Related papers: Extended Projection Method for Massive Fermion
The short-range modes of the fermionic determinant can be absorbed in the gauge action using the loop expansion. The coefficients of this expansion and the zeroes of the polynomial approximating the remainder can be optimized by a simple,…
We consider one-loop scalar and tensor integrals with an arbitrary number of external legs relevant for multi-parton processes in massless theories. We present a procedure to reduce N-point scalar functions with generic 4-dimensional…
In this study, we address the challenge of solving elliptic equations with quasiperiodic coefficients. To achieve accurate and efficient computation, we introduce the projection method, which enables the embedding of quasiperiodic systems…
The staggered fermion approach to build models with chiral fermions is briefly reviewed. The method is tested in a U(1) model with axial vector coupling in two and four dimensions.
In this paper we study $p$-order methods for unconstrained minimization of convex functions that are $p$-times differentiable ($p\geq 2$) with $\nu$-H\"{o}lder continuous $p$th derivatives. We propose tensor schemes with and without…
We present a method for symbolic calculation of Feynman amplitudes for processes involving both massless and massive fermions. With this approach fermion strings in a specific amplitude can be easily evaluated and expressed as basic Lorentz…
An essential ingredient of a spectral method is the choice of suitable bases for test and trial spaces. On complex domains, these bases are harder to devise, necessitating the use of domain partitioning techniques such as the spectral…
The trace amplitude method (TAM) provides us a straightforward way to calculate the helicity amplitudes with massive fermions analytically. In this work, we review the basic idea of this method, and then discuss how it can be applied to…
Methods which aim at universal applicability must be able to describe both weak and strong electronic correlation with equal facility. Such methods are in short supply. The combination of symmetry projection for strong correlation and…
We introduce new methods for integrating nonlinear differential equations on low-rank manifolds. These methods rely on interpolatory projections onto the tangent space, enabling low-rank time integration of vector fields that can be…
The quadratic Casimir operator of the special unitary $SU(N)$ group is used to construct projection operators, which can decompose any of its reducible finite-dimensional representation spaces contained in the tensor product of two and…
A software library is presented for the polynomial expansion method (PEM) of the density of states (DOS) developed by two of the authors (N.F. and Y. M.). The library provides all necessary functions for the use of the PEM and its truncated…
This thesis discusses how the pure spinor formalism can be used to efficiently compute superstring scattering amplitudes. We emphasize the pure spinor superspace form of the kinematic factors, where the simplifying features of this language…
We design an efficient and balanced approach that captures major effects of collective electronic fluctuations in strongly correlated fermionic systems using a simple diagrammatic expansion on a basis of dynamical mean-field theory. For…
Random projection (RP) is a powerful dimension reduction technique widely used in the analysis of high dimensional data. We demonstrate how this technique can be used to improve the computational efficiency of gravitational wave searches…
The tensor contribution can be directly incorporated in the cluster model in a simplified way. In conventional $\alpha$ cluster models, the contribution of the non-central interactions exactly cancels because of the antisymmetrization…
Using the parallel/orthogonal space method, we calculate the planar two-loop three-point diagram and two rotated reduced planar two-loop three-point diagrams. Together with the crossed topology, these diagrams are the most complicated ones…
We outline two methods of constructing improved composite operators using Wilson fermions.
We present OPITeR, a FORM program for the reduction of multi-loop tensor Feynman integrals. The program can handle tensors, including spinor indices, with rank of up to 20 and can deal with up to 8 independent external momenta. The…
Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…