Related papers: An Algorithm for Computing Four-Ramond Vertices at…
We discuss the relationship between quaternion algebras and quadratic forms with a focus on computational aspects. Our basic motivating problem is to determine if a given algebra of rank 4 over a commutative ring R embeds in the 2x2-matrix…
We derive a rigorous, quantum mechanical map of fermionic creation and annihilation operators to continuous Cartesian variables that exactly reproduces the matrix structure of the many-fermion problem. We show how our scheme can be used to…
I discuss a simple numerical algorithm for the direct evaluation of multiple Grassmann integrals. The approach is exact, suffers no Fermion sign problems, and allows arbitrarily complicated interactions. Memory requirements grow…
Quadratic descent of hermitian and skew hermitian forms over division algebras with involution of the first kind in arbitrary characteristic is investigated and a criterion, in terms of systems of quadratic forms, is obtained. A refined…
We study lattice fermions from the viewpoint of spectral graph theory (SGT). We find that a fermion defined on a certain lattice is identified as a spectral graph. SGT helps us investigate the number of zero eigenvalues of lattice Dirac…
We discuss the lattice formulation of gauge theories with fermions in arbitrary representations of the color group, and present in detail the implementation of the HMC/RHMC algorithm for simulating dynamical fermions. We discuss the…
This paper presents an experimental study on the application of quaternions in several machine learning algorithms. Quaternion is a mathematical representation of rotation in three-dimensional space, which can be used to represent complex…
We propose and test an algorithm to simulate a lattice system of interacting fermions in two spatial dimensions. The approach is an extension of the entanglement renormalization technique [Phys. Rev. Lett. 99, 220405 (2007)] and the related…
By generalizing our automated algebra approach from homogeneous space to harmonically trapped systems, we have calculated the fourth- and fifth-order virial coefficients of universal spin-1/2 fermions in the unitary limit, confined in an…
The exactly solvable four-vertex model with the fixed boundary conditions in the presence of inhomogeneous linearly growing external field is considered. The partition function of the model is calculated and represented in the determinantal…
A numerical approach to compute tensor integrals in one-loop calculations is presented. The algorithm is based on a recursion relation which allows to express high rank tensor integrals as a function of lower rank ones. At each level of…
We present a new formulation of the staggered fermion on the D-dimensional lattice based on the SO(2D) Clifford algebra, which is naturally present in the action. The action of the massless staggered fermion is invariant under the discrete…
We discuss the lattice formulation of gauge theories with fermions in arbitrary representations of the color group, and present the implementation of the RHMC algorithm for simulating dynamical Wilson fermions. A first dataset is presented…
We present a multiplication algorithm to recursively construct vertices for the Schroedinger functional in the abelian background field case. The algorithm is suited for automatic perturbative calculations with a variety of actions. As…
Using techniques from hopping expansion we identically map the lattice Schwinger model with Wilson fermions to a model of oriented loops on the lattice. This is done by first computing the explicit form of the fermion determinant in the…
We study the rank one completion problem for tensors of arbitrary orders. The notion of rank one determinable tensors is introduced. We explore its properties and propose a recursive algorithm for computing rank one tensor completion. This…
Fermionic linear optics corresponds to the dynamics of free fermions, and is known to be efficiently simulable classically. We define fermionic anyon models by deforming the fermionic algebra of creation and annihilation operators, and…
We formulate a model of relativistic fermions moving in two Euclidean dimensions based on a tight-binding model of graphene. The eigenvalue spectrum of the resulting Dirac operator is solved numerically in smooth U(1) gauge field…
This is a survey primarily about determining the border rank of tensors, especially those relevant for the study of the complexity of matrix multiplication. This is a subject that on the one hand is of great significance in theoretical…
We find that unitarity cuts and the duality between color and kinematics are sufficient constraints to bootstrap $D$-dimensional QCD scattering amplitudes starting from three-particle tree-level. Specifically, we calculate tree level…