One-loop quark contributions to the dimension-four gluon condensate term in the operator product expansion (OPE) of the scalar glueball correlation function are calculated in the MS scheme in the chiral limit of nf quark flavours. The presence of quark effects is shown not to alter the cancellation of infrared (IR) singularities in the gluon condensate OPE coefficients. The dimension-four gluon...

In integrable field theories the S-matrix is usually a product of a relatively simple matrix and a complicated scalar factor. We make an observation that in many relativistic integrable field theories the scalar factor can be expressed as a convolution of simple kernels appearing in the nested levels of the nested Bethe ansatz. We formulate a proposal, up to some discrete ambiguities, how to re...

INTRODUCTION .................................................................................................. . . . . . . . . 608 A NEW TAXONOMY OF MEASUREMENT DATA AND OF MULTIDIMENSIONAL MEASUREMENT MODELS .............. ............ 608 ONE-MODE TWO-WAY DATA.................................................................................. 612 Spatial Distance Models (for One-mode Two-way D...

Abstract It is emphasized that for interactions with derivative couplings, the Ward Identity (WI) securing preservation of a global symmetry should be modified. Scalar QED taken as an explicit example. More precisely, it rigorously shown in scalar naive WI and improved (‘Master Identity’, MWI) are related to each other by finite renormalization time-ordered product (‘ T -product’) fields, we po...

If C is a cocommutative coalgebra, a bialgebra structure can be given to the symmetric algebra S(C). The symmetric product is twisted by a Laplace pairing and the twisted product of any number of elements of S(C) is calculated explicitly. This is used to recover important identities in the quantum field theory of interacting scalar bosons.

This article develops a Gricean account for the computation of scalar implicatures in cases where one scalar term is in the scope of another. It shows that a cross-product of two quantitative scales yields the appropriate scale for many such cases. One exception is cases involving disjunction. For these, I propose an analysis that makes use of a novel, partially ordered quantitative scale for d...

We introduce max-plus analogues of basic Euclidian geometry notions: scalar product is replaced by a scalar division, and the associated distance is essentially Hilbert’s projective distance. We introduce an orthogonal projection and prove a Hahn-Banach type theorem: a point can be separated from a semimodule by a hyperplane orthogonal to the direction of projection. We use these results to sep...