96 research outputs found
Substituting fields within the action: consistency issues and some applications
In field theory, as well as in mechanics, the substitution of some fields in
terms of other fields at the level of the action raises an issue of consistency
with respect to the equations of motion. We discuss this issue and give an
expression which neatly displays the difference between doing the substitution
at the level of the Lagrangian or at the level of the equations of motion. Both
operations do not commute in general. A very relevant exception is the case of
auxiliary variables, which are discussed in detail together with some of their
relevant applications. We discuss the conditions for the preservation of
symmetries - Noether as well as non-Noether - under the reduction of degrees of
freedom provided by the mechanism of substitution. We also examine how the
gauge fixing procedures fit in our framework and give simple examples on the
issue of consistency in this case.Comment: 17 page
Vector Correlators in Lattice QCD: methods and applications
We discuss the calculation of the leading hadronic vacuum polarization in
lattice QCD. Exploiting the excellent quality of the compiled experimental data
for the e^+e^- --> hadrons cross-section, we predict the outcome of
large-volume lattice calculations at the physical pion mass, and design
computational strategies for the lattice to have an impact on important
phenomenological quantities such as the leading hadronic contribution to
(g-2)mu and the running of the electromagnetic coupling constant. First, the
R(s) ratio can be calculated directly on the lattice in the threshold region,
and we provide the formulae to do so with twisted boundary conditions. Second,
the current correlator projected onto zero spatial momentum, in a Euclidean
time interval where it can be calculated accurately, provides a potentially
critical test of the experimental R(s) ratio in the region that is most
relevant for (g-2)mu. This observation can also be turned around: the vector
correlator at intermediate distances can be used to determine the lattice
spacing in fm, and we make a concrete proposal in this direction. Finally, we
quantify the finite-size effects on the current correlator coming from
low-energy two-pion states and provide a general parametrization of the vacuum
polarization on the torus.Comment: 16 pages, 9 figure files; corrected a factor 2 in Eq. (7) over the
published versio
Are there Local Minima in the Magnetic Monopole Potential in Compact QED?
We investigate the influence of the granularity of the lattice on the
potential between monopoles. Using the flux definition of monopoles we
introduce their centers of mass and are able to realize continuous shifts of
the monopole positions. We find periodic deviations from the -behavior of
the monopole-antimonopole potential leading to local extrema. We suppose that
these meta-stabilities may influence the order of the phase transition in
compact QED.Comment: 11 pages, 5 figure
Hadronic Contributions to the Muon Anomaly in the Constituent Chiral Quark Model
The hadronic contributions to the anomalous magnetic moment of the muon which
are relevant for the confrontation between theory and experiment at the present
level of accuracy, are evaluated within the same framework: the constituent
chiral quark model. This includes the contributions from the dominant hadronic
vacuum polarization as well as from the next--to--leading order hadronic vacuum
polarization, the contributions from the hadronic light-by-light scattering,
and the contributions from the electroweak hadronic vertex.
They are all evaluated as a function of only one free parameter: the
constituent quark mass. We also comment on the comparison between our results
and other phenomenological evaluations.Comment: Several misprints corrected and a clarifying sentence added. Three
figures superposed and two references added. Version to appear in JHE
High-statistics finite size scaling analysis of U(1) lattice gauge theory with Wilson action
We describe the results of a systematic high-statistics Monte-Carlo study of
finite-size effects at the phase transition of compact U(1) lattice gauge
theory with Wilson action on a hypercubic lattice with periodic boundary
conditions. We find unambiguously that the critical exponent nu is lattice-size
dependent for volumes ranging from 4^4 to 12^4. Asymptotic scaling formulas
yield values decreasing from nu(L >= 4) = 0.33 to nu(L >= 9) = 0.29. Our
statistics are sufficient to allow the study of different phenomenological
scenarios for the corrections to asymptotic scaling. We find evidence that
corrections to a first-order transition with nu=0.25 provide the most accurate
description of the data. However the corrections do not follow always the
expected first-order pattern of a series expansion in the inverse lattice
volume V^{-1}. Reaching the asymptotic regime will require lattice sizes
greater than L=12. Our conclusions are supported by the study of many cumulants
which all yield consistent results after proper interpretation.Comment: revtex, 12 pages, 9 figure
Non-Gaussian fixed point in four-dimensional pure compact U(1) gauge theory on the lattice
The line of phase transitions, separating the confinement and the Coulomb
phases in the four-dimensional pure compact U(1) gauge theory with extended
Wilson action, is reconsidered. We present new numerical evidence that a part
of this line, including the original Wilson action, is of second order. By
means of a high precision simulation on homogeneous lattices on a sphere we
find that along this line the scaling behavior is determined by one fixed point
with distinctly non-Gaussian critical exponent nu = 0.365(8). This makes the
existence of a nontrivial and nonasymptotically free four-dimensional pure U(1)
gauge theory in the continuum very probable. The universality and duality
arguments suggest that this conclusion holds also for the monopole loop gas,
for the noncompact abelian Higgs model at large negative squared bare mass, and
for the corresponding effective string theory.Comment: 11 pages, LaTeX, 2 figure
Probing the non-perturbative dynamics of SU(2) vacuum
The vacuum dynamics of SU(2) lattice gauge theory is studied by means of a
gauge-invariant effective action defined using the lattice Schr\"odinger
functional. Numerical simulations are performed both at zero and finite
temperature. The vacuum is probed using an external constant Abelian
chromomagnetic field. The results suggest that at zero temperature the external
field is screened in the continuum limit. On the other hand at finite
temperature it seems that confinement is restored by increasing the strength of
the applied field.Comment: 29 pages, 10 figures, LaTeX2
Perturbations of Self-Accelerated Universe
We discuss small perturbations on the self-accelerated solution of the DGP
model, and argue that claims of instability of the solution that are based on
linearized calculations are unwarranted because of the following: (1) Small
perturbations of an empty self-accelerated background can be quantized
consistently without yielding ghosts. (2) Conformal sources, such as radiation,
do not give rise to instabilities either. (3) A typical non-conformal source
could introduce ghosts in the linearized approximation and become unstable,
however, it also invalidates the approximation itself. Such a source creates a
halo of variable curvature that locally dominates over the self-accelerated
background and extends over a domain in which the linearization breaks down.
Perturbations that are valid outside the halo may not continue inside, as it is
suggested by some non-perturbative solutions. (4) In the Euclidean continuation
of the theory, with arbitrary sources, we derive certain constraints imposed by
the second order equations on first order perturbations, thus restricting the
linearized solutions that could be continued into the full nonlinear theory.
Naive linearized solutions fail to satisfy the above constraints. (5) Finally,
we clarify in detail subtleties associated with the boundary conditions and
analytic properties of the Green's functions.Comment: 39 LaTex page
Multicanonical Hybrid Monte Carlo: Boosting Simulations of Compact QED
We demonstrate that substantial progress can be achieved in the study of the
phase structure of 4-dimensional compact QED by a joint use of hybrid Monte
Carlo and multicanonical algorithms, through an efficient parallel
implementation. This is borne out by the observation of considerable speedup of
tunnelling between the metastable states, close to the phase transition, on the
Wilson line. We estimate that the creation of adequate samples (with order 100
flip-flops) becomes a matter of half a year's runtime at 2 Gflops sustained
performance for lattices of size up to 24^4.Comment: 15 pages, 8 figure
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