Discrete approaches to quantum gravity in four dimensions

The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of space-time and the Einstein action. I review here three major areas of research: gauge-theoretic approaches, both in a path-integral and a Hamiltonian formulation, quantum Regge calculus, and the method of dynamical triangulations, confining attention to work that is strictly four-dimensional, strictly discrete, and strictly quantum in nature.Comment: 33 pages, invited contribution to Living Reviews in Relativity; the author welcomes any comments and suggestion

The transfer matrix in four-dimensional CDT

The Causal Dynamical Triangulation model of quantum gravity (CDT) has a transfer matrix, relating spatial geometries at adjacent (discrete lattice) times. The transfer matrix uniquely determines the theory. We show that the measurements of the scale factor of the (CDT) universe are well described by an effective transfer matrix where the matrix elements are labeled only by the scale factor. Using computer simulations we determine the effective transfer matrix elements and show how they relate to an effective minisuperspace action at all scales.Comment: 32 pages, 19 figure

Lorentzian and Euclidean Quantum Gravity - Analytical and Numerical Results

We review some recent attempts to extract information about the nature of quantum gravity, with and without matter, by quantum field theoretical methods. More specifically, we work within a covariant lattice approach where the individual space-time geometries are constructed from fundamental simplicial building blocks, and the path integral over geometries is approximated by summing over a class of piece-wise linear geometries. This method of ``dynamical triangulations'' is very powerful in 2d, where the regularized theory can be solved explicitly, and gives us more insights into the quantum nature of 2d space-time than continuum methods are presently able to provide. It also allows us to establish an explicit relation between the Lorentzian- and Euclidean-signature quantum theories. Analogous regularized gravitational models can be set up in higher dimensions. Some analytic tools exist to study their state sums, but, unlike in 2d, no complete analytic solutions have yet been constructed. However, a great advantage of our approach is the fact that it is well-suited for numerical simulations. In the second part of this review we describe the relevant Monte Carlo techniques, as well as some of the physical results that have been obtained from the simulations of Euclidean gravity. We also explain why the Lorentzian version of dynamical triangulations is a promising candidate for a non-perturbative theory of quantum gravity.Comment: 69 pages, 16 figures, references adde

Genetic Variants in Nuclear-Encoded Mitochondrial Genes Influence AIDS Progression

Background: The human mitochondrial genome includes only 13 coding genes while nuclear-encoded genes account for 99% of proteins responsible for mitochondrial morphology, redox regulation, and energetics. Mitochondrial pathogenesis occurs in HIV patients and genetically, mitochondrial DNA haplogroups with presumed functional differences have been associated with differential AIDS progression. Methodology/Principal Findings: Here we explore whether single nucleotide polymorphisms (SNPs) within 904 of the estimated 1,500 genes that specify nuclear-encoded mitochondrial proteins (NEMPs) influence AIDS progression among HIV-1 infected patients. We examined NEMPs for association with the rate of AIDS progression using genotypes generated by an Affymetrix 6.0 genotyping array of 1,455 European American patients from five US AIDS cohorts. Successfully genotyped SNPs gave 50% or better haplotype coverage for 679 of known NEMP genes. With a Bonferroni adjustment for the number of genes and tests examined, multiple SNPs within two NEMP genes showed significant association with AIDS progression: acyl-CoA synthetase medium-chain family member 4 (ACSM4) on chromosome 12 and peroxisomal D3,D2-enoyl- CoA isomerase (PECI) on chromosome 6. Conclusions: Our previous studies on mitochondrial DNA showed that European haplogroups with presumed functional differences were associated with AIDS progression and HAART mediated adverse events. The modest influences of nuclearencoded mitochondrial genes found in the current study add support to the idea that mitochondrial function plays a role in AIDS pathogenesis

Fine-Mapping the Genetic Association of the Major Histocompatibility Complex in Multiple Sclerosis: HLA and Non-HLA Effects

Janna Saarela on työryhmien jäsen.Peer reviewe

Geometry and field theory in multi-fractional spacetime

We construct a theory of fields living on continuous geometries with fractional Hausdorff and spectral dimensions, focussing on a flat background analogous to Minkowski spacetime. After reviewing the properties of fractional spaces with fixed dimension, presented in a companion paper, we generalize to a multi-fractional scenario inspired by multi-fractal geometry, where the dimension changes with the scale. This is related to the renormalization group properties of fractional field theories, illustrated by the example of a scalar field. Depending on the symmetries of the Lagrangian, one can define two models. In one of them, the effective dimension flows from 2 in the ultraviolet (UV) and geometry constrains the infrared limit to be four-dimensional. At the UV critical value, the model is rendered power-counting renormalizable. However, this is not the most fundamental regime. Compelling arguments of fractal geometry require an extension of the fractional action measure to complex order. In doing so, we obtain a hierarchy of scales characterizing different geometric regimes. At very small scales, discrete symmetries emerge and the notion of a continuous spacetime begins to blur, until one reaches a fundamental scale and an ultra-microscopic fractal structure. This fine hierarchy of geometries has implications for non-commutative theories and discrete quantum gravity. In the latter case, the present model can be viewed as a top-down realization of a quantum-discrete to classical-continuum transition.Comment: 1+82 pages, 1 figure, 2 tables. v2-3: discussions clarified and improved (especially section 4.5), typos corrected, references added; v4: further typos correcte