constraints from BATSE

We have monitored a sample of 27 nearby globular clusters in the hard X-ray band (20-120 keV) for approximately 1400 days using the BATSE instrument on board the Compton Gamma-Ray Observatory. Globular clusters may contain a large number of compact objects (e.g., pulsars or X-ray binaries containing neutron stars) which can produce hard X-ray emission. Our search provides a sensitive (~50 mCrab) monitor for hard X-ray transient events on time scales of >1 day and a means for observing persistent hard X-ray emission. We have discovered no transient events from any of the clusters and no persistent emission. Our observations include a sensitive search of four nearby clusters containing dim X-ray sources: 47 Tucanae, NGC 5139, NGC 6397, and NGC 6752. The non-detection in these clusters implies a lower limit for the recurrence time of transients of 2 to 6 years for events with luminosities >10^36 erg s^-1 (20-120 keV) and ~20 years if the sources in these clusters are taken collectively. This suggests that the dim X-ray sources in these clusters are not transients similar to Aql~X-1. We also place upper limits on the persistent emission in the range 2-10*10^34 erg s^-1 (2 sigma, 20-120 keV) for these four clusters. For 47 Tuc the upper limit is more sensitive than previous measurements by a factor of 3. We find a model dependent upper limit of 19 isolated millisecond pulsars (MSPs) producing gamma-rays in 47 Tuc, compared to the 11 observed radio MSPs in this cluster.Comment: 20 pages; accepted, ApJ; uu encoded tar file; 7 figure

Bounds on negative energy densities in flat spacetime

We generalise results of Ford and Roman which place lower bounds -- known as quantum inequalities -- on the renormalised energy density of a quantum field averaged against a choice of sampling function. Ford and Roman derived their results for a specific non-compactly supported sampling function; here we use a different argument to obtain quantum inequalities for a class of smooth, even and non-negative sampling functions which are either compactly supported or decay rapidly at infinity. Our results hold in $d$-dimensional Minkowski space ($d\ge 2$) for the free real scalar field of mass $m\ge 0$. We discuss various features of our bounds in 2 and 4 dimensions. In particular, for massless field theory in 2-dimensional Minkowski space, we show that our quantum inequality is weaker than Flanagan's optimal bound by a factor of 3/2.Comment: REVTeX, 13 pages and 2 figures. Minor typos corrected, one reference adde