Related papers: Potential theory with multivariate kernels
A systematic structure of particle interactions is predicted within and beyond the standard model. The proof is performed either on the basis of (A) a generalisable form of general relativity or, equivalently, (B) minimum information…
This is a survey article on Mercer's Theorem in its most general form and its relations with the theory of reproducing kernel Hilbert spaces and the spectral theory of compact operators. We provide a modern introduction to the basics of the…
The relativistic two-body potentials of constraint theory for systems composed of two spin-0 or two spin-1/2 particles are calculated, in perturbation theory, by means of the Lippmann-Schwinger type equation that relates them to the…
In this paper we construct a hierarchy of multivariate polynomial approximation kernels via semidefinite programming. We give details on the implementation of the semidefinite programs defining the kernels. Finally, we show how a symmetry…
Links between two well known methods: methods of zero-range and non-overlapped (muffin-tin) potentials are discussed. Some difficulties of the method of zero-range potentials and its possible elimination are discussed. We argue that such…
The principle of local covariance which was recently introduced admits a generally covariant formulation of quantum field theory. It allows a discussion of structural properties of quantum field theory as well as the perturbative…
This short communication investigates impurity coupling in generalized field theories where scalar coupling is introduced directly at the level of the kinetic and gradient contributions of the energy. We show that the fundamental aspects of…
We consider classical N-particle system with arbitrary central pair potential. Mechanical equilibrium condition in spherically-symmetric case leads to a nonlinear integro-differential equation for concentration n(r). For special state…
Physics-informed machine learning combines the expressiveness of data-based approaches with the interpretability of physical models. In this context, we consider a general regression problem where the empirical risk is regularized by a…
For a relativistic particle moving in the presence of mean scalar and vector fields, the energy at second order in the scalar field is shown to contain two contributions in general. One is a momentum-dependent repulsive interaction…
The concept of effective particles is introduced in the Minkowski space-time Hamiltonians in quantum field theory using a new kind of the relativistic renormalization group procedure that does not integrate out high-energy modes but instead…
A simple theory for the leading-order correction g_1(r) to the structure of a hard-sphere liquid with discrete (e.g. square-well) potential perturbations is proposed. The theory makes use of a general approximation that effectively…
We analyze the evolution of the effective potential and the particle spectrum of two-parameter families of non-integrable quantum field theories. These theories are defined by deformations of conformal minimal models M_m by using the…
In this paper we consider nonlocal energies defined on probability measures in the plane, given by a convolution interaction term plus a quadratic confinement. The interaction kernel is $-\log|z|+\alpha\, x^2/|z|^2, \; z=x+iy,$ with $-1 <…
In strongly coupled field theories, perturbation theory cannot be employed to study the low-energy spectrum. Thus, non-perturbative techniques are required. We employ the variational method, a rigorous, non-perturbative approach which…
Here we present a many-body theory based on a solution of the $N$-representability problem in which the ground-state two-particle reduced density matrix (2-RDM) is determined directly without the many-particle wave function. We derive an…
Quantum coherence is one of the most important resources in quantum information. Indeed, preventing the loss of coherence is one of the most important technical challenges obstructing the development of large-scale quantum computers.…
The low-energy theory on the world volume of parallel static D3-branes of type 0 strings is the Yang-Mills theory with six scalar fields in the adjoint representation. One-loop corrections in this theory induce Coleman-Weinberg effective…
Recently developed strong-coupling theory open up the possibility of treating quantum-mechanical systems with hard-wall potentials via perturbation theory. To test the power of this theory we study here the exactly solvable quantum…
We propose an interpretation of physics named potentiality realism. This view, which can be applied to classical as well as to quantum physics, regards potentialities (i.e. intrinsic, objective propensities for individual events to obtain)…