Related papers: Examples of reflection positive Euclidean field th…
The $f(R)$ theory of gravity can be expressed as a scalar tensor theory with a scalar degree of freedom $\phi$. By a conformal transformation, the action and its Gibbons-York-Hawking boundary term are written in the Einstein frame and the…
The Wick rotation provides the standard technique of computing Feynman diagrams by means of Euclidean propagators. Let us suppose that quantum fields in an interaction zone are really Euclidean. In contrast with the well-known Euclidean…
We study one-loop perturbative properties of scalar field theories on the $\rho$-Minkowski space. The corresponding star-product, together with the involution are characterized from a combination of Weyl quantization and defining properties…
Non-commutative Euclidean scalar field theory is shown to have an eigenvalue sector which is dominated by a well-defined eigenvalue density, and can be described by a matrix model. This is established using regularizations of R^{2n}_\theta…
It is shown that the $n$-point functions of scalar massive free fields on the noncommutative Minkowski space are distributions which are boundary values of analytic functions. Contrary to what one might expect, this construction does not…
We consider scalar field theory defined over a direct product of the real and $p$-adic numbers. An adjustable dynamical scaling exponent $z$ enters into the microscopic lagrangian, so that the Gaussian theories provide a line of fixed…
There is a dilemma in constructing interacting scale invariant but not conformal invariant Euclidean field theories. On one hand, scale invariance without conformal invariance seems more generic by requiring only a smaller symmetry. On the…
Inspired by the problem of Planckian scattering we describe a classical effective field theory for weak ultra relativistic scattering in which field propagation is instantaneous and transverse and the particles' equations of motion localize…
We revisit the long-standing conjecture that in unitary field theories, scale invariance implies conformality. We explain why the Zamolodchikov-Polchinski proof in D=2 does not work in higher dimensions. We speculate which new ideas might…
Taking Euclidean signature space-time with its local Spin(4)=SU(2)xSU(2) group of space-time symmetries as fundamental, one can consistently gauge one SU(2) factor to get a chiral spin connection formulation of general relativity, the other…
A light scalar degree of freedom, as the one possibly responsible for the accelerated expansion of the Universe, could leave observable traces in the inspiral gravitational wave signal of binary systems. In order to study these effects, we…
A field theory is developed based on the idea that the effective action of yet unknown fundamental theory, at energy scale below M_{p} has the form of expansion in two measures: S=\intd^{4}x[\Phi L_{1}+\sqrt{-g}L_{2}] where the new measure…
We assume that the noncommutativity starts to be visible continuously from a scale $\Lambda_{NC}$. According to this assumption, a two-loop effective action is derived for noncommutative $\phi^{4}$ and $\phi^{3}$ theories from a Wilsonian…
We introduce the notion of $N$-reflection equation which provides a large generalization of the usual classical reflection equation describing integrable boundary conditions. The latter is recovered as a special example of the $N=2$ case.…
In this article we specialize a construction of a reflection positive Hilbert space due to Dimock and Jaffe--Ritter to the sphere $\mathbb{S}^n$. We determine the resulting Osterwalder--Schrader Hilbert space, a construction that can be…
The theory of positive kernels and associated reproducing kernel Hilbert spaces, especially in the setting of holomorphic functions, has been an important tool for the last several decades in a number of areas of complex analysis and…
It is shown that graphs that generalize the ADE Dynkin diagrams and have appeared in various contexts of two-dimensional field theory may be regarded in a natural way as encoding the geometry of a root system. After recalling what are the…
Effective theories are non-local at the scale of the eliminated heavy particles modes. The gradient expansion which represents such non-locality must be truncated to have treatable models. This step leads to the proliferation of the degrees…
Effective field theory provides a way of parameterizing strong-field deviations from General Relativity that might be observable in the gravitational waves emitted in a black hole merger. To perform numerical simulations of mergers in such…
We present an effective field theory of the $\Delta$-resonance as an interacting Weinberg's $(3/2,0)\oplus (0,3/2)$ field in the multi-spinor formalism. We derive its interactions with nucleons $N$, pions $\pi$ and photons $\gamma$, and…