Related papers: Schroedinger functional formalism with domain-wall…
After reviewing the problematic behavior of some previously suggested finite interval spatial operators of the symmetric Riesz type, we create a wish list leading toward a new spatial operator suitable to use in the space-time fractional…
We present a consistent fusion of functional renormalization group and mean-field theory which explicitly introduces a bosonic field via a Hubbard-Stratonovich transformation at the critical scale, at which the order sets in. We show that a…
Here we understand \textit{dimensional reduction} as a procedure to obtain an effective model in $D-1$ dimensions that is related to the original model in $D$ dimensions. To explore this concept we use both a self-interacting fermionic…
The efficient encoding of the fermionic Schr\"odinger equation as a spin system Hamiltonian is a long-term problem. I describe an encoding for the fermionic position space Schr\"odinger equation on a finite-volume periodic lattice with a…
The recently proposed construction of chiral fermions on lattices with boundaries is tested in an interacting theory up to first order of perturbation theory. We confirm that, in the bulk of the lattice, the chiral Ward identities take…
We perform a non-perturbative study of the scale-dependent renormalization factors of a multiplicatively renormalizable basis of $\Delta{B}=2$ parity-odd four-fermion operators in quenched lattice QCD. Heavy quarks are treated in the static…
We address the issue of the relation between the canonical functional Schr\"odinger representation in quantum field theory and the approach of precanonical field quantization proposed by the author, which requires neither a distinguished…
We show that it is possible to use dimensional regularization (DR) beyond the usual $\varepsilon$-expansion in the context of renormalization group (RG) calculations in Critical Phenomena. Based on this fact, we propose a new functional RG…
The solution of partial differential equations (PDEs) on complex domains often presents a significant computational challenge by requiring the generation of fitted meshes. The Diffuse Domain Method (DDM) is an alternative which reformulates…
The chirally rotated Schroedinger functional provides a test bed for universality and automatic O(a) improvement. We here report on extensive quenched simulations of lattice QCD with Wilson quarks in the massless limit. We demonstrate that,…
Background field method is used to perform renormalization group transformations for Schr\"odinger equation in QCD. The dependence of the ground state wave functional on rapidly oscillating fields is found.
We investigate the eigenvalues of nearly chiral lattice Dirac operators constructed with five-dimensional implementations. Allowing small violation of the Ginsparg-Wilson relation, the HMC simulation is made much faster while the…
The inverse of the fermion matrix squared is used to define a transfer matrix for domain-wall fermions. When the domain-wall height $M$ is bigger than one, the transfer matrix is complex. Slowly suppressed chiral symmetry violations may…
The semi-analytical wall boundary conditions present a mathematically rigorous framework to prescribe the influence of solid walls in SPH for fluid flows. In this paper they are investigated with respect to the skew-adjoint property which…
We construct domain wall fermions with a staggered kernel and investigate their spectral and chiral properties numerically in the Schwinger model. In some relevant cases we see an improvement of chirality by more than an order of magnitude…
We present work in progress on employing domain wall fermions to simulate N=1 supersymmetric Yang-Mills theories on the lattice in d=4 and d=3 dimensions. The geometrical nature of domain wall fermions gives simple insights into how to…
Density functional theory (DFT) is an indispensable ab initio method in both quantum chemistry and condensed matter physics. Based on recent advancements in reduced density matrix functional theory (RDMFT), a variant of DFT that is believed…
We consider the (2n+1)-dimensional euclidean Dirac operator with a mass term that looks like a domain wall, recently proposed by Kaplan to describe chiral fermions in $2n$ dimensions. In the continuum case we show that the euclidean…
Motivated by the paraxial narrow-angle approximation of the Helmholtz equation in domains of variable topography that appears as an important application in Underwater Acoustics, we analyze a general Schr\"odinger-type equation posed on…
We investigate the interaction of fermion fields with oscillating domain walls, inspired by breather-type solutions of the sine-Gordon equation, a nonlinear system of fundamental importance. Our study focuses on the fermionic bound states…