Infrared behavior of graviton-graviton scattering

The quantum effective theory of general relativity, independent of the eventual full theory at high energy, expresses graviton-graviton scattering at one loop order O(E^4) with only one parameter, Newton's constant. Dunbar and Norridge have calculated the one loop amplitude using string based techniques. We complete the calculation by showing that the 1/(d-4) divergence which remains in their result comes from the infrared sector and that the cross section is finite and model independent when the usual bremsstrahlung diagrams are included.Comment: 12 pages, uses axodra

Electron recombination with multicharged ions via chaotic many-electron states

We show that a dense spectrum of chaotic multiply-excited eigenstates can play a major role in collision processes involving many-electron multicharged ions. A statistical theory based on chaotic properties of the eigenstates enables one to obtain relevant energy-averaged cross sections in terms of sums over single-electron orbitals. Our calculation of the low-energy electron recombination of Au$^{25+}$ shows that the resonant process is 200 times more intense than direct radiative recombination, which explains the recent experimental results of Hoffknecht {\em et al.} [J. Phys. B {\bf 31}, 2415 (1998)].Comment: 9 pages, including 1 figure, REVTe

On Perturbative Gravity and Gauge Theory

We review some applications of tree-level (classical) relations between gravity and gauge theory that follow from string theory. Together with $D$-dimensional unitarity, these relations can be used to perturbatively quantize gravity theories, i.e. they contain the necessary information for obtaining loop contributions. We also review recent applications of these ideas showing that N=1 D=11 supergravity diverges, and review arguments that N=8 D=4 supergravity is less divergent than previously thought, though it does appear to diverge at five loops. Finally, we describe field variables for the Einstein-Hilbert Lagrangian that help clarify the perturbative relationship between gravity and gauge theory.Comment: Talk presented at Third Meeting on Constrained Dynamics and Quantum Gravity, Villasimius (Sardinia, Italy) September 13-17, 1999 and at the Workshop on Light-Cone QCD and Nonperturbative Hadron Physics, University of Adelaide (Australia) December 13-22, 1999. Latex, 9 page

Off-Diagonal Elements of the DeWitt Expansion from the Quantum Mechanical Path Integral

The DeWitt expansion of the matrix element M_{xy} = \left\langle x \right| \exp -[\case{1}{2} (p-A)^2 + V]t \left| y \right\rangle, $(p=-i\partial)$ in powers of $t$ can be made in a number of ways. For $x=y$ (the case of interest when doing one-loop calculations) numerous approaches have been employed to determine this expansion to very high order; when $x \neq y$ (relevant for doing calculations beyond one-loop) there appear to be but two examples of performing the DeWitt expansion. In this paper we compute the off-diagonal elements of the DeWitt expansion coefficients using the Fock-Schwinger gauge. Our technique is based on representing $M_{xy}$ by a quantum mechanical path integral. We also generalize our method to the case of curved space, allowing us to determine the DeWitt expansion of \tilde M_{xy} = \langle x| \exp \case{1}{2} [\case{1}{\sqrt {g}} (\partial_\mu - i A_\mu)g^{\mu\nu}{\sqrt{g}}(\partial_\nu - i A_\nu) ] t| y \rangle by use of normal coordinates. By comparison with results for the DeWitt expansion of this matrix element obtained by the iterative solution of the diffusion equation, the relative merit of different approaches to the representation of $\tilde M_{xy}$ as a quantum mechanical path integral can be assessed. Furthermore, the exact dependence of $\tilde M_{xy}$ on some geometric scalars can be determined. In two appendices, we discuss boundary effects in the one-dimensional quantum mechanical path integral, and the curved space generalization of the Fock-Schwinger gauge.Comment: 16pp, REVTeX. One additional appendix concerning end-point effects for finite proper-time intervals; inclusion of these effects seem to make our results consistent with those from explicit heat-kernel method

