Related papers: Perfect simulation for the Feynman-Kac law on the …
Starting from the parametric representation of a Feynman diagram, we obtain it's well defined value in dimensional regularisation by changing the integrals over parameters into contour integrals. That way we eventually arrive at a…
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…
This review gives a survey of numerical algorithms and software to simulate quantum computers.It covers the basic concepts of quantum computation and quantum algorithms and includes a few examples that illustrate the use of simulation…
Inspired by the work of Feynman, Deutsch, We formally propose the theory of physical computability and accordingly, the physical complexity theory. To achieve this, a framework that can evaluate almost all forms of computation using various…
Complete Feynman diagram automatic computation systems are now coming of age after many years of development. They are made available to the high energy physics community through user-friendly interfaces. Theorists and experimentalists can…
For distinguishable particles it is well known that Brownian motion and a Feynman-Kac functional can be used to calculate the path integral (for imaginary times) for a general class of scalar potentials. In order to treat identical…
Path integrals are a ubiquitous tool in theoretical physics. However, their use is sometimes hindered by the lack of control on various manipulations -- such as performing a change of the integration path -- one would like to carry out in…
Quantum walks constitute important tools in different applications, especially in quantum algorithms. To a great extent their usefulness is due to unusual diffusive features, allowing much faster spreading than their classical counterparts.…
The mathematical similarities between non-relativistic wavefunction propagation in quantum mechanics and image propagation in scalar diffraction theory are used to develop a novel understanding of time and paths through spacetime as a…
The path integral formulation of quantum mechanics, i.e., the idea that the evolution of a quantum system is determined as a sum over all the possible trajectories that would take the system from the initial to its final state of its…
It is wellknown that the Feynman kernel for the free particle on the half-line can be expressed as a sum over classical paths if we take the contribution from the reflected path into account. The minus sign for the reflected path needs to…
These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…
To date, all proposed quantum algorithms for simulating quantum field theory (QFT) simulate (continuous-time) Hamiltonian lattice QFT as a stepping stone. Two overlooked issues are how large we can take the timestep in these simulations…
This paper introduces a framework for simulating finite dimensional representations of (jump) diffusion sample paths over finite intervals, without discretisation error (exactly), in such a way that the sample path can be restored at any…
In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler…
We consider Feynman's path integral approach to quantum mechanics with a noncommutativity in position and momentum sectors of the phase space. We show that a quantum-mechanical system with this kind of noncommutativity is equivalent to the…
This paper suggests a new way to compute the path integral for simple quantum mechanical systems. The new algorithm originated from previous research in string theory. However, its essential simplicity is best illustrated in the case of a…
The article is an overview of the role of graph complexes in the Feynman path integral quantization. The underlying mathematical language is that of PROPs and operads, and their representations. The sum over histories approach, the Feynman…
We study the convergence in $L^2$ of the time slicing approximation of Feynman path integrals under low regularity assumptions on the potential. Inspired by the custom in Physics and Chemistry, the approximate propagators considered here…
In this paper we develop a quantization method for flat compact manifolds based on path integrals. In this method the Hilbert space of holomorphic functions in the complexification of the manifold is used. This space is a reproducing kernel…