Research interests:
General field of activity: Quantum Field Theory on the Lattice/Statistical Mechanics
Specific research interests: Confinement in non-Abelian gauge theories Recent research subjects: 1) Confinement and Greens-functions: The Gribov-Zwanziger confinement scenario in lattice Coulomb gauge:
We have been able to show via ab-initio lattice calculation that the Gribov
conjecture on the functional form of the static gluon propagator in Coulomb
gauge, D(p)-1=√(p2 + M4/p2), is correct and
that the ghost propagator is indeed IR enahnced in such gauge, in agreement
with previous (approximated) predictions in the Hamiltonian picture using the variational principle. This means, in sharp contrast to Landau gauge (see below), that the Gribov-Zwanziger confinement picture in Coulomb gauge
can be confirmed and opens the path to promising applications.
The Kugo-Ojima BRS scenario in lattice Landau gauge:
Lattice results in Landau gauge agree only with the so called subcritical
(a.k.a. decoupling) solution obtained via Dyson-Schwinger/renormalization
group flow analysis. Such a solution is still compatible with confinement but would
reject the standard Kugo-Ojima picture that colorless states arise via a
"perturbative-like" realization of BRS singlets. More work is still needed to
understand the issues involved and the differences with the Coulomb gauge case. 2) Vortex free energy in the continuum limit of lattice Yang-Mills theories We have studied Maximal 't Hooft loops in SO(3) lattice gauge theory
at finite temperature T. Tunneling barriers among twist sectors
causing loss of ergodicity for local update algorithms have been overcome
through parallel tempering, enabling us to measure the vortex free
energy F and to identify a deconfinement transition at some
βAc. The behavior of F below βAc shows
however striking differences to what is expected from discretizations
in the fundamental representation.
I have later showed evidence that for dimension d≤4 SU(2) lattice
Yang-Mills theories discretized on the lattice through standard Wilson
action undergo bulk transitions (T = 0) at a βc lying in the weak coupling
region. Such phase transitions are, in Ehrenfest's classifications, of high
order and therefore hardly recognizable by direct investigation of the free
energy. Suitable order parameter is the 't Hooft loop, measuring the twist
as allowed by the algebra compatible with the boundary conditions imposed
on the d-torus; in contrast to its continuum limit, due to lattice artifacts
below βc the theory does not possesses a well defined Z2
magnetic flux. The result extends to higher SU(N) groups and to a more
general class of lattice actions. More numerical evidence is needed to pin
down the order of the transition and the consequences for usual lattice simulations. 3) Hamiltonian formulation of lattice gauge theories Given the succes of continuum Hamiltonian variational methods in describing
some features of Yang-Mills theories, my old interest in
Hamiltonian formulation of lattice gauge theories has been recently revived.
We hope to further extend and apply a formalism we developed some time ago,
where non-linear fourier analysis on compact groups is used to construct an
orthonormal basis of the physical Hilbert space of Hamiltonian Lattice Gauge
Theories, thus overcoming the problem of Mandelstam identities. In particular,
the matrix elements of the hamiltonian operator involved are
explicitly computable on such basis, turning the solution of Lattice Gauge
Theories into a well defined eigenvalues-eigenvector problem. |
