31 research outputs found
The Schwinger Model on a circle: relation between Path Integral and Hamiltonian approaches
We solve the massless Schwinger model exactly in Hamiltonian formalism on a
circle. We construct physical states explicitly and discuss the role of the
spectral flow and nonperturbative vacua. Different thermodynamical correlation
functions are calculated and after performing the analytical continuation are
compared with the corresponding expressions obtained for the Schwinger model on
the torus in Euclidean Path Integral formalism obtained before.Comment: 40 page
The General Correlation Function in the Schwinger Model on a Torus
In the framework of the Euclidean path integral approach we derive the exact
formula for the general N-point chiral densities correlator in the Schwinger
model on a torusComment: 17 pages, misprints corrected, references adde
Witten-Veneziano Relation for the Schwinger Model
The Witten-Veneziano relation between the topological susceptibility of puregauge theories without fermions and the main contribution of the completetheory and the corresponding formula of Seiler and Stamatescu with theso-called contact term are discussed for the Schwinger model on a circle. Usingthe (Euclidean) path integral and the canonical (Hamiltonian) approaches atfinite temperatures we demonstrate that both formulae give the same result inthe limit of infinite volume and (or) zero temperature
Some more remarks on the Witten-Veneziano formula for the mass
We discuss some subtleties in connection with the new attempts to provide a
firm basis for ths Witten-Veneziano formula.Comment: 9 page
Chiral crystals in strong-coupling lattice QCD at nonzero chemical potential
We study the effective action for strong-coupling lattice QCD with
one-component staggered fermions in the case of nonzero chemical potential and
zero temperature. The structure of this action suggests that at large chemical
potentials its ground state is a crystalline `chiral density wave' that
spontaneously breaks chiral symmetry and translation invariance. In mean-field
theory, on the other hand, we find that this state is unstable. We show that
lattice artifacts are partly responsible for this, and suggest that if this
phase exists in QCD, then finding it in Monte-Carlo simulations would require
simulating on relatively fine lattices. In particular, the baryon mass in
lattice units, m_B, should be considerably smaller than its strong-coupling
limit of m_B~3.Comment: 33 pages, 8 figure
Remarks on the thermodynamics and the vacuum energy of a quantum Maxwell gas on compact and closed manifolds
The quantum Maxwell theory at finite temperature at equilibrium is studied on
compact and closed manifolds in both the functional integral- and Hamiltonian
formalism. The aim is to shed some light onto the interrelation between the
topology of the spatial background and the thermodynamic properties of the
system. The quantization is not unique and gives rise to inequivalent quantum
theories which are classified by {\theta}-vacua. Based on explicit
parametrizations of the gauge orbit space in the functional integral approach
and of the physical phase space in the canonical quantization scheme, the
Gribov problem is resolved and the equivalence of both quantization schemes is
elucidated. Using zeta-function regularization the free energy is determined
and the effect of the topology of the spatial manifold on the vacuum energy and
on the thermal gauge field excitations is clarified. The general results are
then applied to a quantum Maxwell gas on a n-dimensional torus providing
explicit formulae for the main thermodynamic functions in the low- and high
temperature regimes, respectively.Comment: 41 page
Four-point Green functions in the Schwinger Model
The evaluation of the 4-point Green functions in the 1+1 Schwinger model is
presented both in momentum and coordinate space representations. The crucial
role in our calculations play two Ward identities: i) the standard one, and ii)
the chiral one. We demonstrate how the infinite set of Dyson-Schwinger
equations is simplified, and is so reduced, that a given n-point Green function
is expressed only through itself and lower ones. For the 4-point Green
function, with two bosonic and two fermionic external `legs', a compact
solution is given both in momentum and coordinate space representations. For
the 4-fermion Green function a selfconsistent equation is written down in the
momentum representation and a concrete solution is given in the coordinate
space. This exact solution is further analyzed and we show that it contains a
pole corresponding to the Schwinger boson. All detailed considerations given
for various 4-point Green functions are easily generizable to higher functions.Comment: In Revtex, 12 pages + 2 PostScript figure
Bosonization in Particle Physics
Path integral techniques in collective fields are shown to be a useful
analytical tool to reformulate a field theory defined in terms of microscopic
quark (gluon) degrees of freedom as an effective theory of collective boson
(meson) fields. For illustrations, the path integral bosonization approach is
applied to derive a (non)linear sigma model from a Nambu-Jona-Lasinio (NJL)
quark model. The method can be extended to include higher order derivative
terms in meson fields or heavy-quark symmetries. It is also approximately
applicable to QCD.Comment: 12 pages, LaTeX, uses lamuphys.sty, 5 LaTeX figures, talk given at
the Workshop "Field Theoretical Tools in Polymer and Particle Physics",
University Wuppertal, June 17-19, 199
Fermi-Einstein condensation in dense QCD-like theories
While pure Yang-Mills theory feature the centre symmetry, this symmetry is
explicitly broken by the presence of dynamical matter. We study the impact of
the centre symmetry in such QCD-like theories. In the analytically solvable
Schwinger model, centre transitions take place even under extreme conditions,
temperature and/or density, and we show that they are key to the solution of
the Silver-Blaze problem. We then develop an effective SU(3) quark model which
confines quarks by virtue of centre sector transitions. The phase diagram by
confinement is obtained as a function of the temperature and the chemical
potential. We show that at low temperatures and intermediate values for the
chemical potential the centre dressed quarks undergo condensation due to Bose
like statistics. This is the Fermi Einstein condensation. To corroborate the
existence of centre sector transitions in gauge theories with matter, we study
(at vanishing chemical potential) the interface tension in the
three-dimensional Z2 gauge theory with Ising matter, the distribution of the
Polyakov line in the four-dimensional SU(2)-Higgs model and devise a new type
of order parameter which is designed to detect centre sector transitions. Our
analytical and numerical findings lead us to conjecture a new state of cold,
but dense matter in the hadronic phase for which Fermi Einstein condensation is
realised.Comment: 51 pages, 32 figure