827 research outputs found
Lattice QCD-2+1
We consider a 2+1-dimensional SU(N) lattice gauge theory in an axial gauge
with the link field U in the 1-direction set to one. The term in the
Hamiltonian containing the square of the electric field in the 1-direction is
non-local. Despite this non-locality, we show that weak-coupling perturbation
theory in this term gives a finite vacuum-energy density to second order, and
suggest that this property holds to all orders. Heavy quarks are confined, the
spectrum is gapped, and the space-like Wilson loop has area decay.Comment: Still Latex, 18 pages, no figures, with some further typographical
errors corrected. Version to appear in Phys. Rev.
The rooting issue for a lattice fermion formulation similar to staggered fermions but without taste mixing
To investigate the viability of the 4th root trick for the staggered fermion
determinant in a simpler setting, we consider a two taste (flavor) lattice
fermion formulation with no taste mixing but with exact taste-nonsinglet chiral
symmetries analogous to the taste-nonsinglet symmetry of staggered
fermions. M. Creutz's objections to the rooting trick apply just as much in
this setting. To counter them we show that the formulation has robust would-be
zero-modes in topologically nontrivial gauge backgrounds, and that these
manifest themselves in a viable way in the rooted fermion determinant and also
in the disconnected piece of the pseudoscalar meson propagator as required to
solve the U(1) problem. Also, our rooted theory is heuristically seen to be in
the right universality class for QCD if the same is true for an unrooted mixed
fermion action theory.Comment: 22 revtex pages, to appear in PRD. v4: correction in the relation of
the 2-flavor theory to twisted mass fermion
High Energy Physics from High Performance Computing
We discuss Quantum Chromodynamics calculations using the lattice regulator.
The theory of the strong force is a cornerstone of the Standard Model of
particle physics. We present USQCD collaboration results obtained on Argonne
National Lab's Intrepid supercomputer that deepen our understanding of these
fundamental theories of Nature and provide critical support to frontier
particle physics experiments and phenomenology.Comment: Proceedings of invited plenary talk given at SciDAC 2009, San Diego,
June 14-18, 2009, on behalf of the USQCD collaboratio
A further study of the possible scaling region of lattice chiral fermions
In the possible scaling region for an SU(2) lattice chiral fermion advocated
in {\it Nucl. Phys.} B486 (1997) 282, no hard spontaneous symmetry breaking
occurs and doublers are gauge-invariantly decoupled via mixing with composite
three-fermion-states that are formed by local multifermion interactions.
However the strong coupling expansion breaks down due to no ``static limit''
for the low-energy limit (). In both neutral and charged channels, we
further analyze relevant truncated Green functions of three-fermion-operators
by the strong coupling expansion and analytical continuation of these Green
functions in the momentum space. It is shown that in the low-energy limit,
these relevant truncated Green functions of three-fermion-states with the
``wrong'' chiralities positively vanish due to the generalized form factors
(the wave-function renormalizations) of these composite three-fermion-states
vanishing as O((pa)^4) for . This strongly implies that the composite
three-fermion-states with ``wrong'' chirality are ``decoupled'' in this limit
and the low-energy spectrum is chiral, as a consequence, chiral gauge
symmetries can be exactly preserved.Comment: A few typing-errors, in particular in Eq.50, have been correcte
On Flavor Symmetry in Lattice Quantum Chromodynamics
Using a well established method to engineer non abelian symmetries in
superstring compactifications, we study the link between the point splitting
method of Creutz et al of refs [1,2] for implementing flavor symmetry in
lattice QCD; and singularity theory in complex algebraic geometry. We show
amongst others that Creutz flavors for naive fermions are intimately related
with toric singularities of a class of complex Kahler manifolds that are
explicitly built here. In the case of naive fermions of QCD, Creutz
flavors are shown to live at the poles of real 2-spheres and carry quantum
charges of the fundamental of . We show moreover that the two
Creutz flavors in Karsten-Wilczek model, with Dirac operator in reciprocal
space of the form , are related with the small resolution of conifold
singularity that live at . Other related features are also
studied.Comment: LaTex, 40 pages, 8 figure
Lattice methods and the nuclear few- and many-body problem
We begin with a brief overview of lattice calculations using chiral effective
field theory and some recent applications. We then describe several methods for
computing scattering on the lattice. After that we focus on the main goal,
explaining the theory and algorithms relevant to lattice simulations of nuclear
few- and many-body systems. We discuss the exact equivalence of four different
lattice formalisms, the Grassmann path integral, transfer matrix operator,
Grassmann path integral with auxiliary fields, and transfer matrix operator
with auxiliary fields. Along with our analysis we include several coding
examples and a number of exercises for the calculations of few- and many-body
systems at leading order in chiral effective field theory.Comment: 20 pages, 3 figures, Submitted to Lect. Notes Phys., "An advanced
course in computational nuclear physics: Bridging the scales from quarks to
neutron stars", M. Hjorth-Jensen, M. P. Lombardo, U. van Kolck, Editor
Integrable Models and Confinement in (2+1)-Dimensional Weakly-Coupled Yang-Mills Theory
We generalize the (2+1)-dimensional Yang-Mills theory to an anisotropic form
with two gauge coupling constants and . In an axial gauge, a
regularized version of the Hamiltonian of this gauge theory is
, where is the Hamiltonian of a set of
(1+1)-dimensional principal chiral nonlinear sigma models. We treat as
the interaction Hamiltonian. For gauge group SU(2), we use form factors of the
currents of the principal chiral sigma models to compute the string tension for
small , after reviewing exact S-matrix and form-factor methods. In
the anisotropic regime, the dependence of the string tension on the coupling
constant is not in accord with generally-accepted dimensional arguments.Comment: Now 37 pages, Section 5 moved to an appendix, more motivation given
in the introduction, a few more typos correcte
Temperature in Fermion Systems and the Chiral Fermion Determinant
We give an interpretation to the issue of the chiral determinant in the
heat-kernel approach. The extra dimension (5-th dimension) is interpreted as
(inverse) temperature. The 1+4 dim Dirac equation is naturally derived by the
Wick rotation for the temperature. In order to define a ``good'' temperature,
we choose those solutions of the Dirac equation which propagate in a fixed
direction in the extra coordinate. This choice fixes the regularization of the
fermion determinant. The 1+4 dimensional Dirac mass () is naturally
introduced and the relation: 4 dim electron momentum
ultraviolet cut-off, naturally appears. The chiral anomaly is explicitly
derived for the 2 dim Abelian model. Typically two different regularizations
appear depending on the choice of propagators. One corresponds to the chiral
theory, the other to the non-chiral (hermitian) theory.Comment: 24 pages, some figures, to be published in Phys.Rev.
Species Doubling and Chiral Lagrangians
Coupling gauge fields to the chiral currents from an effective Lagrangian for
pseudoscalar mesons naturally gives rise to a species doubling phenomenon
similar to that seen with fermionic fields in lattice gauge theory.Comment: 11 pages, revte
Lattice Discretization in Quantum Scattering
The utility of lattice discretization technique is demonstrated for solving
nonrelativistic quantum scattering problems and specially for the treatment of
ultraviolet divergences in these problems with some potentials singular at the
origin in two and three space dimensions. This shows that lattice
discretization technique could be a useful tool for the numerical solution of
scattering problems in general. The approach is illustrated in the case of the
Dirac delta function potential.Comment: 9 page
- …