791 research outputs found
On anomalies in classical dynamical systems
The definition of "classical anomaly" is introduced. It describes the
situation in which a purely classical dynamical system which presents both a
lagrangian and a hamiltonian formulation admits symmetries of the action for
which the Noether conserved charges, endorsed with the Poisson bracket
structure, close an algebra which is just the centrally extended version of the
original symmetry algebra. The consistency conditions for this to occur are
derived. Explicit examples are given based on simple two-dimensional models.
Applications of the above scheme and lines of further investigations are
suggested.Comment: arXiv version is already officia
Resolving the Large-N Nuclear Potential Puzzle
The large nuclear potential puzzle arose because three- and
higher-meson exchange contributions to the nucleon-nucleon potential did not
automatically yield cancellations that make these contributions consistent with
the general large scaling rules for the potential. Here it is proposed
that the resolution to this puzzle is that the scaling rules only apply for
energy-independent potentials while all of the cases with apparent
inconsistencies were for energy-dependent potentials. It is shown explicitly
how energy-dependent potentials can have radically different large N behavior
than an equivalent energy-independent one. One class of three-meson graphs is
computed in which the contribution to the energy-independent potential is
consistent with the general large N rules even though the energy-dependent
potential is not.Comment: Corrections to the toy mode
Correlation functions in super Liouville theory
We calculate three- and four-point functions in super Liouville theory
coupled to super Coulomb gas on world sheets with spherical topology. We first
integrate over the zero mode and assume that a parameter takes an integer
value. After calculating the amplitudes, we formally continue the parameter to
an arbitrary real number. Remarkably the result is completely parallel to the
bosonic case, the amplitudes being of the same form as those of the bosonic
case.Comment: 11 page
Subcritical Superstrings
We introduce the Liouville mode into the Green-Schwarz superstring. Like
massive supersymmetry without central charges, there is no kappa symmetry.
However, the second-class constraints (and corresponding Wess-Zumino term)
remain, and can be solved by (twisted) chiral superspace in dimensions D=4 and
6. The matter conformal anomaly is c = 4-D < 1. It thus can be canceled for
physical dimensions by the usual Liouville methods, unlike the bosonic string
(for which the consistency condition is c = D <= 1).Comment: 9 pg., compressed postscript file (.ps.Z), other formats (.dvi, .ps,
.ps.Z, 8-bit .tex) available at
http://insti.physics.sunysb.edu/~siegel/preprints/ or at
ftp://max.physics.sunysb.edu/preprints/siege
Antiferrodistortive phase transition in EuTiO3
X-ray diffraction, dynamical mechanical analysis and infrared reflectivity
studies revealed an antiferrodistortive phase transition in EuTiO3 ceramics.
Near 300K the perovskite structure changes from cubic Pm-3m to tetragonal
I4/mcm due to antiphase tilting of oxygen octahedra along the c axis (a0a0c- in
Glazer notation). The phase transition is analogous to SrTiO3. However, some
ceramics as well as single crystals of EuTiO3 show different infrared
reflectivity spectra bringing evidence of a different crystal structure. In
such samples electron diffraction revealed an incommensurate tetragonal
structure with modulation wavevector q ~ 0.38 a*. Extra phonons in samples with
modulated structure are activated in the IR spectra due to folding of the
Brillouin zone. We propose that defects like Eu3+ and oxygen vacancies strongly
influence the temperature of the phase transition to antiferrodistortive phase
as well as the tendency to incommensurate modulation in EuTiO3.Comment: PRB, in pres
Quantum Diffeomorphisms and Conformal Symmetry
We analyze the constraints of general coordinate invariance for quantum
theories possessing conformal symmetry in four dimensions. The character of
these constraints simplifies enormously on the Einstein universe . The global conformal symmetry algebra of this space determines
uniquely a finite shift in the Hamiltonian constraint from its classical value.
In other words, the global Wheeler-De Witt equation is {\it modified} at the
quantum level in a well-defined way in this case. We argue that the higher
moments of should not be imposed on the physical states {\it a priori}
either, but only the weaker condition . We
present an explicit example of the quantization and diffeomorphism constraints
on for a free conformal scalar field.Comment: PlainTeX File, 37 page
R-matrix Quantization of the Elliptic Ruijsenaars--Schneider model
It is shown that the classical L-operator algebra of the elliptic
Ruijsenaars-Schneider model can be realized as a subalgebra of the algebra of
functions on the cotangent bundle over the centrally extended current group in
two dimensions. It is governed by two dynamical r and -matrices
satisfying a closed system of equations. The corresponding quantum R and
-matrices are found as solutions to quantum analogs of these
equations. We present the quantum L-operator algebra and show that the system
of equations on R and arises as the compatibility condition for
this algebra. It turns out that the R-matrix is twist-equivalent to the Felder
elliptic R^F-matrix with playing the role of the twist. The
simplest representation of the quantum L-operator algebra corresponding to the
elliptic Ruijsenaars-Schneider model is obtained. The connection of the quantum
L-operator algebra to the fundamental relation RLL=LLR with Belavin's elliptic
R matrix is established. As a byproduct of our construction, we find a new
N-parameter elliptic solution to the classical Yang-Baxter equation.Comment: latex, 29 pages, some misprints are corrected and the meromorphic
version of the quantum L-operator algebra is discusse
Semiclassical Quantization of Effective String Theory and Regge Trajectories
We begin with an effective string theory for long distance QCD, and evaluate
the semiclassical expansion of this theory about a classical rotating string
solution, taking into account the the dynamics of the boundary of the string.
We show that, after renormalization, the zero point energy of the string
fluctuations remains finite when the masses of the quarks on the ends of the
string approach zero. The theory is then conformally invariant in any spacetime
dimension D. For D=26 the energy spectrum of the rotating string formally
coincides with that of the open string in classical Bosonic string theory.
However, its physical origin is different. It is a semiclassical spectrum of an
effective string theory valid only for large values of the angular momentum.
For D=4, the first semiclassical correction adds the constant 1/12 to the
classical Regge formula.Comment: 65 pages, revtex, 3 figures, added 2 reference
Chern - Simons Gauge Field Theory of Two - Dimensional Ferromagnets
A Chern-Simons gauged Nonlinear Schr\"odinger Equation is derived from the
continuous Heisenberg model in 2+1 dimensions. The corresponding planar magnets
can be analyzed whithin the anyon theory. Thus, we show that static magnetic
vortices correspond to the self-dual Chern - Simons solitons and are described
by the Liouville equation. The related magnetic topological charge is
associated with the electric charge of anyons. Furthermore, vortex - antivortex
configurations are described by the sinh-Gordon equation and its conformally
invariant extension. Physical consequences of these results are discussed.Comment: 15 pages, Plain TeX, Lecce, June 199
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