99 research outputs found
Renormalization Group and Universality
It is argued that universality is severely limited for models with multiple
fixed points. As a demonstration the renormalization group equations are
presented for the potential and the wave function renormalization constants in
the scalar field theory. Our equations are superior compared with the
usual approach which retains only the contributions that are non-vanishing in
the ultraviolet regime. We find an indication for the existence of relevant
operators at the infrared fixed point, contrary to common expectations. This
result makes the sufficiency of using only renormalizable coupling constants in
parametrizing the long distance phenomena questionable.Comment: 32pp in plain tex; revised version to appear in PR
Non-perturbative thermal flows and resummations
We construct a functional renormalisation group for thermal fluctuations.
Thermal resummations are naturally built in, and the infrared problem of
thermal fluctuations is well under control. The viability of the approach is
exemplified for thermal scalar field theories. In gauge theories the present
setting allows for the construction of a gauge-invariant thermal
renormalisation group.Comment: 16 pages, eq (38) added to match published versio
Quantum phenomena inside a black hole: quantization of the scalar field iniside horizon in Schwarzschild spacetime
We discuss the problem of the quantization and dynamic evolution of a scalar
free field in the interior of a Schwarzschild black hole. A unitary approach to
the dynamics of the quantized field is proposed: a time-dependent Hamiltonian
governing the Heisenberg equations is derived. It is found that the system is
represented by a set of harmonic oscillators coupled via terms corresponding to
the creation and annihilation of pairs of particles and that the symmetry
properties of the spacetime, homogeneity and isotropy are obeyed by the
coupling terms in the Hamiltonian. It is shown that Heisenberg equations for
annihilation and creation operators are transformed into ordinary differential
equations for appropriate Bogolyubov coefficients. Such a formulation leads to
a general question concerning the possibility of gravitationally driven
instability, that is however excluded in this case.Comment: 12 page
Current-density functional for disordered systems
The effective action for the current and density is shown to satisfy an
evolution equation, the functional generalization of Callan-Symanzik equation.
The solution describes the dependence of the one-particle irreducible vertex
functions on the strength of the quenched disorder and the annealed Coulomb
interaction. The result is non-perturbative, no small parameter is assumed. The
a.c. conductivity is obtained by the numerical solution of the evolution
equation on finite lattices in the absence of the Coulomb interaction. The
static limit is performed and the conductivity is found to be vanishing beyond
a certain threshold of the impurity strength.Comment: final version, 28 pages, 17 figures, to appear in Phys. Rev.
Chronological Inversion Method for the Dirac Matrix in Hybrid Monte Carlo
In Hybrid Monte Carlo simulations for full QCD, the gauge fields evolve
smoothly as a function of Molecular Dynamics time. Here we investigate improved
methods of estimating the trial or starting solutions for the Dirac matrix
inversion as superpositions of a chronological sequence of solutions in the
recent past. By taking as the trial solution the vector which minimizes the
residual in the linear space spanned by the past solutions, the number of
conjugate gradient iterations per unit MD time is decreased by at least a
factor of 2. Extensions of this basic approach to precondition the conjugate
gradient iterations are also discussed.Comment: 35 pages, 18 EPS figures A new "preconditioning" method, derived from
the Chronological Inversion, is described. Some new figures are appended.
Some reorganization of the material has taken plac
From quantum to classical dynamics: The relativistic model in the framework of the real-time functional renormalization group
We investigate the transition from unitary to dissipative dynamics in the
relativistic vector model with the
interaction using the nonperturbative functional renormalization group in the
real-time formalism. In thermal equilibrium, the theory is characterized by two
scales, the interaction range for coherent scattering of particles and the mean
free path determined by the rate of incoherent collisions with excitations in
the thermal medium. Their competition determines the renormalization group flow
and the effective dynamics of the model. Here we quantify the dynamic
properties of the model in terms of the scale-dependent dynamic critical
exponent in the limit of large temperatures and in
spatial dimensions. We contrast our results to the behavior expected at
vanishing temperature and address the question of the appropriate dynamic
universality class for the given microscopic theory.Comment: 32 pages, 12 captioned figures; revised and extended version accepted
for publication in PR
The antiferromagnetic phi4 Model, II. The one-loop renormalization
It is shown that the four dimensional antiferromagnetic lattice phi4 model
has the usual non-asymptotically free scaling law in the UV regime around the
chiral symmetrical critical point. The theory describes a scalar and a
pseudoscalar particle. A continuum effective theory is derived for low
energies. A possibility of constructing a model with a single chiral boson is
mentioned.Comment: To appear in Phys. Rev.
Staggered versus overlap fermions: a study in the Schwinger model with
We study the scalar condensate and the topological susceptibility for a
continuous range of quark masses in the Schwinger model with
dynamical flavors, using both the overlap and the staggered discretization. At
finite lattice spacing the differences between the two formulations become
rather dramatic near the chiral limit, but they get severely reduced, at the
coupling considered, after a few smearing steps.Comment: 15 pages, 7 figures, v2: 1 ref corrected, minor change
Chiral Symmetry Restoration at Finite Temperature and Chemical Potential in the Improved Ladder Approximation
The chiral symmetry of QCD is studied at finite temperature and chemical
potential using the Schwinger-Dyson equation in the improved ladder
approximation. We calculate three order parameters; the vacuum expectation
value of the quark bilinear operator, the pion decay constant and the quark
mass gap. We have a second order phase transition at the temperature
MeV along the zero chemical potential line, and a first order phase transition
at the chemical potential MeV along the zero temperature line. We
also calculate the critical exponents of the three order parameters.Comment: 16 pages + 10 uuencoded eps figures, LaTe
Invariant measure in hot gauge theories
We investigate properties of the invariant measure for the gauge field
in finite temperature gauge theories both on the lattice and in the continuum
theory. We have found the cancellation of the naive measure in both cases. The
result is quite general and holds at any finite temperature. We demonstrate,
however, that there is no cancellation at any temperature for the invariant
measure contribution understood as Z(N) symmetrical distribution of gauge field
configurations. The spontaneous breakdown of Z(N) global symmetry is entirely
due to the potential energy term of the gluonic interaction in the effective
potential. The effects of this measure on the effective action, mechanism of
confinement and condensation are discussed.Comment: Latex file, 65.5kB, no figure
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