Comparing the R algorithm and RHMC for staggered fermions

The R algorithm is widely used for simulating two flavours of dynamical staggered fermions. We give a simple proof that the algorithm converges to the desired probability distribution to within O(dt^2) errors, but show that the relevant expansion parameter is (dt/m)^2, m being the quark mass. The Rational Hybrid Monte Carlo (RHMC) algorithm provides an exact (i.e., has no step size errors) alternative for simulating the square root of the staggered Dirac operator. We propose using it to test the validity of the R algorithm for simulations carried out with dt m.Comment: 3 pages, proceedings from Lattice 2002 poster presentatio

Recent results from systematic parameterizations of Ginsparg-Wilson fermions

The Fixed Point Dirac Operator and Chirally Improved Fermions both use large numbers of gauge paths and the full Dirac structure to approximate a solution of the Ginsparg-Wilson equation. After a brief review of the two approaches we present recent results for quenched QCD with pion masses down to 210 MeV. We discuss the limits and advantages of approximate parameterizations and outline future perspectives.Comment: Lattice2002(plenary). References and Fig. 5 updated. Final version submitted to the proceeding

A brief review on the Problem of Divergence in Krein Space Quantization

In this paper we have a brief review on the problem of divergence in quantum field theory and its elimination using the method of Krein space quantization. In this method, the auxiliary negative frequency states have been utilized, the modes of which do not interact with the physical states and are not affected by the physical boundary conditions. It is remarkable that Krein space quantization is similar to Pauli-Villars regularization, so we can call it the "Krein regularization". Considering the QED in Krein space quantization, it could be shown that the theory is automatically regularized. Calculation of the three primitive divergent integrals, the vacuum polarization, electron self energy and vertex function using Krein space method leads to finite values, since the infrared and ultraviolet divergencies do not appear. For another example, the Casimir stress on a spherical shell in de Sitter spacetime for a massless scalar field could be calculated using Krein space quantization.Comment: 6 pages, no figures. arXiv admin note: text overlap with arXiv:1109.2693, arXiv:hep-th/0511077 by other author

Topological Charge Correlators, Spectral Bounds, and Contact Terms

The structure of topological charge fluctuations in the QCD vacuum is strongly restricted by the spectral negativity of the Euclidean 2-point correlator for $x\neq 0$ and the presence of a positive contact term. Some examples are considered which illustrate the physical origin of these properties.Comment: Lattice 2002 Conference Proceeding

Krein Regularization of \lambda\phi^4

We calculate the four-point function in \lambda\phi^4 theory by using Krein regularization and compare our result, which is finite, with the usual result in \lambda\phi^4 theory. The effective coupling constant (\lambda_\mu) is also calculated in this method