A New Class of Group Field Theories for 1st Order Discrete Quantum Gravity

Group Field Theories, a generalization of matrix models for 2d gravity, represent a 2nd quantization of both loop quantum gravity and simplicial quantum gravity. In this paper, we construct a new class of Group Field Theory models, for any choice of spacetime dimension and signature, whose Feynman amplitudes are given by path integrals for clearly identified discrete gravity actions, in 1st order variables. In the 3-dimensional case, the corresponding discrete action is that of 1st order Regge calculus for gravity (generalized to include higher order corrections), while in higher dimensions, they correspond to a discrete BF theory (again, generalized to higher order) with an imposed orientation restriction on hinge volumes, similar to that characterizing discrete gravity. The new models shed also light on the large distance or semi-classical approximation of spin foam models. This new class of group field theories may represent a concrete unifying framework for loop quantum gravity and simplicial quantum gravity approaches.Comment: 48 pages, 4 figures, RevTeX, one reference adde

Current Issues in the Phenomenology of Particle Physics

The present status of the Standard Model and its experimental tests are reviewed, including indications on the likely mass of the Higgs boson. Also discussed are the motivations for supersymmetry and grand unification, searches for sparticles at LEP, neutrino oscillations, and the prospects for physics at the LHC.Comment: 32 pages, LaTeX, 10 figures (included), Invited plenary talk presented at the Inaugural Conference of the APCTP, Seoul, June 199

A new look at loop quantum gravity

I describe a possible perspective on the current state of loop quantum gravity, at the light of the developments of the last years. I point out that a theory is now available, having a well-defined background-independent kinematics and a dynamics allowing transition amplitudes to be computed explicitly in different regimes. I underline the fact that the dynamics can be given in terms of a simple vertex function, largely determined by locality, diffeomorphism invariance and local Lorentz invariance. I emphasize the importance of approximations. I list open problems.Comment: 15 pages, 5 figure

An Interactive Interior Point Method for Multiobjective Nonlinear Programming Problems

An interactive interior point algorithm for solving amultiobjective nonlinear programming problem has beenproposed in this paper. The algorithm uses a single-objectivenonlinear variant based on both logarithmic barrier function andNewton’s method in order to generate, at each iterate, interiorsearch directions. New feasible points are found along thesedirections which will be later used for deriving bestapproximationto the gradient of the implicitly-known utilityfunction at the current iterate. Using this approximate gradient,a single feasible interior direction for the implicitly-utilityfunction could be found by solving a set of linear equations. Itmay be taken an interior step from the current iterate to the nextone along this feasible direction. During the execution of thealgorithm, a sequence of interior points will be generated. It hasbeen proved that this sequence converges to an ε − optimalsolution, whereε is a predetermined error tolerance known apriori. A numerical multiobjective example is illustrated usingthis algorith

A Polynomial Time Algorithm for the Minimum Cost Flow Problem

An efficient polynomial time algorithm forsolving minimum cost flow problems has been proposedin this paper. This algorithm is basically based onsuccessive divisions of capacities by multiples of two,and it solves the minimum cost flow problem as asequence of O(n2 ) shortest path problems on residualnetworks with n nodes and runs in O(n2m r ) time,where m is the number of arcs and r is the smallestinteger greater than or equal to log B , and B is thelargest arc capacity of the network. A numericalexample is illustrated using the proposed algorithm

A logarithmic barrier function method for solving nonlinear multiobjective programming problems

An interior point method for solving nonlinear multiobjective programming problems, over a convex set contained in the real space R^n, has been developed in this paper. In this method a new strictly concave logarithmic barrier function has been suggested in order to transform the orginal problem into a sequence of unconstrained subproblems. These subproblems can be solved using Newton method for determining Newton's directions along which line searches are performed. It also has been proved that the number of iterations required by the suggested algorithm to converge to an [epsilon]-optimal solution is 0(m|ln[epsilon]|), depending on predetermined error tolerance [epsilon] and the number of constraints m