Related papers: $\cal CPT$-invariant two-fermion Dirac equation wi…
This paper presents a twice continuously differentiable penalty function for nonlinear semidefinite programming problems. In some optimization methods, such as penalty methods and augmented Lagrangian methods, their convergence property can…
We study the part of the renormalized, cutoff QED light-front Hamiltonian that does not change particle number. The Hamiltonian contains interactions that must be treated in second-order bound state perturbation theory to obtain hyperfine…
We study continuum quantum field theories in 2+1 dimensions with time-reversal symmetry $\cal T$. The standard relation ${\cal T}^2=(-1)^F$ is satisfied on all the "perturbative operators" i.e. polynomials in the fundamental fields and…
We calculate by the method of dimensional regularization and derivative expansion the one-loop effective action for a Dirac fermion with a Lorentz-violating and CPT-odd kinetic term in the background of a gauge field. We show that this term…
We study a quantum phase transition of electrons on a two-dimensional square lattice. Our lattice model preserves the full $\mathrm{O}(4)$ symmetry of free spin-$\frac{1}{2}$ Dirac fermions on a bipartite lattice. In particular, it not only…
Recently, it was demonstrated that the discrepancy between the fixed-order (FOPT) and contour-improved (CIPT) perturbative expansions for $\tau$-lepton decay hadronic spectral function moments, which had been affecting the precision of…
Global conformal invariance determines the form of two and three-point functions of quasi-primary operators in a conformal field theory, and generates nontrivial relations between terms in the operator product expansion. These ideas are…
We invoke universal Chern-Simons theory to analytically calculate the exact free energy of the refined topological string on the resolved conifold. In the unrefined limit we reproduce non-perturbative corrections for the resolved conifold…
The Dirac electron in the organic conductor $\alpha$-(BEDT-TTF)$_2$I$_3$ under pressure is analyzed using a tight-binding model with nearest-neighbor transfer energies and four molecules per unit cell. By noting that the Dirac point between…
The Dirac equation with mass and axial chemical potential is solved analytically obtaining the mode spinors and corresponding projection operators giving the spectral representations of the principal conserved operators. In this framework,…
The conformal algebra provides powerful constraints, which guarantee that renormalized conformally covariant operators exist in the hypothetical conformal limit of the theory, where the $\beta$-function vanishes. Thus, in this limit also…
We calculate the anomalous dimensions of operators with large global charge $J$ in certain strongly coupled conformal field theories in three dimensions, such as the O(2) model and the supersymmetric fixed point with a single chiral…
The modified Dirac equations for the massive particles with the replacement of the physical mass $m$ with the help of the relation $m\rightarrow m_1+ \gamma_5 m_2$ are investigated. It is shown that for a fermion theory with a…
Within the pion-nucleon chiral perturbation theory we derive the leading chiral correction to the nucleon GPD at $\xi=0$. We discuss the difficulties of consideration of nonlocal light-cone operators within the theory with a heavy particle…
A method based on the Monte Carlo inversion of the Dirac operator on the lattice provides low noise results for the correlations entering the definition of the heavy meson decay constant in the static limit. The method is complementary to…
The derivation of combined prefactored compact schemes for first and second order derivatives is described here, relying on the Fourier analysis of the original prefactored compact schemes. By this approach, the order of accuracy of the…
The treatment of hypercubic lattice artifacts is essential for the calculation of non-perturbative renormalization constants of RI-MOM schemes. It has been shown that for the RI'-MOM scheme a large part of these artifacts can be calculated…
In this paper we study local Hamiltonian operators for multi-component evolutionary differential-difference equations. We address two main problems: the first one is the classification of low order operators for the two-component case. On…
The dual fermion (DF) method allows for calculating corrections due to non-local correlations relative to an effective impurity model. Choosing the impurity as that of a dynamical mean field theory (DMFT) solution at self-consistency is…
We present a continuum operator map that inverts the role of particles and antiparticles in three dimensional QED. This is accomplished by the attachment of specific holomorphic Wilson lines to Dirac fermions. We show that this nonlocal map…