Related papers: Attributing sense to some integrals in Regge calcu…
Infinite graphs are finitary in the sense that their points are connected via finite paths. So what would an infinitary generalization of finite graphs look like? Usually this question is answered with the aid of topology, e.g. in the case…
We have found that the Regge gravity \cite{regge,sorkin}, can be represented as a $superposition$ of less complicated theory of random surfaces with $Euler~character$ as an action. This extends to Regge gravity our previous result…
We investigate the structure of conformal Regge trajectories for the maximally supersymmetric (2,0) theories in six dimensions. The different conformal multiplets in a single superconformal multiplet must all have similarly-shaped Regge…
A method for nonperturbative path integral calculation is proposed. Quantum mechanics as a simplest example of a quantum field theory is considered. All modes are decomposed into hard (with frequencies $\omega^2 >\omega^2_0$) and soft (with…
A comparative analysis of the versions of quantum measure in the area tensor Regge calculus is performed on the simplest configurations of the system. The quantum measure is constructed in such the way that it reduces to the Feynman path…
We adopt the standard definition of diffeomorphism for Regge gravity in D=2 and give an exact expression of the Liouville action in the discretized case. We also give the exact form of the integration measure for the conformal factor. In…
One of the subtleties that has made superstring perturbation theory intricate at high string loop order is the fact that as shown by Donagi and Witten, supermoduli space is not holomorphically projected, nor is it holomorphically split. In…
We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows…
Representations of propagators by means of path integrals over velocities are discussed both in nonrelativistic and relativistic quantum mechanics. It is shown that all the propagators can only be expressed through bosonic path integrals…
It is shown, that the effective action for the reggeized graviton interactions can be formulated in terms of the reggeon fields $A^{++}$ and $A^{--}$ and the metric tensor $g_{\mu \nu}$ in such a way, that it is local in the rapidity space…
An integration by parts formula is derived for the first order differential operator corresponding to the action of translations on the space of locally finite simple configurations of infinitely many points on R^d. As reference measures,…
Regge's method for regularizing euclidean quantum gravity is applied to two dimensional gravity. We use two different strategies to simulate the Regge path integral at a fixed value of the total area: A standard Metropolis simulation…
Based on Gauss's law for the electric field, new integral formulas are deduced. Although the applications are not limited within the physics realm, an application is also presented, for the sake of practicability, specifically in the area…
We discuss a recent approach to quantum field theoretical path integration on noncommutative geometries which imply UV/IR regularising finite minimal uncertainties in positions and/or momenta. One class of such noncommutative geometries…
For the construction of the Lorentzian path integral for gravity one faces two main questions: Firstly, what configurations to include, in particular whether to allow Lorentzian metrics that violate causality conditions. And secondly, how…
We consider the contraction of some non linear sigma models which appear in effective supergravity theories. In particular we consider the contractions of maximally symmetric spaces corresponding to N=1 and N=2 theories, as they appear in…
Instanton calculations in semiclassical quantum mechanics rely on integration along trajectories which solve classical equations of motion. However in systems with higher dimensionality or complexified phase space these are rarely…
We investigate the structure of the meson Regge trajectories based on the quadratic form of the spinless Salpeter-type equation. It is found that the forms of the Regge trajectories depend on the energy region. As the employed Regge…
The standard way to construct a path integral is to use a Legendre transformation to find the hamiltonian, to repeatedly insert complete sets of states into the time-evolution operator, and then to integrate over the momenta. This procedure…
We consider theories for scalar and vector fields coupled to the energy-momentum tensor. Since these fields also carry a non-trivial energy-momentum tensor, the coupling prescription generates self-interactions. In analogy with gravity…