Related papers: Test Function Space for Wick Power Series

The algebraic formulation of Wick's theorem that allows one to present the vacuum or thermal averages of the chronological product of an arbitrary number of field operators as a determinant (permanent) of the matrix is proposed. Each…

It is shown how a physical function, namely the Wigner function, that in principle may be measured, can be used to evaluate divergent series.

A covariant quantization of the free spinor fields (s=1/2) in 4-dimensional de Sitter (dS) space-time based on analyticity in the complexified pseudo-Riemanian manifold is presented. We define the Wigthman two-point function ${\cal…

We propose an independence test for random variables valued into metric spaces by using a test statistic obtained from appropriately centering and rescaling the squared Hilbert-Schmidt norm of the usual empirical estimator of normalized…

We apply a theorem of Wick to rewrite certain classes of exponential measures on random graphs as integrals of Feynman-Gibbs type, on the real line. The analytic properties of these measures can then be studied in terms of phase…

The main aim of this paper is to generalize the classical concept of positive operator, and to develop a general extension theory, which overcomes not only the lack of a Hilbert space structure, but also the lack of a normable topology. The…

The paper presents a model-independent, nonperturbative proof of operator product expansions in quantum field theory. As an input, a recently proposed phase space condition is used that allows a precise description of point field…

We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings, The construction has been used in…

A framework for estimation and hypothesis testing of functional restrictions against general alternatives is proposed. The parameter space is a reproducing kernel Hilbert space (RKHS). The null hypothesis does not necessarily define a…

We give criteria on the existence of a so-called mark function in the context of marked metric measure spaces (mmm-spaces). If an mmm-space admits a mark function, we call it functionally-marked metric measure space (fmm-space). This is not…

The ability of the Rigged Hilbert Space formalism to deal with continuous spectrum is demonstrated within the example of the square barrier potential. The non-square integrable solutions of the time-independent Schrodinger equation are used…

We revisit the power counting of the Higgs Effective Field Theory (HEFT) from first principles, by requiring that predictions for physical observables follow a series expansion in small, dimensionless quantities. Depending on whether HEFT…

Considering a fluctuating scalar field on momentum space, some relativistic statistical field theories are constructed. A Hilbert space of observables is then constructed from functionals of the fluctuating scalar field with an inner…

We establish the bounds on Wilson coefficients of the Higgs effective field theory (HEFT) mandated by unitarity and analyticity. These positivity constraints can be projected into the space of the standard model effective field theory…

The aim of this review is to outline a full route from the fundamental principles of algebraic quantum field theory on curved spacetime in its present-day form to explicit phenomenological applications which allow for comparison with…

A test space is the set of outcome-sets associated with a collection of experiments. This notion provides a simple mathematical framework for the study of probabilistic theories -- notably, quantum mechanics -- in which one is faced with…

In spite of their potential usefulness, Wigner functions for systems with SU(1,1) symmetry have not been explored thus far. We address this problem from a physically-motivated perspective, with an eye towards applications in modern…

Generalized Effective Field Theory (GEFT) is the non-renormalizable extension of an Effective Field Theory where the Wilson coefficients are endowed by their own, independent scale dependence. Such an effective theory can be constructed by…

This article delves into Korovkin-type theorems in Banach function spaces, as established by Yusuf Zeren et al. (2022). We prove that in this theorem, the positivity of the operators is not a necessary requirement and provide example of a…

This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…