Proper time and path integral representations for the commutation function

On the example of the quantized spinor field, interacting with arbitrary external electromagnetic field, the commutation function is studied. It is shown that a proper time representation is available in any dimensions. Using it, all the light cone singularities of the function are found explicitly, generalizing the Fock formula in four dimensions, and a path integral representation is constructed.Comment: 20 pages, LaTeX, uses pictex macro

Quantum gravity at a TeV and the renormalization of Newton's constant

We examine whether renormalization effects can cause Newton¿s constant to change dramatically with energy, perhaps even reducing the scale of quantum gravity to the TeV region without the introduction of extra dimensions. We examine a model that realizes this possibility and describe experimental signatures from the production of small black holes

Quantum Effective Action in Spacetimes with Branes and Boundaries

We construct quantum effective action in spacetime with branes/boundaries. This construction is based on the reduction of the underlying Neumann type boundary value problem for the propagator of the theory to that of the much more manageable Dirichlet problem. In its turn, this reduction follows from the recently suggested Neumann-Dirichlet duality which we extend beyond the tree level approximation. In the one-loop approximation this duality suggests that the functional determinant of the differential operator subject to Neumann boundary conditions in the bulk factorizes into the product of its Dirichlet counterpart and the functional determinant of a special operator on the brane -- the inverse of the brane-to-brane propagator. As a byproduct of this relation we suggest a new method for surface terms of the heat kernel expansion. This method allows one to circumvent well-known difficulties in heat kernel theory on manifolds with boundaries for a wide class of generalized Neumann boundary conditions. In particular, we easily recover several lowest order surface terms in the case of Robin and oblique boundary conditions. We briefly discuss multi-loop applications of the suggested Dirichlet reduction and the prospects of constructing the universal background field method for systems with branes/boundaries, analogous to the Schwinger-DeWitt technique.Comment: LaTeX, 25 pages, final version, to appear in Phys. Rev.

Ultraviolet Divergences in Cosmological Correlations

A method is developed for dealing with ultraviolet divergences in calculations of cosmological correlations, which does not depend on dimensional regularization. An extended version of the WKB approximation is used to analyze the divergences in these calculations, and these divergences are controlled by the introduction of Pauli--Villars regulator fields. This approach is illustrated in the theory of a scalar field with arbitrary self-interactions in a fixed flat-space Robertson--Walker metric with arbitrary scale factor $a(t)$. Explicit formulas are given for the counterterms needed to cancel all dependence on the regulator properties, and an explicit prescription is given for calculating finite regulator-independent correlation functions. The possibility of infrared divergences in this theory is briefly considered.Comment: References added on various regularization methods. Improved discussion of further issues. 26 pages, 1 figur

van Vleck determinants: geodesic focussing and defocussing in Lorentzian spacetimes

The van Vleck determinant is an ubiquitous object, arising in many physically interesting situations such as: (1) WKB approximations to quantum time evolution operators and Green functions. (2) Adiabatic approximations to heat kernels. (3) One loop approximations to functional integrals. (4) The theory of caustics in geometrical optics and ultrasonics. (5) The focussing and defocussing of geodesic flows in Riemannian manifolds. While all of these topics are interrelated, the present paper is particularly concerned with the last case and presents extensive theoretical developments that aid in the computation of the van Vleck determinant associated with geodesic flows in Lorentzian spacetimes. {\sl A fortiori} these developments have important implications for the entire array of topics indicated. PACS: 04.20.-q, 04.20.Cv, 04.60.+n. To appear in Physical Review D47 (1993) 15 March.Comment: plain LaTeX, 18 page

Updating Prior Beliefs based on Ambiguous Evidence

This paper investigates a problem where the solver must firstly determine which of two possible causes are the source of an effect where one cause has a historically higher propensity to cause that effect. Secondly, they must update the propensity of the two causes to produce the effect in light of the observation. Firstly, we find an error commensurate with the ‘double updating’ error observed within the polarisation literature: individuals appear to first use their prior beliefs to interpret the evidence, then use the interpreted form of the evidence, rather than the raw form, when updating. Secondly, we find an error where individuals convert from a probabilistic representation of the evidence to a categorical one and use this representation when updating. Both errors have the effect of exaggerating the evidence in favour of the solver’s prior belief and could lead to confirmation bias and polarisation

The Fermion Self-Energy during Inflation

We compute the one loop fermion self-energy for massless Dirac + Einstein in the presence of a locally de Sitter background. We employ dimensional regularization and obtain a fully renormalized result by absorbing all divergences with BPHZ counterterms. An interesting technical aspect of this computation is the need for a noninvariant counterterm owing to the breaking of de Sitter invariance by our gauge condition. Our result can be used in the quantum-corrected Dirac equation to search for inflation-enhanced quantum effects from gravitons, analogous to those which have been found for massless, minimally coupled scalars.Comment: 63 pages, 3 figures (uses axodraw.sty), LaTeX 2epsilon. Revised version (to appear in Classical and Quantum Gravity) corrects some typoes and contains some new reference

Seasonal rainfall predictability over the Lake Kariba catchment area

The Lake Kariba catchment area in southern Africa has one of the most variable climates of any major river basin, with an extreme range of conditions across the catchment and through time. Marked seasonal and interannual fluctuations in rainfall are a significant aspect of the catchment. To determine the predictability of seasonal rainfall totals over the Lake Kariba catchment area, this study used the low-level atmospheric circulation (850 hPa geopotential height fields) of a coupled ocean-atmosphere general circulation model (CGCM) over southern Africa, statistically  downscaled to gridded seasonal rainfall totals over the catchment. This downscaling configuration was used to retroactively forecast the 3-month rainfall seasons of September-October-November through February-March-April, over a 14-year independent test period extending from 1994. Retroactive forecasts are produced for lead times of up to 5 months and probabilistic forecast performances evaluated for extreme rainfall  thresholds of the 25th and 75th percentile values of the climatological record. The verification of the retroactive forecasts shows that rainfall over the catchment is predictable at extended lead-times, but that predictability is primarily found for austral mid-summer rainfall. This season is also associated with the highest potential economic value that can be derived from seasonal forecasts. A forecast case study of a recent extreme rainfall season (2010/11) that lies outside of the verification period is presented as evidence of the statistical downscaling system’s operational capability.Keywords: Lake Kariba catchment, coupled ocean-atmosphere model, statistical downscaling, seasonal forecasting, economic valu

Superfield extended BRST quantization in general coordinates

We propose a superfield formalism of Lagrangian BRST-antiBRST quantization of arbitrary gauge theories in general coordinates with the base manifold of fields and antifields desribed in terms of both bosonic and fermionic variables.Comment: LaTex, 10 page

Nonlinear couplings and tree amplitudes in gauge theories

Following a remark advanced by Feynman,we study the connection between the form of the nonlinear vertices involving gauge particles and the Abelian gauge invariance of physical tree amplitudes. We show that this requirement, together with some natural assumptions, fixes uniquely the structure of the Yang-Mills theory. However, the constraints imposed by the above property are not sufficient to single out the gauge theory of gravitation.Comment: 12 pages. Requires macros RevTeX, prepictex, pictex, postpictex. TeX source is 69373 byte