9 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
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
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
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
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
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