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Recent developments in light-front dynamics

Vladimir A. Karmanov

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

Abstract. Recent results on relativistic few body systems, obtained in the framework of light-front dynamics, are briefly reviewed. The following subjects are discussed: two scalar bosons with ladder and cross ladder kernel; two fermions with OBE kernel; relativistic scattering (elastic and inelastic); three bosons and fermions with zero-range interaction; many-body contributions.

Related papers

Recent developments in light-front dynamics

Vladimir A. Karmanov

Recent results on relativistic few body systems, obtained in the framework of light‐front dynamics, are briefly reviewed. The following subjects are discussed: two scalar bosons with ladder and cross ladder kernel; two fermions with OBE kernel; relativistic scattering (elastic and inelastic); three bosons and fermions with zero‐range interaction; many‐body contributions.

arXiv:nucl-th/0410033•AIP conference proceedings•Jan 1, 2005•0 citations

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Overview of the recent advances in description of the few two-component fermions is presented. Themodel of zero-range interaction is generally considered to discuss the principal aspects of the few-body dynamics. Particular attention is paid to detailed description of two identical fermions of mass m and a distinct particle of mass m 1: it turns out that two L P = 1− three-body bound states emerge if mass ratio m/m 1 increases up to the critical value µ c ≈ 13.607, abovewhich the Efimov effect takes place. The topics considered include rigorous treatment of the few-fermion problem in the zero-range interaction limit, lowdimensional results, the four-body energy spectrum, crossover of the energy spectra for m/m 1 near µ c , and properties of potential-dependent states. At last, enlisted are the problems, whose solution is in due course.

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Overview of the recent advances in description of the few two-component fermions is presented. The model of zero-range interaction is generally considered to discuss the principal aspects of the few-body dynamics. Particular attention is paid to detailed description of two identical fermions of mass $m$ and a distinct particle of mass $m_1$: it turns out that two $L^P = 1^-$ three-body bound states emerge if mass ratio $m/m_1$ increases up to the critical value $μ_c \approx 13.607$, above which the Efimov effect takes place. The topics considered include rigorous treatment of the few-fermion problem in the zero-range interaction limit, low-dimensional results, the four-body energy spectrum, crossover of the energy spectra for $m/m_1$ near $μ_c $, and properties of potential-dependent states. At last, enlisted are the problems, whose solution is in due course.

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Heavy-Light Few Fermion Clusters at Unitarity

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We examine the physics of two, three, and four heavy fermions interacting with a single light fermion via short-range interactions. Four-particle bosonic Efimov states have proven important experimentally and also been the subject of significant theoretical effort. Similar fermionic systems are just now being investigated. We find that with some simple interactions the four- and five-particle states collapse to the interaction range at smaller mass ratios than the three-body state, and also before larger clusters can collapse. These states and their excitations can be studied in cold atom experiments, providing unique insights into the role of few-body systems in many-body physics.

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Contributions to Theory of Few and Many-Body Systems in Lower Dimensions

Tianhao Ren

Few and many-body systems usually feature interesting and novel behaviors compared with their counterparts in three dimensions. On one hand, low dimensional physics presents challenges due to strong interactions and divergences in the perturbation theory; On the other hand, there exist powerful theoretical tools such as the renormalization group and the Bethe ansatz. In this thesis, I discuss two examples: three interacting bosons in two dimensions and interacting bosons/fermions in one dimension. In both examples, there are intraspecies repulsion as well as interspecies attraction, producing a rich spectrum of phenomena. In the former example, a universal curve of three-body binding energies versus scattering lengths is obtained efficiently by evolving a matrix renormalization group equation. In the latter example, exact solutions for the BCS-BEC crossover are obtained and the unexpected robust features in their excitation spectra are explained by a comprehensive semiclassical analysis.

•Jan 1, 2019•0 citations
Abstract. Recent results on relativistic few body systems, obtained in the framework of light-front dynamics, are briefly reviewed. The following subjects are discussed: two scalar bosons with ladder and cross ladder kernel; two fermions with OBE kernel; relativistic scattering (elastic and inelastic); three bosons and fermions with zero-range interaction; many-body contributions.
The quasi-potential approach is used to project a four-dimensional field-theoretical model of a three-particle system to the light-front (LF) valence sect or. The starting point is the Bethe-Salpeter equation (BSE) for three particles in the ladder approximation. The projection technique allows to eliminate three-body reducible diagrams from the kernel of the LF integral equation for the valence wave function. We construct the next-to-leading order contribution to the kernel of the LF three-body integral equation. We exemplify the method for a three-boson system with a contact interaction.
Overview of the recent advances in description of the few two-component fermions is presented. Themodel of zero-range interaction is generally considered to discuss the principal aspects of the few-body dynamics. Particular attention is paid to detailed description of two identical fermions of mass m and a distinct particle of mass m 1: it turns out that two L P = 1− three-body bound states emerge if mass ratio m/m 1 increases up to the critical value µ c ≈ 13.607, abovewhich the Efimov effect takes place. The topics considered include rigorous treatment of the few-fermion problem in the zero-range interaction limit, lowdimensional results, the four-body energy spectrum, crossover of the energy spectra for m/m 1 near µ c , and properties of potential-dependent states. At last, enlisted are the problems, whose solution is in due course.
Overview of the recent advances in description of the few two-component fermions is presented. The model of zero-range interaction is generally considered to discuss the principal aspects of the few-body dynamics. Particular attention is paid to detailed description of two identical fermions of mass mmm and a distinct particle of mass m1m_1m1​: it turns out that two LP=1−L^P = 1^-LP=1− three-body bound states emerge if mass ratio m/m1m/m_1m/m1​ increases up to the critical value μc≈13.607μ_c \approx 13.607μc​≈13.607, above which the Efimov effect takes place. The topics considered include rigorous treatment of the few-fermion problem in the zero-range interaction limit, low-dimensional results, the four-body energy spectrum, crossover of the energy spectra for m/m1m/m_1m/m1​ near $μ_c $, and properties of potential-dependent states. At last, enlisted are the problems, whose solution is in due course.
We examine the physics of two, three, and four heavy fermions interacting with a single light fermion via short-range interactions. Four-particle bosonic Efimov states have proven important experimentally and also been the subject of significant theoretical effort. Similar fermionic systems are just now being investigated. We find that with some simple interactions the four- and five-particle states collapse to the interaction range at smaller mass ratios than the three-body state, and also before larger clusters can collapse. These states and their excitations can be studied in cold atom experiments, providing unique insights into the role of few-body systems in many-body physics.
Few and many-body systems usually feature interesting and novel behaviors compared with their counterparts in three dimensions. On one hand, low dimensional physics presents challenges due to strong interactions and divergences in the perturbation theory; On the other hand, there exist powerful theoretical tools such as the renormalization group and the Bethe ansatz. In this thesis, I discuss two examples: three interacting bosons in two dimensions and interacting bosons/fermions in one dimension. In both examples, there are intraspecies repulsion as well as interspecies attraction, producing a rich spectrum of phenomena. In the former example, a universal curve of three-body binding energies versus scattering lengths is obtained efficiently by evolving a matrix renormalization group equation. In the latter example, exact solutions for the BCS-BEC crossover are obtained and the unexpected robust features in their excitation spectra are explained by a comprehensive semiclassical analysis.