We study perturbative renormalization of the composite operators in $T\bar T$-deformed two-dimensional free field theories. The pattern for stress-energy tensor is different massive and massless cases. While latter case canonical stress not renormalized up to high order expansion, theory there are induced counterterms at linear order. For a our results match general formula derived recently [1].

Second order anti-holonomic jets as anti-symmetric parts of second order semi-holonomic jets are introduced. The anti-holonomic nature of the Lie bracket is shown. A general result on universality of the Lie bracket is proved. 1. Introduction The concepts of non-holonomic (or iterated) and semi-holonomic jets, rst introduced by Ehresmann in 1], are commonly used in diierential geometry. In this...

We give formulas for the multiplicities of eigenvalues of generalized rotation operators in terms of generalized Frobenius-Schur indicators in a semi-simple spherical tensor category C. In particular, this implies for a finite depth planar algebra, the entire collection of rotation eigenvalues can be computed from the fusion rules and the traces of rotation at finitely many depths. If C is also...

In this paper we show that the output of a nonlinear system with inputs in (L2 [0, T]; R ' ) whose state satisfies a nonlinear differential equation with standard smoothness conditions can be written as the composition of a nonlinear map with a linear Hilbert-Schmidt operator acting on the input. The result also extends to abstract semi-linear infinite dimensional systems. The approach is via t...

Light–cone(LC) dominated hard scattering processes, like deep inelastic scattering and deeply virtual Compton scattering, and various hadronic wave functions, e.g., vector meson amplitudes, appearing in (semi) exclusive processes are most effectively described by the help of the nonlocal light–cone expansion [1].Thereby, the same nonlocal LC–operator, and its anomalous dimension, is related to ...

I defend the introduction of triangular (semi)norms and (semi)conorms on bounded partially ordered sets. First, I give a brief survey of the general properties of these binary operators. Then, I work out a number of examples in diverse fields of mathematics, to show that it is indeed useful and natural to generalize the definition of triangular (semi)norms and (semi)conorms from the unit interv...

This paper introduces the logical system HOL2P that extends classical higher order logic (HOL) with type operator variables and universal types. HOL2P has explicit term operations for type abstraction and type application. The formation of type application terms t [T ] is restricted to small types T that do not contain any universal types. This constraint ensures the existence of a set-theoreti...

Under consideration is the following question. If T is a linear operator from a normed function space 3 into a Banach space X, then may an appropriate topology 3 be defined so that conditions on T may be interpreted in terms of the topology 3? For the present we consider 3 to be the class of Banach function spaces. We define appropriate "semi-norm topologies" on the unit ball x! of the dual of ...