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A derivation of the cyclic form factor equation from quantum field theoretical principles is given; form factors being the matrix elements of a field operator between scattering states. The scattering states are constructed from Haag-Ruelle…

We use a continued fraction approach to compare two statistical ensembles of quadrangulations with a boundary, both controlled by two parameters. In the first ensemble, the quadrangulations are bicolored and the parameters control their…

In previous work, the authors introduced "soft" methods to prove the effective (i.e. with power savings error) equidistribution of "shears" in cusped hyperbolic surfaces. In this paper, we study the same problem but now allow full use of…

Using the Operator Product Expansion for Wilson loops we derive a simple formula giving the discontinuities of the two loop result in terms of the one loop answer. We also argue that the knowledge of these discontinuities should be enough…

We present and demonstrate a version of Levinson's theorem especially dedicated to the asymptotic behavior of form factor phases. Indeed, as required by analyticity, form factors are multi-valued complex functions of a square four-momentum…

We construct `structure invariants' of a one-ended, finitely presented group that describe the way in which the factors of its JSJ decomposition over two-ended subgroups fit together. For groups satisfying two technical conditions, these…

We consider an overdetermined problem of Serrin-type with respect to an operator in divergence form with piecewise constant coefficients. We give sufficient condition for unique solvability near radially symmetric configurations by means of…

Orthogonal polynomials with respect to a weight function defined on a wedge in the plane are studied. A basis of orthogonal polynomials is explicitly constructed for two large class of weight functions and the convergence of Fourier…

The decomposition of the Laughlin wave function in the Slater orthogonal basis appears in the discussion on the second-quantized form of the Laughlin states and is straightforwardly equivalent to the decomposition of the even powers of the…

We apply the strategy proposed in the companion paper [1] for dealing with multiple dispersive bounds, to the case of sub-threshold branch-cuts, which is a topic addressed extensively in the literature (see, e.g., Refs. [2-8]). We consider…

We establish tight upper and lower bounds for the Entanglement of Formation of an arbitrary two-mode Gaussian state employing necessary properties of Gaussian channels. Both bounds are strictly given by the Entanglement of Formation of…

A new method of composition orthogonality is introduced. It is applied to generate new sequences of orthogonal polynomials and functions. In particular, classical orthogonal polynomials are interpreted in the sense of composition…

Matrix elements of Wilson-line dressed operators play a central role in the factorization of soft and collinear modes in gauge theories. When expressed using spinor helicity variables, these so-called form factors admit a classification…

Let X be a tight t-design of dimension n for one of the open cases t=5 or t=7. An investigation of the lattice generated by X using arithmetic theory of quadratic forms allows to exclude infinitely many values for n.

We construct new examples of cylinder flows, given by skew product extensions of irrational rotations on the circle, that are ergodic and rationally ergodic along a subsequence of iterates. In particular, they exhibit law of large numbers.…

The main outcomes of the paper are divided into two parts. First, we present a new dual for quadratic programs, in which, the dual variables are affine functions, and we prove strong duality. Since the new dual is intractable, we consider a…

It is shown that the scaling operators in the conformal limit of a two-dimensional field theory have massive form factors which obey a simple factorisation property in rapidity space. This has been used to identify such operators within the…

We review on the calculation of the heavy-quark photo-production vector form factors, with the full dependence on the mass of the heavy-quark. The Feynman diagrams are evaluated within the dimensional regularization scheme and expressed in…

We obtain a new formula to relate the value of a Schur polynomial with variables $(x_1,\ldots,x_N)$ with values of Schur polynomials at $(1,\ldots,1)$. This allows to study the limit shape of perfect matchings on a square hexagon lattice…

We calculate the phase space factor for a two-body decay in which one of the products is a tachyon. Two threshold conditions, a lower and an upper one, are derived in terms of the masses of the particles and the speed of a preferred frame.…