Kinematical singularities of the three-body decay helicity amplitudes

The kinematical behaviour of the three-body decay helicity amplitudes at the boundary of the physical region and of the decay transversity amplitudes at the thresholds and pseudo- thresholds is discussed. The three-body decay amplitudes possess the threshold and pseudo- threshold singularities in s, t and u

Helicity crossing relations between the two-body scattering and three-body decay channels

The helicity crossing relations between the two-body scattering channels and the three. body decay channel are derived under the assumption that analytic properties of spinor amplitudes allow such a crossing. Each relation contains two or three crossing angles

A c=1 phase transition in two-dimensional CDT/Horava-Lifshitz gravity?

We study matter with central charge $c >1$ coupled to two-dimensional (2d) quantum gravity, here represented as causal dynamical triangulations (CDT). 2d CDT is known to provide a regularization of (Euclidean) 2d Ho\v{r}ava-Lifshitz quantum gravity. The matter fields are massive Gaussian fields, where the mass is used to monitor the central charge $c$. Decreasing the mass we observe a higher order phase transition between an effective $c=0$ theory and a theory where $c>1$. In this sense the situation is somewhat similar to that observed for "standard" dynamical triangulations (DT) which provide a regularization of 2d quantum Liouville gravity. However, the geometric phase observed for $c >1$ in CDT is very different from the corresponding phase observed for DT.Comment: 16 pages, 10 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

The Ising model on a random lattice with a coordnation numer equal 3

The micro- and grand-canonical partition functions for a system of spins on a dynamical two-dimensional random spherical surface with a coordination number 3 restricted to the set of lattices without the ‘tadpole’ and ‘self-energy’ insertions is calculated. The critical properties are shown to be the same as in the case of the unrestricted set of the $\phi^{3}$ lattices

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

Searching for a continuum limit in causal dynamical triangulation quantum gravity

We search for a continuum limit in the causal dynamical triangulation (CDT) approach to quantum gravity by determining the change in lattice spacing using two independent methods. The two methods yield similar results that may indicate how to tune the relevant couplings in the theory in order to take a continuum limit.Comment: 19 pages, 8 figures. Title change and journal reference adde

Signature Change of the Metric in CDT Quantum Gravity?

We study the effective transfer matrix within the semiclassical and bifurcation phases of CDT quantum gravity. We find that for sufficiently large lattice volumes the kinetic term of the effective transfer matrix has a different sign in each of the two phases. We argue that this sign change can be viewed as a Wick rotation of the metric. We discuss the likely microscopic mechanism responsible for the bifurcation phase transition, and propose an order parameter that can potentially be used to determine the precise location and order of the transition. Using the effective transfer matrix we approximately locate the position of the bifurcation transition in some region of coupling constant space, allowing us to present an updated version of the CDT phase diagram.Comment: 16 pages, 9 figure