11,636 research outputs found
The q-WZ Method for Infinite Series
Motivated by the telescoping proofs of two identities of Andrews and Warnaar,
we find that infinite q-shifted factorials can be incorporated into the
implementation of the q-Zeilberger algorithm in the approach of Chen, Hou and
Mu to prove nonterminating basic hypergeometric series identities. This
observation enables us to extend the q-WZ method to identities on infinite
series. As examples, we will give the q-WZ pairs for some classical identities
such as the q-Gauss sum, the sum, Ramanujan's sum and
Bailey's sum.Comment: 17 page
Simultaneous generation for zeta values by the Markov-WZ method
By application of the Markov-WZ method, we prove a more general form of a
bivariate generating function identity containing, as particular cases,
Koecher's and Almkvist-Granville's Ap\'ery-like formulae for odd zeta values.
As a consequence, we get a new identity producing Ap\'ery-like series for all
convergent at the geometric rate with ratio
Comment: 7 page
The signed loop approach to the Ising model: foundations and critical point
The signed loop method is a beautiful way to rigorously study the
two-dimensional Ising model with no external field. In this paper, we explore
the foundations of the method, including details that have so far been
neglected or overlooked in the literature. We demonstrate how the method can be
applied to the Ising model on the square lattice to derive explicit formal
expressions for the free energy density and two-point functions in terms of
sums over loops, valid all the way up to the self-dual point. As a corollary,
it follows that the self-dual point is critical both for the behaviour of the
free energy density, and for the decay of the two-point functions.Comment: 38 pages, 7 figures, with an improved Introduction. The final
publication is available at link.springer.co
A -microscope for supercongruences
By examining asymptotic behavior of certain infinite basic (-)
hypergeometric sums at roots of unity (that is, at a "-microscopic" level)
we prove polynomial congruences for their truncations. The latter reduce to
non-trivial (super)congruences for truncated ordinary hypergeometric sums,
which have been observed numerically and proven rarely. A typical example
includes derivation, from a -analogue of Ramanujan's formula of the two supercongruences valid
for all primes , where denotes the truncation of the infinite sum
at the -th place and stands for the quadratic character
modulo .Comment: 26 page
Higher-Derivative Terms in N=2 Supersymmetric Effective Actions
We show how to systematically construct higher-derivative terms in effective
actions in harmonic superspace despite the infinite redundancy in their
description due to the infinite number of auxiliary fields. Making an
assumption about the absence of certain superspace Chern-Simons-like terms
involving vector multiplets, we write all 3- and 4-derivative terms on Higgs,
Coulomb, and mixed branches. Among these terms are several with only
holomorphic dependence on fields, and at least one satisfies a
non-renormalization theorem. These holomorphic terms include a novel
3-derivative term on mixed branches given as an integral over 3/4 of
superspace. As an illustration of our method, we search for Wess-Zumino terms
in the low energy effective action of N=2 supersymmetric QCD. We show that such
terms occur only on mixed branches. We also present an argument showing that
the combination of space-time locality with supersymmetry implies locality in
the anticommuting superspace coordinates of for unconstrained superfields.Comment: 30 pages. Added references and simplified final form of WZ ter
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