We discuss the anomaly in the axial vector current for the improved fermion action on the lattice. A detailed discussion of the fermion regularization dependence of the anomaly is given and it is shown that for finite lattice spacing the improved fermion action gives a more reasonable value for the anomaly contribution at finite quark mass than the Wilson action. We also present some results on...

We investigate multipartite entanglement in a noninteracting fermion gas, as a function of fermion separation, starting from the many particle fermion density matrix. We prove that all multiparticle entanglement can be built only out of two-fermion entanglement. Although from the Pauli exclusion principle we would always expect entanglement to decrease with fermion distance, we surprisingly fin...

We consider a dilute homogeneous mixture of bosons and spin-polarized fermions at zero temperature. We first construct the formal scheme for carrying out systematic perturbation theory in terms of single particle Green’s functions. We especially focus on the description of the boson-fermion interaction. To do so we need to introduce a new relevant object, the renormalized boson-fermion T -matri...

A complete study of QCD on the lattice requires the numerical simulation of dynamical fermions. These Monte Carlo calculations are extremely computationally costly, since the effects of quarks must be included by first integrating out the fermion path integral, and then describing the resulting non-local dynamics of the fermion determinant. For a review of recent developments, see e.g. [1, 2]. ...

We discuss the renormalizability of the massless Thirring model in terms of the causal fermion Green functions and correlation functions of left—right fermion densities. We obtain the most general solution of the massless Thirring model with dynamical dimensions of fermion fields, parameterized by two arbitrary parameters. We show that in the massless Thirring model there are no solutions which...

The dynamically generated fermion mass is investigated in the flat brane world with (4 + δ)-dimensional bulk space-time, and in the Randall-Sundrum (RS) brane world. We consider the bulk Yang-Mills theory interacting with the fermion confined on a fourdimensional brane. Based on the effective theory below the reduced cutoff scale on the brane, we formulate the Schwinger-Dyson equation of the br...

This paper is based on four lectures given at the Trieste Summer School 1994 on theories of fermion masses. The first two lectures introduce three mechanisms which have been used to construct models of fermion masses. We then discuss some recent applications of these ideas. In the last lecture we briefly review SO(10) and some predictive theories of fermion masses.

SSOR preconditioning of fermion matrix inversions which is parallelized using a locally-lexicographic lattice sub-division has been shown to be very efficient for standard Wilson fermions. We demonstrate here the power of this method for the Sheikholeslami-Wohlert improved fermion action and for a renormalization group improved action incorporating couplings of the lattice fermion fields up to ...