20 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
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
Lattice Study of the Massive Schwinger Model with a term under L\"uscher's "Admissibility" condition
We present a numerical study of the massive two-flavor QED in two dimensions
with the gauge action proposed by L\"uscher, which allows only ``admissible''
gauge fields. We find that the admissibility condition does not allow any
topology changes by the local updation in Hybrid Monte Carlo algorithm so that
the configurations in each topological sector can be generated separately. By
developing a new method to sum over different topological sectors, we
investigate vacuum effects. Combining with domain-wall fermion action,
we obtain the fermion mass dependence and dependence of the meson
masses, which are consistent with the analytic results by mass perturbation in
the continuum theory.Comment: 3 pages, Lattice2003(chiral
QCD with Chemical Potential in a Small Hyperspherical Box
To leading order in perturbation theory, we solve QCD, defined on a small
three sphere in the large N and Nf limit, at finite chemical potential and map
out the phase diagram in the (mu,T) plane. The action of QCD is complex in the
presence of a non-zero quark chemical potential which results in the sign
problem for lattice simulations. In the large N theory, which at low
temperatures becomes a conventional unitary matrix model with a complex action,
we find that the dominant contribution to the functional integral comes from
complexified gauge field configurations. For this reason the eigenvalues of the
Polyakov line lie off the unit circle on a contour in the complex plane. We
find at low temperatures that as mu passes one of the quark energy levels there
is a third-order Gross-Witten transition from a confined to a deconfined phase
and back again giving rise to a rich phase structure. We compare a range of
physical observables in the large N theory to those calculated numerically in
the theory with N=3. In the latter case there are no genuine phase transitions
in a finite volume but nevertheless the observables are remarkably similar to
the large N theory.Comment: 44 pages, 18 figures, jhep3 format. Small corrections and
clarifications added in v3. Conclusions cleaned up. Published versio
Weak coupling large-N transitions at finite baryon density
We study thermodynamics of free SU(N) gauge theory with a large number of
colours and flavours on a three-sphere, in the presence of a baryon number
chemical potential. Reducing the system to a holomorphic large-N matrix
integral, paying specific attention to theories with scalar flavours (squarks),
we identify novel third-order deconfining phase transitions as a function of
the chemical potential. These transitions in the complex large-N saddle point
configurations are interpreted as "melting" of baryons into (s)quarks. They are
triggered by the exponentially large (~ exp(N)) degeneracy of light baryon-like
states, which include ordinary baryons, adjoint-baryons and baryons made from
different spherical harmonics of flavour fields on the three-sphere. The phase
diagram of theories with scalar flavours terminates at a phase boundary where
baryon number diverges, representing the onset of Bose condensation of squarks.Comment: 38 pages, 7 figure