Related papers: The two-loop scalar and tensor pentabox graph with…
We show that, for a class of systems described by a Lagrangian L(x,\dot{x},t) = 1/2\dot{x}^{2} - V(x,t) the propagator can be reduced via Noether's Theorem to a standard path integral multiplied by a phase factor. Using Henstock's…
One-loop integrands can be written in terms of a simple, process-independent basis. We show that a similar basis exists for integrands of phase-space integrals for the real-emission contribution at next-to-leading order. Our demonstration…
We investigate numerically the scattering of waves on discrete graphs. An efficient algorithm is developed to compute the reflection and transmission (spectral) coefficients. We then explore various configurations of input and output leads,…
In this paper, we revisit topological-like features in the extended Temperley--Lieb diagrammatical representation for quantum circuits including the teleportation, dense coding and entanglement swapping. We perform these quantum circuits…
We show that for a class of two-loop diagrams, the on-shell part of the integration-by-parts (IBP) relations correspond to exact meromorphic one-forms on algebraic curves. Since it is easy to find such exact meromorphic one-forms from…
We investigate a quantum non-relativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. Assuming that the Hamiltonian is rotationally invariant and parity conserving we identify all such systems…
We present the analytic calculation of all master integrals for 3-, 4-, and 5-particle semi-inclusive cuts of four-loop massless propagators by means of differential equations. We fix the integration constants by reducing the semi-inclusive…
Tensor robust principal component analysis (robust PCA) has been applied to the lightning images. Robust PCA aims to classify the images into low-rank and sparse components. The low rank and sparse components correspond to static background…
We explain the construction of Forcer, a FORM program for the reduction of four-loop massless propagator-type integrals to master integrals. The resulting program performs parametric IBP reductions similar to the three-loop Mincer program.…
Path-integral techniques are a powerful tool used in open quantum systems to provide an exact solution for the non-Markovian dynamics. However, the exponential scaling of the tensor size with quantum memory length of these techniques limits…
In an earlier article, we presented a method to obtain integrals of motion and polynomial algebras for a class of two-dimensional superintegrable systems from creation and annihilation operators. We discuss the general case and present its…
We propose a framework for calculating two-loop Feynman diagrams which appear within a renormalizable theory in the general mass case and at finite external momenta. Our approach is a combination of analytical results and of high accuracy…
In this review, we detail the commonality of mathematical intuitions that underlie three numerical methods used for the quantitative description of electron swarms propagating in a gas under the effect of externally applied electric and/or…
For the first time, as far as we know, in field theory are found explicit forms of propagators satisfying the K\"allen -- Lehmann representation. To be exact, it is shown that scalar meson propagators, taking into account a virtual…
By a tensor we mean an element of a tensor product of vector spaces over a field. Up to a choice of bases in factors of tensor products, every tensor may be coordinatized, that is, represented as an array consisting of numbers. This note is…
We compute structure constants in N=4 SYM at one loop using Integrability. This requires having full control over the two loop eigenvectors of the dilatation operator for operators of arbitrary size. To achieve this, we develop an algebraic…
We derive an analytic representation of the ten-particle, two-loop double-box integral as an elliptic integral over weight-three polylogarithms. To obtain this form, we first derive a four-fold, rational (Feynman-)parametric representation…
Tensor Networks are graph representations of summation expressions in which vertices represent tensors and edges represent tensor indices or vector spaces. In this work, we present EinExprs.jl, a Julia package for contraction path…
We numerically find that transmission coefficients have a rich structure as a function of wavelength in Cantor media. Complete transmission and complete reflection are observed. We also find that light propagation has scalings with respect…
We describe a new, convenient, recursive tensor integral reduction scheme for one-loop $n$-point Feynman integrals. The reduction is based on the algebraic Davydychev-Tarasov formalism where the tensors are represented by scalars with…