A Mode-Sum Prescription for Vacuum Polarization in Even Dimensions

We present a mode-sum regularization prescription for computing the vacuum polarization of a scalar field in static spherically-symmetric black hole spacetimes in even dimensions. This is the first general and systematic approach to regularized vacuum polarization in higher even dimensions, building upon a previous scheme we developed for odd dimensions. Things are more complicated here since the even-dimensional propagator possesses logarithmic singularities which must be regularized. However, in spite of this complication, the regularization parameters can be computed in closed form in arbitrary even dimensions and for arbitrary metric function $f(r)$. As an explicit example of our method, we show plots for vacuum polarization of a massless scalar field in the Schwarzschild-Tangherlini spacetime for even $d=4,...,10$. However, the method presented applies straightforwardly to massive fields or to nonvacuum spacetimes.Comment: arXiv admin note: text overlap with arXiv:1609.0816

Table_1_Diet of the earliest modern humans in East Asia.DOCX

Reconstructing diet can offer an improved understanding toward the origin and evolution of modern humans. However, the diet of early modern humans in East Asia is poorly understood. Starch analysis of dental calculus is harmless to precious fossil hominins and provides the most direct evidence of plant food sources in early modern human dietary records. In this paper, we examined the starch grains in dental calculus from Fuyan Cave hominins in Daoxian (South China), which were the earliest modern humans in East Asia. Our results reveal the earliest direct evidence of a hominin diet made of acorns, roots, tubers, grass seeds, and other yet-unidentified plants in marine isotope stage 5 between 120 and 80 ka. Our study also provides the earliest evidence that acorns may have played an important role in subsistence strategies. There may have been a long-lasting tradition of using these plants during the Late Pleistocene in China. Plant foods would have been a plentiful source of carbohydrates that greatly increased energy availability to human tissues with high glucose demands. Our study provides the earliest direct consumption of carbohydrates-rich plant resources from modern humans in China for the first time. In addition, it also helps elucidate the evolutionary advantages of early modern humans in the late Middle and early Upper Pleistocene.</p