On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences

String theory implies that field theories containing gravity are in a certain sense `products' of gauge theories. We make this product structure explicit up to two loops for the relatively simple case of N=8 supergravity four-point amplitudes, demonstrating that they are `squares' of N=4 super-Yang-Mills amplitudes. This is accomplished by obtaining an explicit expression for the $D$-dimensional two-loop contribution to the four-particle S-matrix for N=8 supergravity, which we compare to the corresponding N=4 Yang-Mills result. From these expressions we also obtain the two-loop ultraviolet divergences in dimensions D=7 through D=11. The analysis relies on the unitarity cuts of the two theories, many of which can be recycled from a one-loop computation. The two-particle cuts, which may be iterated to all loop orders, suggest that squaring relations between the two theories exist at any loop order. The loop-momentum power-counting implied by our two-particle cut analysis indicates that in four dimensions the first four-point divergence in N=8 supergravity should appear at five loops, contrary to the earlier expectation, based on superspace arguments, of a three-loop counterterm.Comment: Latex, 52 pages, discussion of 2 loop divergences in D=8,10 adde

Reparameterization invariants for anisotropic Bianchi I cosmology with a massless scalar source

Intrinsic time-dependent invariants are constructed for classical, flat, homogeneous, anisotropic cosmology with a massless scalar material source. Invariance under the time reparameterization-induced canonical symmetry group is displayed explicitly.Comment: 28 pages, to appear in General Relativity and Gravitation. Substantial revisions: added foundational overview section 2, chose new intrinsic time variable, worked with dimensionless variables, added appendix with comparison and criticism of other approache

The Hamiltonian formulation of General Relativity: myths and reality

A conventional wisdom often perpetuated in the literature states that: (i) a 3+1 decomposition of space-time into space and time is synonymous with the canonical treatment and this decomposition is essential for any Hamiltonian formulation of General Relativity (GR); (ii) the canonical treatment unavoidably breaks the symmetry between space and time in GR and the resulting algebra of constraints is not the algebra of four-dimensional diffeomorphism; (iii) according to some authors this algebra allows one to derive only spatial diffeomorphism or, according to others, a specific field-dependent and non-covariant four-dimensional diffeomorphism; (iv) the analyses of Dirac [Proc. Roy. Soc. A 246 (1958) 333] and of ADM [Arnowitt, Deser and Misner, in "Gravitation: An Introduction to Current Research" (1962) 227] of the canonical structure of GR are equivalent. We provide some general reasons why these statements should be questioned. Points (i-iii) have been shown to be incorrect in [Kiriushcheva et al., Phys. Lett. A 372 (2008) 5101] and now we thoroughly re-examine all steps of the Dirac Hamiltonian formulation of GR. We show that points (i-iii) above cannot be attributed to the Dirac Hamiltonian formulation of GR. We also demonstrate that ADM and Dirac formulations are related by a transformation of phase-space variables from the metric $g_{\mu\nu}$ to lapse and shift functions and the three-metric $g_{km}$, which is not canonical. This proves that point (iv) is incorrect. Points (i-iii) are mere consequences of using a non-canonical change of variables and are not an intrinsic property of either the Hamilton-Dirac approach to constrained systems or Einstein's theory itself.Comment: References are added and updated, Introduction is extended, Subsection 3.5 is added, 83 pages; corresponds to the published versio

Selberg Supertrace Formula for Super Riemann Surfaces III: Bordered Super Riemann Surfaces

This paper is the third in a sequel to develop a super-analogue of the classical Selberg trace formula, the Selberg supertrace formula. It deals with bordered super Riemann surfaces. The theory of bordered super Riemann surfaces is outlined, and the corresponding Selberg supertrace formula is developed. The analytic properties of the Selberg super zeta-functions on bordered super Riemann surfaces are discussed, and super-determinants of Dirac-Laplace operators on bordered super Riemann surfaces are calculated in terms of Selberg super zeta-functions.Comment: 43 pages, amste

Should science educators deal with the science/religion issue?

I begin by examining the natures of science and religion before looking at the ways in which they relate to one another. I then look at a number of case studies that centre on the relationships between science and religion, including attempts to find mechanisms for divine action in quantum theory and chaos theory, creationism, genetic engineering and the writings of Richard Dawkins. Finally, I consider some of the pedagogical issues that would need to be considered if the science/religion issue is to be addressed in the classroom. I conclude that there are increasing arguments in favour of science educators teaching about the science/religion issue. The principal reason for this is to help students better to learn science. However, such teaching makes greater demands on science educators than has generally been the case. Certain of these demands are identified and some specific suggestions are made as to how a science educator might deal with the science/religion issue. © 2008 Taylor & Francis