98 research outputs found
Second Quantization of the Wilson Loop
Treating the QCD Wilson loop as amplitude for the propagation of the first
quantized particle we develop the second quantization of the same propagation.
The operator of the particle position (the endpoint of the
"open string") is introduced as a limit of the large Hermitean matrix. We
then derive the set of equations for the expectation values of the vertex
operators \VEV{ V(k_1)\dots V(k_n)} . The remarkable property of these
equations is that they can be expanded at small momenta (less than the QCD mass
scale), and solved for expansion coefficients. This provides the relations for
multiple commutators of position operator, which can be used to construct this
operator. We employ the noncommutative probability theory and find the
expansion of the operator in terms of products of creation
operators . In general, there are some free parameters left
in this expansion. In two dimensions we fix parameters uniquely from the
symplectic invariance. The Fock space of our theory is much smaller than that
of perturbative QCD, where the creation and annihilation operators were
labelled by continuous momenta. In our case this is a space generated by creation operators. The corresponding states are given by all sentences made
of the four letter words. We discuss the implication of this construction for
the mass spectra of mesons and glueballs.Comment: 41 pages, latex, 3 figures and 3 Mathematica files uuencode
Induced QCD at Large N
We propose and study at large N a new lattice gauge model , in which the
Yang-Mills interaction is induced by the heavy scalar field in adjoint
representation. At any dimension of space and any the gauge fields can be
integrated out yielding an effective field theory for the gauge invariant
scalar field, corresponding to eigenvalues of the initial matrix field. This
field develops the vacuum average, the fluctuations of which describe the
elementary excitations of our gauge theory. At we find two phases
of the model, with asymptotic freedom corresponding to the strong coupling
phase (if there are no phase transitions at some critical ). We could not
solve the model in this phase, but in the weak coupling phase we have derived
exact nonlinear integral equations for the vacuum average and for the scalar
excitation spectrum. Presumably the strong coupling equations can be derived by
the same method.Comment: 20 page
Wilson line correlators in two-dimensional noncommutative Yang-Mills theory
We study the correlator of two parallel Wilson lines in two-dimensional
noncommutative Yang-Mills theory, following two different approaches. We first
consider a perturbative expansion in the large-N limit and resum all planar
diagrams. The second approach is non-perturbative: we exploit the Morita
equivalence, mapping the two open lines on the noncommutative torus (which
eventually gets decompacted) in two closed Wilson loops winding around the dual
commutative torus. Planarity allows us to single out a suitable region of the
variables involved, where a saddle-point approximation of the general Morita
expression for the correlator can be performed. In this region the correlator
nicely compares with the perturbative result, exhibiting an exponential
increase with respect to the momentum p.Comment: 21 pages, 1 figure, typeset in JHEP style; some formulas corrected in
Sect.3, one reference added, results unchange
Notes on the Hamiltonian formulation of 3D Yang-Mills theory
Three-dimensional Yang-Mills theory is investigated in the Hamiltonian
formalism based on the Karabali-Nair variable. A new algorithm is developed to
obtain the renormalized Hamiltonian by identifying local counterterms in
Lagrangian with the use of fictitious holomorphic symmetry existing in the
framework with the KN variable. Our algorithm is totally algebraic and enables
one to calculate the ground state wave functional recursively in gauge
potentials. In particular, the Gaussian part thus calculated is shown to
coincide with that obtained by Leigh et al. Higher-order corrections to the
Gaussian part are also discussed.Comment: 26 pages, LaTeX; discussions on IR regulators and local counterterms
improved, references adde
A non trivial extension of the two-dimensional Ising model: the d-dimensional "molecular" model
A recently proposed molecular model is discussed as a non-trivial extension
of the Ising model. For d=2 the two models are shown to be equivalent, while
for d>2 the molecular model describes a peculiar second order transition from
an isotropic high temperature phase to a low-dimensional anisotropic low
temperature state. The general mean field analysis is compared with the results
achieved by a variational Migdal-Kadanoff real space renormalization group
method and by standard Monte Carlo sampling for d=3. By finite size scaling the
