4,889 research outputs found
Spin-S bilayer Heisenberg models: Mean-field arguments and numerical calculations
Spin-S bilayer Heisenberg models (nearest-neighbor square lattice
antiferromagnets in each layer, with antiferromagnetic interlayer couplings)
are treated using dimer mean-field theory for general S and high-order
expansions about the dimer limit for S=1, 3/2,...,4. We suggest that the
transition between the dimer phase at weak intraplane coupling and the Neel
phase at strong intraplane coupling is continuous for all S, contrary to a
recent suggestion based on Schwinger boson mean-field theory. We also present
results for S=1 layers based on expansions about the Ising limit: In every
respect the S=1 bilayers appear to behave like S=1/2 bilayers, further
supporting our picture for the nature of the order-disorder phase transition.Comment: 6 pages, Revtex 3.0, 8 figures (not embedded in text
Noncommutative symmetric functions and Laplace operators for classical Lie algebras
New systems of Laplace (Casimir) operators for the orthogonal and symplectic
Lie algebras are constructed. The operators are expressed in terms of paths in
graphs related to matrices formed by the generators of these Lie algebras with
the use of some properties of the noncommutative symmetric functions associated
with a matrix. The decomposition of the Sklyanin determinant into a product of
quasi-determinants play the main role in the construction. Analogous
decomposition for the quantum determinant provides an alternative proof of the
known construction for the Lie algebra gl(N).Comment: 25 page
Tree-level scattering amplitudes from the amplituhedron
7 pages, 2 figures, to be published in the Journal of Physics: Conference Series. Proceedings for the "7th Young Researcher Meeting", Torino, 2016A central problem in quantum field theory is the computation of scattering amplitudes. However, traditional methods are impractical to calculate high order phenomenologically relevant observables. Building on a few decades of astonishing progress in developing non-standard computational techniques, it has been recently conjectured that amplitudes in planar N=4 super Yang-Mills are given by the volume of the (dual) amplituhedron. After providing an introduction to the subject at tree-level, we discuss a special class of differential equations obeyed by the corresponding volume forms. In particular, we show how they fix completely the amplituhedron volume for next-to-maximally helicity violating scattering amplitudes.Peer reviewe
Quantum Sturm-Liouville Equation, Quantum Resolvent, Quantum Integrals, and Quantum KdV : the Fast Decrease Case
We construct quantum operators solving the quantum versions of the
Sturm-Liouville equation and the resolvent equation, and show the existence of
conserved currents. The construction depends on the following input data: the
basic quantum field and the regularization .Comment: minor correction
Zero Curvature Formalism for Supersymmetric Integrable Hierarchies in Superspace
We generalize the Drinfeld-Sokolov formalism of bosonic integrable
hierarchies to superspace, in a way which systematically leads to the zero
curvature formulation for the supersymmetric integrable systems starting from
the Lax equation in superspace. We use the method of symmetric space as well as
the non-Abelian gauge technique to obtain the supersymmetric integrable
hierarchies of the AKNS type from the zero curvature condition in superspace
with the graded algebras, sl(n+1,n), providing the Hermitian symmetric space
structure.Comment: LaTeX, 9 pg
Dynamical Structure Factors for Dimerized Spin Systems
We discuss the transition strength between the disordered ground state and
the basic low-lying triplet excitation for interacting dimer materials by
presenting theoretical calculations and series expansions as well as inelastic
neutron scattering results for the material KCuCl_3. We describe in detail the
features resulting from the presence of two differently oriented dimers per
unit cell and show how energies and spectral weights of the resulting two modes
are related to each other. We present results from the perturbation expansion
in the interdimer interaction strength and thus demonstrate that the wave
vector dependence of the simple dimer approximation is modified in higher
orders. Explicit results are given in 10th order for dimers coupled in 1D, and
in 2nd order for dimers coupled in 3D with application to KCuCl_3 and TlCuCl_3.Comment: 17 pages, 6 figures, part 2 is based on cond-mat/021133
Some comments on the divergence of perturbation series in Quantum Eletrodynamics
It has been argued by Dyson that the perturbation series in coupling constant
in QED can not be convergent. We find that similiar albeit slightly different
arguments lead to the divergence of the series of expansion in QED.Comment: Final Version, To appear in Modern Physics Letters
An Effective Field Theory Look at Deep Inelastic Scattering
This talk discusses the effective field theory view of deep inelastic
scattering. In such an approach, the standard factorization formula of a hard
coefficient multiplied by a parton distribution function arises from matching
of QCD onto an effective field theory. The DGLAP equations can then be viewed
as the standard renormalization group equations that determines the cut-off
dependence of the non-local operator whose forward matrix element is the parton
distribution function. As an example, the non-singlet quark splitting functions
is derived directly from the renormalization properties of the non-local
operator itself. This approach, although discussed in the literature, does not
appear to be well known to the larger high energy community. In this talk we
give a pedagogical introduction to this subject.Comment: 11 pages, 1 figure, To appear in Modern Physics Letters
On the algebraic structures connected with the linear Poisson brackets of hydrodynamics type
The generalized form of the Kac formula for Verma modules associated with
linear brackets of hydrodynamics type is proposed. Second cohomology groups of
the generalized Virasoro algebras are calculated. Connection of the central
extensions with the problem of quntization of hydrodynamics brackets is
demonstrated
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