Related papers: A Conformal Fixed-Point Equation for the Effective…
We consider an inverse extremal problem for variational functionals on arbitrary time scales. Using the Euler-Lagrange equation and the strengthened Legendre condition, we derive a general form for a variational functional that attains a…
The problem of individualized prediction can be addressed using variants of conformal prediction, obtaining the intervals to which the actual values of the variables of interest belong. Here we present a method based on detecting the…
Fixed point lattice actions are designed to have continuum classical properties unaffected by discretization effects and reduced lattice artifacts at the quantum level. They provide a possible way to extract continuum physics with coarser…
Based on a methodological analysis of the effective action approach certain conceptual foundations of quantum field theory are reconsidered to establish a quest for an equation for the effective action. Relying on the functional integral…
In a four dimensional theory of gravity with lagrangian quadratic in curvature and torsion, we compute the effective action for metrics of the form $g_{\mu\nu}=\rho^2\delta_{\mu\nu}$, with $\rho$ constant. Using standard field-theoretic…
The gauge dependence of effective average action in the functional renormalization group is studied. The effective average action is considered as non-perturbative solution to the flow equation which is the basic equation of the method. It…
Conformal prediction is a popular method to construct prediction intervals with marginal coverage guarantees from black-box machine learning models. In applications with potentially high-impact events, such as flooding or financial crises,…
We introduce a theory of integration with respect to the fixed point index, offering a substantial improvement over previous approaches based on the Lefschetz number. This framework eliminates several restrictive assumptions -- such as the…
Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of…
In this paper a new method for inverting the Laplace transform from the real axis is formulated. This method is based on a quadrature formula. We assume that the unknown function $f(t)$ is continuous with (known) compact support. An…
The role of the conformal group in electrodynamics in four space-time dimensions is re-examined. As a pedagogic example we use the application of conformal transformations to find the electromagnetic field for a charged particle moving with…
Effective dynamics using conditional expectation was proposed in [F. Legoll and T. Leli\`evre, Nonlinearity, 2010] to approximate the essential dynamics of high-dimensional diffusion processes along a given reaction coordinate. The…
In this work, the power series solutions are given around a regular-singular point, in the case of variable coefficients for homogeneous sequential linear conformable fractional differential equations of order 2{\alpha}.
The implications of restricted conformal invariance under conformal transformations preserving a plane boundary are discussed for general dimensions $d$. Calculations of the universal function of a conformal invariant $\xi$ which appears in…
We calculate the quantum corrections to the classical action of a particle with coordinate-dependent mass. The result is made self-consistent by a variational approach, thus making it applicable to strong-couplings and singular potentials.…
We show how conformal invariance predicts the functional form of two-point correlators in one-dimensional periodic quantum systems. Numerical evidence for this functional form in a wide class of models --- including long-ranged ones --- is…
We gauge fix the Standard Model Effective Field Theory in a manner invariant under background field gauge transformations using a geometric description of the field connections.
We study weak and strong solutions of nonlinear non-compact operator equations in abstract spaces of adapted random points. The main result of the paper is similar to Schauder's fixed-point theorem for compact operators. The illustrative…
The conformal fixed points of the generalized Thirring model are investigated with the help of bosonization, the large N limit and the operator product expansion. Necessary conditions on the coupling constants for conformal invariance are…
The implications of conformal invariance, as relevant in quantum field theories at a renormalisation group fixed point, are analysed with particular reference to results for correlation functions involving conserved currents and the energy…