One-Loop Amplitudes in Euclidean Quantum Gravity

This paper studies the linearized gravitational field in the presence of boundaries. For this purpose, $\zeta$-function regularization is used to perform the mode-by-mode evaluation of BRST-invariant Faddeev-Popov amplitudes in the case of flat Euclidean four-space bounded by a three-sphere. On choosing the de Donder gauge-averaging term, the resulting $\zeta(0)$ value is found to agree with the space-time covariant calculation of the same amplitudes, which relies on the recently corrected geometric formulas for the asymptotic heat kernel in the case of mixed boundary conditions. Two sets of mixed boundary conditions for Euclidean quantum gravity are then compared in detail. The analysis proves that one cannot restrict the path-integral measure to transverse-traceless perturbations. By contrast, gauge-invariant amplitudes are only obtained on considering from the beginning all perturbative modes of the gravitational field, jointly with ghost modes.Comment: 26 pages, plain TeX, no figure

Correlação entre teores de nitrogênio e de clorofila na folha com o rendimento de grãos de aveia branca Correlation among nitrogen and chlorophyll contents of leaves and grain yield of oat

Um experimento foi conduzido na Universidade de Passo Fundo (UPF) com o objetivo de avaliar as correlações entre teores de N e de clorofila em folhas de aveia branca e entre estes e o rendimento de grãos (RG), massa de mil grãos (MMG), período de enchimento (PEG) e taxa de enchimento de grãos (TEG). O ensaio foi conduzido no ano agrícola de 2003, utilizando-se 21 cultivares de aveia branca desenvolvidas pela FAMV/UPF, distribuídas em blocos ao acaso, em quatro repetições. Estimou-se o teor de clorofila por meio do índice SPAD (clorofilômetro) e determinou-se o seu teor pelo método químico e também os teores de N, nas folhas bandeia e bandeira-1, no estádio de antese. Na maturação (colheita), determinou-se o RG, o MMG, o TEG e o PEG. Verificou-se que não houve correlações significativas entre teores de clorofila com os teores de N, com RG, MMG, TEG e PEG, porém, houve correlações significativas entre teores de N com o RG, MMG e PEG.<br>An experiment was conducted at the Passo Fundo University, with the aim of evaluate the correlations among nitrogen contents, chlorophyll contents, grain yield (GY), thousand grain weight (TGW), grain filling period (GFP) and grain filling rate (GFR) in oat cultivars. The experiment was conducted during 2003 agriculture year, with oat cultivars developed by Passo Fundo University, with four replications, at random blocks distribution. The chlorophyll contents, estimated by chlorophyll meter (SPAD 502 model) and chemical method, and nitrogen contents were determined at anthesis stage. At maturation stage, the GY, TGW, GFP and GFR variables were determined. It was observed that there were no significant correlations among chlorophyll contents with nitrogen contents, with GY, TGW and GFP, but there were significant correlations among nitrogen contents and GY, TGW and GFP