Related papers: Towards symmetric discretization schemes via weak …
We study and simulate N=2 supersymmetric Wess-Zumino models in one and two dimensions. For any choice of the lattice derivative, the theories can be made manifestly supersymmetric by adding appropriate improvement terms corresponding to…
Novel chirally symmetric fermion actions containing the minimum amount of fermion doubling have been recently proposed in the literature. We study the symmetries and renormalization of these actions and find that in each case, discrete…
We discuss possible definitions of discrete Dirac operators, and discuss their continuum limits. It is well-known in the lattice field theory that the straightforward discretization of the Dirac operator introduces unwanted spectral…
We address in this work the question of the discretization of two-dimensional periodic Dirac Hamiltonians. Standard finite differences methods on rectangular grids are plagued with the so-called Fermion doubling problem, which creates…
This paper deals with the Darcy-Forchheimer problem with two kinds of boundary conditions. We discretize the system by using the finite element methods and we propose two iterative schemes to solve the discrete problems. The well-posedness…
Two popular methods to reduce discretisation effects are Symanzik improvement and gauge field smearing in the Dirac operator. Tree-level $O(a^2)$-improved Wilson fermions can be obtained from $O(a)$-improved Wilson fermions by adding one…
To solve the Dirac equation with the finite difference method, one has to face up to the spurious-state problem due to the fermion doubling problem when using the conventional central difference formula to calculate the first-order…
A new formulation for fermions on the lattice based on a discretization of a second order formalism is proposed. A comparison with the first order formalism in connection with the $U(1)$ anomaly and the doubling problem is presented. The…
We study and simulate N=2 supersymmetric Wess-Zumino models in one and two dimensions. For any choice of the lattice derivative, the theories can be made manifestly supersymmetric by adding appropriate improvement terms corresponding to…
Recently several lattice collaborations have studied the scale dependence of the coupling in theories with different gauge groups and fermion representations using the Schr\"odinger functional method. This has motivated us to look at the…
Lattice simulations on SU(2) and SU(3) gauge theories with matter fields in the fundamental, adjoint and two index symmetric representations are needed to determine if these theories are near or within the conformal window as required for…
The Wilson formulation of fermions in lattice gauge theory provides a unified description of the chiral anomalies in the standard model. The discrete Dirac operator diagonalizes into a series of two by two blocks. In each block the possible…
The simulation of real-time dynamics in lattice gauge theories is particularly hard for classical computing due to the exponential scaling of the required resources. On the other hand, quantum algorithms can potentially perform the same…
We study a systematic improvement of perturbation theory for gauge fields on the lattice; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method, originally proposed…
A general framework is presented for the renormalization of Hamiltonians via a similarity transformation. Divergences in the similarity flow equations may be handled with dimensional regularization in this approach, and the resulting…
In this paper, by means of a standard model problem, we devise an approach to computing approximate dual bounds for use in global optimization of coefficient identification in partial differential equations (PDEs) by, e.g., (spatial)…
We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the…
We consider two-flavor QCD in the lattice regularization with improved Wilson fermions. In this formulation chiral symmetry is explicitly broken at order a and hence the isovector axial currents require improvement as well as a finite…
Quantum simulators have the exciting prospect of giving access to real-time dynamics of lattice gauge theories, in particular in regimes that are difficult to compute on classical computers. Future progress towards scalable quantum…
Motivated by the fact that both the classical and quantum description of nature rest on causality and a variational principle, we develop a novel and highly versatile discretization prescription for classical initial value problems (IVPs).…