Numerical simulations of PT-symmetric quantum field theories

Abstract

Many non-Hermitian but PT -symmetric theories are known to have a real positive spectrum. Since the action is complex for there theories, Monte Carlo methods do not apply. In this paper the first field-theoretic method for numerical simulations of PT -symmetric Hamiltonians is presented. The method is the complex Langevin equation, which has been used previously to study complex Hamiltonians in statistical physics and in Minkowski space. We compute the equal-time one-point and two-point Green's functions in zero and one dimension, where comparisons to known results can be made. The method should also be applicable in four-dimensional space-time. Our approach may also give insight into how to formulate a probabilistic interpretation of PTsymmetric theories.

Quark transverse charge densities in the from lattice QCD

“…8, the transverse densities of Eqs. (31,32) are compared for a ∆ + that has a transverse spin. It is seen that the quark charge density in a ∆ + in a state of transverse spin projection s ⊥ = +3/2 is elongated along the axis of the spin (prolate deformation) whereas in a state of transverse spin projection s ⊥ = +1/2 it is elongated along the axis perpendicular to the spin.…”

“…One notices from Eqs. (31,32) that the transverse charge densities display monopole, dipole, quadrupole, and octupole field patterns, which are determined by the helicity form factors with zero, one, two, or three units of helicity flip respectively between the initial and final ∆ states. It is instructive to evaluate the electric dipole moment (EDM) corresponding to the transverse charge densities ρ ∆ T s ⊥ , which is defined as :…”

“…For the valence quarks we use domain wall fermions (DWF) that preserve a form of chiral symmetry on the lattice. The domain wall quark mass takes the values given in Tables 1 and has been tuned by adjusting the lightest pseudoscalar meson in the Asqtad calculation [31] to have the same mass as the pseudoscalar meson using domain-wall fermions. Technical details of this tuning procedure are given in Refs.…”

“…Finally, in the SIM-III simulations, we use the following mixed action scheme. For the dynamical sea quarks, we use the staggered Asqtad action by the MILC collaboration [31] and include two degenerate flavors of light quarks plus strange quarks. The strange quark mass is fixed to the physical strange quark mass.…”

Semileptonic and decays in flavor lattice QCD

“…We use n f = 2 + 1 dynamical gauge configurations obtained with an improved staggered ("Asqtad") quark action on a lattice with a −1 ≈ 1.6 GeV, generated by the MILC collaboration [2]. To form the heavy-light bilinears from the staggered-type light quark and the Wilson-type heavy quark, we convert the staggered-type quark to the naive-type quark, as in Refs.…”