Related papers: Renormalization of the Inverse Square Potential
We review two different noncommutative gauge models generalizing approaches which lead to renormalizable scalar quantum field theories. One of them implements the crucial IR damping of the gauge field propagator in the so-called ``soft…
A general discussion of the renormalization of the quantum theory of a scalar field as an effective field theory is presented. The renormalization group equations in a mass-independent renormalization scheme allow us to identify the…
A nonlocal generalization of quantum field theory in which momentum space is the space of continuous maps of a circle into $\mathbf{R}^4$ is proposed. Functional integrals in this theory are proved to exist. Renormalized quantum field model…
Supersymmetric quantum mechanics is well known to provide, together with the so-called shape invariance condition, an elegant method to solve the eigenvalue problem of some one-dimensional potentials by simple algebraic manipulations. In…
The quantum renormalization group method is applied to study the quantum criticality and entanglement entropy of the ground state of the Ising chain in the presence of antisymmetric anisotropic couplings and alternating exchange…
A generalized definition of superpotential has proposed, which connects two one-dimensional potentials $V_{1}$ and $V_{2}$ with discrete energy spectra completely and where: 1) energy of factorization equals to arbitrary level of spectrum…
Results of perturbation theory in quantum field theory generally depend on the renormalization scheme that is in use. In particular, they depend on the scale. We try to make perturbation theory scheme invariant by re-expanding with respect…
A Cox-Thompson fixed-energy quantum inverse scattering method is developed further to treat long-range Coulomb interaction. Depending on the reference potentials chosen, two methods have been formulated which produce inverse potentials with…
In these lectures we consider some topics of Quantum Field Theory in Curved Space. In the first one particle creation in curved space is studied from a mathematical point of view, especially, particle production at a given time using the so…
We reinterpret the spectral dimension of spacetimes as the scaling of an effective self-energy transition amplitude in quantum field theory (QFT), when the system is probed at a given resolution. This picture has four main advantages: (a)…
We consider a scalar quantum field theory with global $O(N)^3$ symmetry in four Euclidean dimensions and solve it numerically in closed form in the large-N limit. For imaginary tetrahedral coupling the theory is asymptotically free, with…
In this work we address the reconstruction problem, investigating the construction of field theories from supersymmetric quantum mechanics. The procedure is reviewed, starting from reflectionless potentials that admit one and two bound…
We discuss the renormalon-based approach to power corrections in non-singlet deep inelastic scattering structure functions and compare it with the general operator product expansion. The renormalon technique and its variations relate the…
We propose and test a scheme for entanglement renormalization capable of addressing large two-dimensional quantum lattice systems. In a translationally invariant system, the cost of simulations grows only as the logarithm of the lattice…
We consider a non relativistic charged particle in a 1-dimensional infinite square potential well. This quantum system is subjected to a control, which is a uniform (in space) time depending electric field. It is represented by a complex…
We develop a reformulation of the functional integral for bosons in terms of bilocal fields. Correlation functions correspond to quantum probabilities instead of probability amplitudes. Discrete and continuous global symmetries can be…
The renormalization of a system of coupled scalars fields is analyzed. By introducing a momentum dependent mixing angle we diagonalize the inverse propagator matrix at any momentum $p^2$. The zeros of the inverse propagator matrix, \ie, the…
Using a recent reformulation of quantum mechanics where the potential function is not required, we are able to obtain the energy spectrum and wave function associated with the infinite square well analytically. Therefore, this work…
Scale invariant theories are often used to address the hierarchy problem, however the regularization of their quantum corrections introduces a dimensionful coupling (dimensional regularization) or scale (Pauli-Villars, etc) which break this…
In what follows we first set the context for inverse scattering in nuclear physics with a brief account of inverse problems in general. We then turn to inverse scattering which involves the S-matrix, which connects the interaction potential…