Related papers: Path Sums for Propagators in Causal Sets
We show how the induction law is correctly used in the path integral computation of the free particle propagator. The way this primary path integral example is treated in most textbooks is a little bit missleading.
A stochastic metric can appear in classical as well as in quantum gravity. We show that if the linearized stochastic Gaussian gravitational plane wave has the frequency spectrum $\omega^{4\gamma-1}$ ($0\leq \gamma<1$) then the equal-time…
A unitarily invariant projective framework is introduced to analyze the complexity of path-following methods for the eigenvalue problem. A condition number, and its relation to the distance to ill-posedness, is given. A Newton map…
As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…
Sum-over-histories quantization of particle-like theory in curved space is discussed. It is reviewed that the propagator satisfies the Schrodinger equation respective wave equation with a Laplace-like operator. The exact dependence of the…
The regular set tolerance is an important term in sensitivity analysis. For combinatorial sum problems, e.g., the Traveling Salesman Problem, Shortest Path Problem and Minimum Spanning Tree Problem, it determines how much the sum of the…
The purpose of this paper is two-fold. First, we would like to get rid of common assumption that causal set is bounded and attempt to model its scalar field action under the assumption that it isn't. Secondly, we would like to propose…
We investigate the hitherto unexplored relation between the superparticle path integral and superfield theory. Requiring that the path integral has the global symmetries of the classical action and obeys the natural composition property of…
We introduce the method of path-sums which is a tool for exactly evaluating a function of a discrete matrix with possibly non-commuting entries, based on the closed-form resummation of infinite families of terms in the corresponding Taylor…
A method for calculating the relativistic path integral solution via sum over perturbation series is given. As an application the exact path integral solution of the relativistic Aharonov-Bohm-Coulomb system is obtained by the method.…
The path integral for the propagator is expanded into a perturbation series, which can be exactly summed in the case of $\delta$-function perturbations giving a closed expression for the (energy-dependent) Green function. Making the…
A new method of path averaging for waves propagating in a random dilute system of identical scatterers is developed. The scattering matrix of such a system is calculated. The method systematically takes into account repeating scatterings on…
In this paper we present a stepwise construction of the path integral over relativistic orbits in Euclidean spacetime. It is shown that the apparent problems of this path integral, like the breakdown of the naive Chapman-Kolmogorov…
This paper derives a new strong Gaussian approximation bound for the sum of independent random vectors. The approach relies on the optimal transport theory and yields \textit{explicit} dependence on the dimension size $p$ and the sample…
In nuclear and particle physics one is often faced with problems where perturbation theory is not applicable. An example of this is the description of bound states. Therefore, an exact solution of field theory to all orders is an…
We investigate the Hamiltonian formulation of quantum scalar fields in a static quantum metric. We derive a functional integral formula for the propagator. We show that the quantum metric substantially changes the behaviour of the scalar…
The quantum propagator and characteristic equation in the presence of a chain of $\delta$-potentials are obtained in the rectangular, cylindrical and spherical coordinate systems. The simplicity and efficiency of the method is illustrated…
We discuss extensions of a recently introduced model of multi-critical CDT to higher multi-critical points. As in the case of pure CDT the continuum limit can be taken on the level of the action and the resulting continuum surface model is…
The semiclassical formula for the quantum propagator in the coherent state representation $<\mathbf{z}'' | e^{-i\hat{H}T/\hbar} | \mathbf{z}'>$ is not free from the problem of caustics. These are singular points along the complex classical…
We construct a bosonic quantum field on a general quantum graph. Consistency of the construction leads to the calculation of the total scattering matrix of the graph. This matrix is equivalent to the one already proposed using generalized…