139,221 research outputs found
A local and integrable lattice regularization of the massive Thirring model
The light--cone lattice approach to the massive Thirring model is
reformulated using a local and integrable lattice Hamiltonian written in terms
of discrete fermi fields. Several subtle points concerning boundary conditions,
normal--ordering, continuum limit, finite renormalizations and decoupling of
fermion doublers are elucidated. The relations connecting the six--vertex
anisotropy and the various coupling constants of the continuum are analyzed in
detail.Comment: Latex, 24 pages, some corrected misprints and minor changes, 2
Postscript figures unchange
Generalized Permutohedra from Probabilistic Graphical Models
A graphical model encodes conditional independence relations via the Markov
properties. For an undirected graph these conditional independence relations
can be represented by a simple polytope known as the graph associahedron, which
can be constructed as a Minkowski sum of standard simplices. There is an
analogous polytope for conditional independence relations coming from a regular
Gaussian model, and it can be defined using multiinformation or relative
entropy. For directed acyclic graphical models and also for mixed graphical
models containing undirected, directed and bidirected edges, we give a
construction of this polytope, up to equivalence of normal fans, as a Minkowski
sum of matroid polytopes. Finally, we apply this geometric insight to construct
a new ordering-based search algorithm for causal inference via directed acyclic
graphical models.Comment: Appendix B is expanded. Final version to appear in SIAM J. Discrete
Mat
Ghost story. II. The midpoint ghost vertex
We construct the ghost number 9 three strings vertex for OSFT in the natural
normal ordering. We find two versions, one with a ghost insertion at z=i and a
twist-conjugate one with insertion at z=-i. For this reason we call them
midpoint vertices. We show that the relevant Neumann matrices commute among
themselves and with the matrix representing the operator K1. We analyze the
spectrum of the latter and find that beside a continuous spectrum there is a
(so far ignored) discrete one. We are able to write spectral formulas for all
the Neumann matrices involved and clarify the important role of the integration
contour over the continuous spectrum. We then pass to examine the (ghost) wedge
states. We compute the discrete and continuous eigenvalues of the corresponding
Neumann matrices and show that they satisfy the appropriate recursion
relations. Using these results we show that the formulas for our vertices
correctly define the star product in that, starting from the data of two ghost
number 0 wedge states, they allow us to reconstruct a ghost number 3 state
which is the expected wedge state with the ghost insertion at the midpoint,
according to the star recursion relation.Comment: 60 pages. v2: typos and minor improvements, ref added. To appear in
JHE
From Temporal to Contemporaneous Iterative Causal Discovery in the Presence of Latent Confounders
We present a constraint-based algorithm for learning causal structures from
observational time-series data, in the presence of latent confounders. We
assume a discrete-time, stationary structural vector autoregressive process,
with both temporal and contemporaneous causal relations. One may ask if
temporal and contemporaneous relations should be treated differently. The
presented algorithm gradually refines a causal graph by learning long-term
temporal relations before short-term ones, where contemporaneous relations are
learned last. This ordering of causal relations to be learnt leads to a
reduction in the required number of statistical tests. We validate this
reduction empirically and demonstrate that it leads to higher accuracy for
synthetic data and more plausible causal graphs for real-world data compared to
state-of-the-art algorithms.Comment: Proceedings of the 40-th International Conference on Machine Learning
(ICML), 202
Out of Nowhere: Spacetime from causality: causal set theory
This is a chapter of the planned monograph "Out of Nowhere: The Emergence of
Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and
Christian W\"uthrich and under contract with Oxford University Press. (More
information at www.beyondspacetime.net.) This chapter introduces causal set
theory and identifies and articulates a 'problem of space' in this theory.Comment: 29 pages, 5 figure
Hierarchical Dobinski-type relations via substitution and the moment problem
We consider the transformation properties of integer sequences arising from
the normal ordering of exponentiated boson ([a,a*]=1) monomials of the form
exp(x (a*)^r a), r=1,2,..., under the composition of their exponential
generating functions (egf). They turn out to be of Sheffer-type. We demonstrate
that two key properties of these sequences remain preserved under
substitutional composition: (a)the property of being the solution of the
Stieltjes moment problem; and (b) the representation of these sequences through
infinite series (Dobinski-type relations). We present a number of examples of
such composition satisfying properties (a) and (b). We obtain new Dobinski-type
formulas and solve the associated moment problem for several hierarchically
defined combinatorial families of sequences.Comment: 14 pages, 31 reference
Ordered Products, -Algebra, and Two-Variable, Definite-Parity, Orthogonal Polynomials
It has been shown that the Cartan subalgebra of - algebra is the
space of the two-variable, definite-parity polynomials. Explicit expressions of
these polynomials, and their basic properties are presented. Also has been
shown that they carry the infinite dimensional irreducible representation of
the algebra having the spectrum bounded from below. A realization of
this algebra in terms of difference operators is also obtained. For particular
values of the ordering parameter they are identified with the classical
orthogonal polynomials of a discrete variable, such as the Meixner,
Meixner-Pollaczek, and Askey-Wilson polynomials. With respect to variable
they satisfy a second order eigenvalue equation of hypergeometric type. Exact
scattering states with zero energy for a family of potentials are expressed in
terms of these polynomials. It has been put forward that it is the
\.{I}n\"{o}n\"{u}-Wigner contraction and its inverse that form bridge between
the difference and differential calculus.Comment: 17 pages,no figure. to appear in J. Math.Phy
q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra U_q(u(n,1))
For the quantum algebra U_q(gl(n+1)) in its reduction on the subalgebra
U_q(gl(n)) an explicit description of a Mickelsson-Zhelobenko reduction
Z-algebra Z_q(gl(n+1),gl(n)) is given in terms of the generators and their
defining relations. Using this Z-algebra we describe Hermitian irreducible
representations of a discrete series for the noncompact quantum algebra
U_q(u(n,1)) which is a real form of U_q(gl(n+1)), namely, an orthonormal
Gelfand-Graev basis is constructed in an explicit form.Comment: Invited talk given by V.N.T. at XVIII International Colloquium
"Integrable Systems and Quantum Symmetries", June 18--20, 2009, Prague, Czech
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