Abelian gauge fields coupled to simplicial quantum gravity

We study the coupling of Abelian gauge theories to four-dimensional simplicial quantum gravity. The gauge fields live on dual links. This is the correct formulation if we want to compare the effect of gauge fields on geometry with similar effects studied so far for scalar fields. It shows that gauge fields couple equally weakly to geometry as scalar fields, and it offers an understanding of the relation between measure factors and Abelian gauge fields observed so-far.Comment: 20 page

The Concept of Time in 2D Quantum Gravity

We show that the ``time'' t_s defined via spin clusters in the Ising model coupled to 2d gravity leads to a fractal dimension d_h(s) = 6 of space-time at the critical point, as advocated by Ishibashi and Kawai. In the unmagnetized phase, however, this definition of Hausdorff dimension breaks down. Numerical measurements are consistent with these results. The same definition leads to d_h(s)=16 at the critical point when applied to flat space. The fractal dimension d_h(s) is in disagreement with both analytical prediction and numerical determination of the fractal dimension d_h(g), which is based on the use of the geodesic distance t_g as ``proper time''. There seems to be no simple relation of the kind t_s = t_g^{d_h(g)/d_h(s)}, as expected by dimensional reasons.Comment: 14 pages, LaTeX, 2 ps-figure

How to evaluate cross-sections in models where the S-matrix is unitary but does not conserve energy

The standard time-dependent description of the scattering processes is used to explain that, when the S-matrix does not conserve energy, the coefficient relating the squared modulus of the S-matrix element to the cross-section becomes model-dependent, and the optical theorem does not necessarily follow from the unitarity of the S-matrix. It is suggested that, if one insists on using such models, the optical theorem should be imposed as a constraint and used to fix the model-dependent coefficient

Thermodynamics and two-dimensional lattice Gauge models

he gauge theory with the gauge group U(N $\to \infty$) is solved on a two-dimensional lattice. The single plaquette action used depends on L parameters, where L is an arbitrary integer, and thus results for a wide class of variant actions may be compared. A rich structure of second order and third order phase transitions appears. Besides the exact analytic solution a thermodynamical discussion clarifying the qualitative features of the results is given

Multiplicity distribution in unitarized uncorrelated cluster production models

It is shown that the unitarity corrections dramatically change the multiplicity distributions expected from uncorrelated cluster emission models

A new perspective on matter coupling in 2d quantum gravity

We provide compelling evidence that a previously introduced model of non-perturbative 2d Lorentzian quantum gravity exhibits (two-dimensional) flat-space behaviour when coupled to Ising spins. The evidence comes from both a high-temperature expansion and from Monte Carlo simulations of the combined gravity-matter system. This weak-coupling behaviour lends further support to the conclusion that the Lorentzian model is a genuine alternative to Liouville quantum gravity in two dimensions, with a different, and much `smoother' critical behaviour.Comment: 24 pages, 7 figures (postscript

The moduli space of isometry classes of globally hyperbolic spacetimes

This is the last article in a series of three initiated by the second author. We elaborate on the concepts and theorems constructed in the previous articles. In particular, we prove that the GH and the GGH uniformities previously introduced on the moduli space of isometry classes of globally hyperbolic spacetimes are different, but the Cauchy sequences which give rise to well-defined limit spaces coincide. We then examine properties of the strong metric introduced earlier on each spacetime, and answer some questions concerning causality of limit spaces. Progress is made towards a general definition of causality, and it is proven that the GGH limit of a Cauchy sequence of $\mathcal{C}^{\pm}_{\alpha}$, path metric Lorentz spaces is again a $\mathcal{C}^{\pm}_{\alpha}$, path metric Lorentz space. Finally, we give a necessary and sufficient condition, similar to the one of Gromov for the Riemannian case, for a class of Lorentz spaces to be precompact.Comment: 29 pages, 9 figures, submitted to Class. Quant. Gra

Influence of diet on the risk of developing endometriosis

Endometriosis is a hormone-dependent chronic inflammatory disease characterized by the presence of endometrium beyond the uterine cavity. The disease affects 5–15% of women of child-bearing age, 30–50% of whom suffer from infertility. Understanding the role of dietary factors in the development of endometriosis is critical to development of effective dietary instructions for prevention. Existing studies concerning nutrition and endometriosis suggest that diet is a potentially modifiable risk factor for endometriosis. Fruits and vegetables, fish oils, dairy products rich in calcium and vitamin D, and Omega-3 fatty acids are likely connected with a lower risk of developing endometriosis. Risk factors that increase the risk of endometriosis include consumption of products rich in trans-unsaturated fatty acids, consumption of fats generally, and consumption of beef and other kinds of red meat and alcohol. Currently, there are no clear correlations between par­ticular food products and the risk of endometriosis. Further research is needed in order to fully understand the influence of consumed food products on the risk of development of this disease