相关论文: On the Inequivalence of Renormalization and Self-A…
A multichannel S-matrix framework for singular quantum mechanics (SQM) subsumes the renormalization and self-adjoint extension methods and resolves its boundary-condition ambiguities. In addition to the standard channel accessible to a…
The singular behavior of conformal interactions is examined within a comparative analysis of renormalization frameworks. The effective approach--inspired by the effective-field theory program--and its connection with the core framework are…
The renormalization procedure is proved to be a rigorous way to get finite answers in a renormalizable class of field theories. We claim, however, that it is redundant if one reduces the requirement of finiteness to S-matrix elements only…
We study the question of whether two frames of a given physical theory are equivalent or not in the presence of quantum corrections. By using field theory arguments we claim that equivalence is broken in the presence of anomalous symmetries…
In this work, we review two methods used to approach singular Hamiltonians in (2+1) dimensions. Both methods are based on the self-adjoint extension approach. It is very common to find singular Hamiltonians in quantum mechanics, especially…
Regularization and renormalization is discussed in the context of low-energy effective field theory treatments of two or more heavy particles (such as nucleons). It is desirable to regulate the contact interactions from the outset by…
Arguments are provided which show that extension of renormalizability in quantum field theory is possible. A dressed scheme for the perturbation expansion is proposed. It is proven that in this scheme a nonrenormalizable interaction becomes…
The relation between renormalization and short distance singular divergencies in quantum field theory is studied. As a consequence a finite theory is presented. It is shown that these divergencies are originated by the multiplication of…
We prove that the separable and local approximations of the discontinuity-inducing zero-range interaction in one-dimensional quantum mechanics are equivalent. We further show that the interaction allows the perturbative treatment through…
The similarity renormalization group (SRG) is based on unitary transformations that suppress off-diagonal matrix elements, forcing the hamiltonian towards a band-diagonal form. A simple SRG transformation applied to nucleon-nucleon…
In the present paper we deal with the issue of finding the self-adjoint extensions of a $p^4$-corrected Hamiltonian. The importance of this subject lies on the application of the concepts of quantum mechanics to the minimal-length scale…
The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon…
We use renormalization as a tool to extract universal features of the NN interaction in quark and soliton nucleon models, having the same long distance behaviour but different short distance components. While fine tuning conditions in the…
The objective of the present paper is the study of a one-dimensional Hamiltonian with the interaction term given by the sum of two nonlocal attractive $\delta'$-interactions of equal strength and symmetrically located with respect to the…
We discuss an alternative method to mass renormalize a quantum field Hamiltonian based on a requirement that the vacuum and single-particle sectors are not self-scattering. We illustrate the feasibility of this method for the concrete…
We study the self-similar structure of loop amplitudes in quantum field theory and apply it to amplitude generation and renormalization. A renormalized amplitude can be regarded as an effective coupling that recursively appears within…
We study self-adjoint operators defined by factorizing second order differential operators in first order ones. We discuss examples where such factorizations introduce singular interactions into simple quantum mechanical models like the…
Considerable attention has been recently focused on quantum-mechanical systems with boundaries and/or singular potentials for which the construction of physical observables as self-adjoint (s.a.) operators is a nontrivial problem. We…
In this paper, we present a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential $\alpha x^{-2}$. Although the problem is quite old and well-studied, we believe that our…
We consider the Hamiltonian renormalisation group flow of discretised one-dimensional physical theories. In particular, we investigate the influence the choice of different embedding maps has on the RG flow and the resulting continuum…