93 research outputs found
The Landau Pole at Finite Temperature
We study the Landau pole in the lambda phi^4 field theory at non-zero and
large temperatures. We show that the position of the thermal Landau pole
Lambda_L(T) is shifted to higher energies with respect to the zero temperature
Landau pole Lambda_L(0). We find for high temperatures T > Lambda_L(0),
Lambda_L(T) simeq pi^2 T / log (T / Lambda_L(0)). Therefore, the range of
applicability in energy of the lambda phi^4 field theory increases with the
temperature.Comment: LaTex, 6 pages, 2 .ps figures. Improved version. To appear in Phys.
Rev. D, Rapid Communication
Infrared Behaviour of Systems With Goldstone Bosons
We develop various complementary concepts and techniques for handling quantum
fluctuations of Goldstone bosons.We emphasise that one of the consequences of
the masslessness of Goldstone bosons is that the longitudinal fluctuations also
have a diverging susceptibility characterised by an anomalous dimension
in space-time dimensions .In these fluctuations diverge
logarithmically in the infrared region.We show the generality of this
phenomenon by providing three arguments based on i). Renormalization group
flows, ii). Ward identities, and iii). Schwinger-Dyson equations.We obtain an
explicit form for the generating functional of one-particle irreducible
vertices of the O(N) (non)--linear --models in the leading 1/N
approximation.We show that this incorporates all infrared behaviour correctly
both in linear and non-linear -- models. Our techniques provide an
alternative to chiral perturbation theory.Some consequences are discussed
briefly.Comment: 28 pages,2 Figs, a new section on some universal features of
multipion processes has been adde
Dynamical Mass Generation in a Finite-Temperature Abelian Gauge Theory
We write down the gap equation for the fermion self-energy in a
finite-temperature abelian gauge theory in three dimensions. The instantaneous
approximation is relaxed, momentum-dependent fermion and photon self-energies
are considered, and the corresponding Schwinger-Dyson equation is solved
numerically. The relation between the zero-momentum and zero-temperature
fermion self-energy and the critical temperature T_c, above which there is no
dynamical mass generation, is then studied. We also investigate the effect
which the number of fermion flavours N_f has on the results, and we give the
phase diagram of the theory with respect to T and N_f.Comment: 20 LaTeX pages, 4 postscript figures in a single file, version to
appear in Physical Review
Fermion-scalar interactions with domain wall fermions
Domain wall fermions are defined on a lattice with an extra direction the
size of which controls the chiral properties of the theory. When gauge fields
are coupled to domain wall fermions the extra direction is treated as an
internal flavor space. Here it is found that this is not the case for scalar
fields. Instead, the interaction takes place only along the link that connects
the boundaries of the extra direction. This reveals a richness in the way
different spin particles are coupled to domain wall fermions. As an
application, 4-Fermi models are studied using large N techniques and the
results are supported by numerical simulations with N=2. It is found that the
chiral properties of domain wall fermions in these models are good across a
large range of couplings and that a phase with parity-flavor broken symmetry
can develop for negative bare masses if the number of sites along the extra
direction is finite.Comment: LaTeX, 17 pages, 8 eps figures; comment regarding the width of Aoki
phase added in sec. 3; references adde
Chiral transition and monopole percolation in lattice scalar QED with quenched fermions
We study the interplay between topological observables and chiral and Higgs
transitions in lattice scalar QED with quenched fermions. Emphasis is put on
the chiral transition line and magnetic monopole percolation at strong gauge
coupling. We confirm that at infinite gauge coupling the chiral transition is
described by mean field exponents. We find a rich and complicated behaviour at
the endpoint of the Higgs transition line which hampers a satisfactory analysis
of the chiral transition. We study in detail an intermediate coupling, where
the data are consistent both with a trivial chiral transition clearly separated
from monopole percolation and with a chiral transition coincident with monopole
percolation, and characterized by the same critical exponent .
