Related papers: Operator product expansions as a consequence of ph…
We study the regularity of Fourier integral operators, by allowing their symbols to satisfy certain multi-parameter characteristics. As a result, we give an extension of Seeger-Sogge-Stein theorem on product spaces.
The product of local operators in a topological quantum field theory in dimension greater than one is commutative, as is more generally the product of extended operators of codimension greater than one. In theories of cohomological type…
Form factors in planar N=4 Super-Yang-Mills theory admit a type of non-perturbative operator product expansion (OPE), as we have recently shown in arXiv:2009.11297. This expansion is based on a decomposition of the dual periodic Wilson loop…
We describe rigorous quantum measurement theory in the Heisenberg picture by applying operator deformation techniques previously used in noncommutative quantum field theory. This enables the conventional observables (represented by…
The role of the operator-product expansion in QCD calculations is discussed. Approximating the two-point correlation function by several terms and assuming an upper bound on the truncation error along the euclidean ray, we consider two…
The short-distance singularity of the product of a composite scalar field that deforms a field theory and an arbitrary composite field can be expressed geometrically by the beta functions, anomalous dimensions, and a connection on the…
The problem of asymptotic expansions of Green functions in perturbative QFT is studied for the class of Euclidean asymptotic regimes. Phenomenological applications are analyzed to obtain a meaningful mathematical formulation of the problem.…
Boundary conditions changing operators have played an important role in conformal field theory. Here, we study their equivalent in the case where a mass scale is introduced, in an integrable way, either in the bulk or at the boundary. More…
Based on a recent proof of free choices in linking equations to the experiments they describe, I clarify relations among some purely mathematical entities featured in quantum mechanics (probabilities, density operators, partial traces, and…
We determine the form of the Wigner functional for several types of quantum free field theories in order to analyze the representation of QFT in phase space, as well as to compare it to other mainstream formulations. We use Jackiw's…
The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being…
Quantum Field Theory with fields as Operator Valued Distributions with adequate test functions, -the basis of Epstein-Glaser approach known now as Causal Perturbation Theory-, is recalled. Its recent revival is due to new developments in…
We study Witten's open string field theory in the presence of a constant B field. We construct the string field theory in the operator formalism and find that, compared to the ordinary theory with no B field, the vertices in the resulting…
In this paper, we present some fixed point theorems for operator systems in the line of Krasnosel'skii's theorem in cones. The cone-compression and cone-expansion type conditions are imposed in a component-wise manner. Unlike related…
We review the theory of quantum fields propagating in an arbitrary, classical, globally hyperbolic spacetime. Our review emphasizes the conceptual issues arising in the formulation of the theory and presents known results in a…
We review some quantum-phase descriptions of optical fields. We focus on real fields that can be generated in practice in various nonlinear optical processes. Thus, we rather avoid discussions of phase formalisms as such and try to exploit…
Certain quantum mechanical potentials give rise to a vanishing perturbation series for at least one energy level (which as we here assume is the ground state), but the true ground-state energy is positive. We show here that in a typical…
The symmetrized product for quantum mechanical observables is defined. It is seen as consisting of the ordinary multiplication and the application of the superoperator that orders the operators of coordinate and momentum. This superoperator…
We study self-adjoint extensions of operators which are the product of the multiplication operator by an analytic function and the analytic continuation in a strip. We compute the deficiency indices of the product operator for a wide class…
Limits on the regions of $Q^2$ and x where the operator product expansion canbe safely used, at small values of x are given. For a fixed large $Q^2$ there is an $x_0(Q^2)$ such that for Bjorken x-values below $x_0$ the operator product…