Related papers: Three Etudes in QFT
This paper is primarily intended as an introduction for the mathematically inclined to some of the rich algebraic combinatorics arising in for instance CFT. It is essentially self-contained, apart from some of the background motivation and…
We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the existence of invariant measures with respect to the…
Higher dimensional conformal QFT possesses an interesting braided structure which, different from the d=1+1 models, is restricted to the timelike region and therefore easily escapes euclidean action methods. It lies behind the spectrum of…
We construct the new q-extension of Bernoulli numbers and polynomials in this paper. Finally we consider the q-zeta functions which interpolate the new q-extension of Bernoulli numbers and polynomials.
We determine the additional structure which arises on the classical limit of a DQ-algebroid.
Invariants of 3-manifolds from a non semi-simple category of modules over a version of quantum $sl(2)$ were obtained by the last three authors in arXiv:1202.3553 . They are invariants of $3$-manifolds together with a cohomology class which…
We revisit scalar $\phi^4$ theory and construct a reorganized perturbative expansion in which the kinetic operator, rather than the quartic interaction, is treated as the perturbation. Starting from the exactly solvable $0$-dimensional…
We study nonlinear effective field theories (EFTs) with factorially growing perturbative expansions, focusing on a class in which the relative entropy encodes an infinite tower of higher-dimensional operators. Using the resummed relative…
Examples are given of q-deformed systems that may be interpreted by the standard rules of quantum theory in terms of new degrees of freedom and supplementary quantum numbers.
We show how to construct unramified qoaternion extensions of quadratic number fields.
The continuous big $q$-Hermite polynomials are shown to realize a basis for a representation space of an extended $q$-oscillator algebra. An expansion formula is algebraically derived using this model.
In this survey we discuss the results on the finitistic dimension of various stratified algebras. We describe what is already known, present some recent estimates, and list some open problems.
In this paper, we begin constructing a new finite-dimensional topological quantum field theory (TQFT) for three-manifolds, based on group PSL(2,C) and its action on a complex variable by fractional-linear transformations, by providing its…
Motivated by the limited interaction between the mathematical physics community and theoretical physicists - particularly in high-energy theory - we present a computation that is typically the first example in QFT courses but, to our…
Developments in QCD at finite density are reviewed. I begin by discussing some new algorithms which have been applied to other theories with sign problems. Then I discuss the method of analytic continuation in QCD using a series expansion…
In a recent paper, one of us posed three open problems concerning squarefree arithmetic progressions in infinite words. In this note we solve these problems and prove some additional results.
We investigate factorizability of a quadratic split quaternion polynomial. In addition to inequality conditions for existence of such factorization, we provide lucid geometric interpretations in the projective space over the split…
We find general relations between RG equations and planar unitarity-analyticity. These relations are summarized in meromorphization procedure, generalizing the Pad\'e approximation in the limit of infinite order. We also investigate…
We give a short review on the status of research on the theoretical foundations of $f(T)$ gravity theories. We discuss recent results on perturbative and non-perturbative approaches, causality and degrees of freedom, and discuss future…
The quaternion Fourier transform (QFT) satisfies some uncertainty principles similar to the Euclidean Fourier transform. In this paper, we establish Miyachi's theorem for this transform.