We discuss the relevance (or lack thereof) of these quenched results to our
understanding of the \chupiv\ model. We comment on the interplay of magnetic
monopoles and fermion dynamics in more general contexts.Comment: 29 pages, 13 figures included, LaTeX2e (elsart
Regularization-independent study of renormalized non-perturbative quenched QED
A recently proposed regularization-independent method is used for the first
time to solve the renormalized fermion Schwinger-Dyson equation numerically in
quenched QED. The Curtis-Pennington vertex is used to illustrate the
technique and to facilitate comparison with previous calculations which used
the alternative regularization schemes of modified ultraviolet cut-off and
dimensional regularization. Our new results are in excellent numerical
agreement with these, and so we can now conclude with confidence that there is
no residual regularization dependence in these results. Moreover, from a
computational point of view the regularization independent method has enormous
advantages, since all integrals are absolutely convergent by construction, and
so do not mix small and arbitrarily large momentum scales. We analytically
predict power law behaviour in the asymptotic region, which is confirmed
numerically with high precision. The successful demonstration of this efficient
new technique opens the way for studies of unquenched QED to be undertaken in
the near future.Comment: 20 pages,5 figure
On Nonperturbative Calculations in Quantum Electrodynamics
A new approach to nonperturbative calculations in quantum electrodynamics is
proposed. The approach is based on a regular iteration scheme for solution of
Schwinger-Dyson equations for generating functional of Green functions. The
approach allows one to take into account the gauge invariance conditions (Ward
identities) and to perform the renormalization program. The iteration scheme
can be realized in two versions. The first one ("perturbative vacuum")
corresponds to chain summation in the diagram language. In this version in
four-dimensional theory the non-physical singularity (Landau pole) arises which
leads to the triviality of the renormalized theory. The second version
("nonperturbative vacuum") corresponds to ladder summation and permits one to
make non-perturbative calculations of physical quantities in spite of the
triviality problem. For chiral-symmetrical leading approximation two terms of
the expansion of the first-step vertex function over photon momentum are
calculated. A formula for anomalous magnetic moment is obtained. A problem of
dynamical chiral symmetry breaking (DCSB) is considered, the calculations are
performed for renormalized theory in Minkowsky space. In the strong coupling
region DCSB-solutions arise. For the renormalized theory a DCSB-solution is
also possible in the weak coupling region but with a subsidiary condition on
the value of .Comment: 31 pages, Plain LaTex, no figures. Journal version: some discussion
and refs. are adde
The instanton liquid in QCD at zero and finite temperature
In this paper we study the statistical mechanics of the instanton liquid in
QCD. After introducing the partition function as well as the gauge field and
quark induced interactions between instantons we describe a method to calculate
the free energy of the instanton system. We use this method to determine the
equilibrium density and the equation of state from numerical simulations of the
instanton ensemble in QCD for various numbers of flavors. We find that there is
a critical number of flavors above which chiral symmetry is restored in the
groundstate. In the physical case of two light and one intermediate mass flavor
the system undergoes a chiral phase transition at MeV. We show
that the mechanism for this transition is a rearrangement of the instanton
liquid, going from a disordered, random, phase at low temperatures to a
strongly correlated, molecular, phase at high temperature. We also study the
behavior of mesonic susceptibilities near the phase transition.Comment: 50 pages, revtex, 16 figures, uuencode
Deviations from Fermi-Liquid behaviour in (2+1)-dimensional Quantum Electrodynamics and the normal phase of high- Superconductors
We argue that the gauge-fermion interaction in multiflavour quantum
electrodynamics in -dimensions is responsible for non-fermi liquid
behaviour in the infrared, in the sense of leading to the existence of a
non-trivial (quasi) fixed point that lies between the trivial fixed point (at
infinite momenta) and the region where dynamical symmetry breaking and mass
generation occurs. This quasi-fixed point structure implies slowly varying,
rather than fixed, couplings in the intermediate regime of momenta, a situation
which resembles that of (four-dimensional) `walking technicolour' models of
particle physics. The inclusion of wave-function renormalization yields
marginal -corrections to the `bulk' non-fermi liquid behaviour caused
by the gauge interaction in the limit of infinite flavour number. Such
corrections lead to the appearance of modified critical exponents. In
particular, at low temperatures there appear to be logarithmic scaling
violations of the linear resistivity of the system of order .
Connection with the anomalous normal-state properties of certain condensed
matter systems relevant for high-temperature superconductivity is briefly
discussed. The relevance of the large (flavour) expansion to the
fermi-liquid problem is emphasized. As a partial result of our analysis, we
point out the absence of Charge-Density-Wave Instabilities from the effective
low-energy theory, as a consequence of gauge invariance.Comment: Latex file, 35 pages, Two figures not included, available upon
reques
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