critical exponent has been found to be 0.44\pm 0.02 thus establishing that the
molecular model does not belong to the universality class of the Ising model
for d>2.Comment: 25 pages, 5 figure
Critical Behavior of Dynamically Triangulated Quantum Gravity in Four Dimensions
We performed detailed study of the phase transition region in Four
Dimensional Simplicial Quantum Gravity, using the dynamical triangulation
approach. The phase transition between the Gravity and
Antigravity phases turned out to be asymmetrical, so that we observed the
scaling laws only when the Newton constant approached the critical value from
perturbative side. The curvature susceptibility diverges with the scaling index
. The physical (i.e. measured with heavy particle propagation) Hausdorff
dimension of the manifolds, which is
2.3 in the Gravity phase and 4.6 in the Antigravity phase, turned out to be 4
at the critical point, within the measurement accuracy. These facts indicate
the existence of the continuum limit in Four
Dimensional Euclidean Quantum Gravity.Comment: 12pg
Spontaneous P-violation in QCD in extreme conditions
We investigate the possibility of parity being spontaneously violated in QCD
at finite baryon density and temperature. The analysis is done for an idealized
homogeneous and infinite nuclear matter where the influence of density can be
examined with the help of constant chemical potential. QCD is approximated by a
generalized sigma-model with two isomultiplets of scalars and pseudoscalars.
The interaction with the chemical potential is introduced via the coupling to
constituent quark fields as nucleons are not considered as point-like degrees
of freedom in our approach. This mechanism of parity violation is based on
interplay between lightest and heavier degrees of freedom and it cannot be
understood in simple models retaining the pion and nucleon sectors solely. We
argue that, in the appropriate environment (dense and hot nuclear matter of a
few normal densities and moderate temperatures), parity violation may be the
rule rather than the exception and its occurrence is well compatible with the
existence of stable bound state of normal nuclear matter. We prove that the so
called 'chiral collapse' never takes place for the parameter region supporting
spontaneous parity violation.Comment: 9 page
Cluster Analysis of Extremely High Energy Cosmic Rays in the Northern Sky
The arrival directions of extremely high energy cosmic rays (EHECR) above
eV, observed by four surface array experiments in the northern
hemisphere,are examined for coincidences from similar directions in the sky.
The total number of cosmic rays is 92.A significant number of double
coincidences (doublet) and triple coincidences (triplet) are observed on the
supergalactic plane within the experimental angular resolution. The chance
probability of such multiplets from a uniform distribution is less than 1 % if
we consider a restricted region within of the supergalactic
plane. Though there is still a possibility of chance coincidence, the present
results on small angle clustering along the supergalactic plane may be
important in interpreting EHECR enigma. An independent set of data is required
to check our claims.Comment: 9 pages, 6 tables, 8 figures. submitted to Astroparticle Physic
Two dimensional lattice gauge theory based on a quantum group
In this article we analyze a two dimensional lattice gauge theory based on a
quantum group.The algebra generated by gauge fields is the lattice algebra
introduced recently by A.Yu.Alekseev,H.Grosse and V.Schomerus we define and
study wilson loops and compute explicitely the partition function on any
Riemann surface. This theory appears to be related to Chern-Simons Theory.Comment: 35 pages LaTex file,CPTH A302-05.94 (we have corrected some misprints
and added more material to be complete
String Propagator: a Loop Space Representation
The string quantum kernel is normally written as a functional sum over the
string coordinates and the world--sheet metrics. As an alternative to this
quantum field--inspired approach, we study the closed bosonic string
propagation amplitude in the functional space of loop configurations. This
functional theory is based entirely on the Jacobi variational formulation of
quantum mechanics, {\it without the use of a lattice approximation}. The
corresponding Feynman path integral is weighed by a string action which is a
{\it reparametrization invariant} version of the Schild action. We show that
this path integral formulation is equivalent to a functional ``Schrodinger''
equation defined in loop--space. Finally, for a free string, we show that the
path integral and the functional wave equation are {\it exactly } solvable.Comment: 15 pages, no figures, ReVTeX 3.
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