基于手征微扰理论构建相对论重子-重子相互作用(英文)

介绍了两个近期基于协变手征微扰理论构建领头阶核子-核子和超子-核子相互作用的工作。理论中未知的低能常数通过拟合核子-核子和超子-核子散射实验数据确定。分析发现,在对散射数据的描述上,领头阶相对论手征力可以媲美次领头阶非相对论手征核力。研究表明,构建相对论手征重子-重子相互作用技术上是可行的。得到的相互作用不仅可以为相对论核结构及反应研究提供重要的理论输入,而且可以进一步加深对低能强相互作用的认识。In this paper, we report on two recent studies of relativistic nucleon-nucleon and hyperonnucleon interactions in covariant chiral perturbation theory, where they are constructed up to leading order. The relevant unknown low energy constants are fixed by fitting to the nucleon-nucleon and hyperon-nucleon scattering data. It is shown that these interactions can describe the scattering data with a quality similar to their next-to-leading order non-relativistic counterparts. These studies show that it is technically feasible to construct relativist baryon-baryon interactions, and in addition, after further refinements, these interactions may provide important inputs to ab initio relativistic nuclear structure and reaction studies and help improve our understanding of low energy strong interactions.     

Information on three-body interactions from inversion of the energy equations

The inversion of the three energy equations, i.e. for the nuclear total energy, the sum of occupied single-particle state energies and the saturation condition, using the experimental data in ¹⁶O and ⁴⁰Ca, is carried out to determine whether three-body effective interactions are necessary in addition to density independent and dependent two-body interactions. In order to fit the data both in a non-relativistic and a relativistic framework, the three-body interaction energy is found to be large and repulsive. We also show that density-dependent two-body effective interactions, which are another requisite in the non-relativistic potential theory, are not necessarily needed in the relativistic mean field framework but allow to increase the effective nucleon mass.     

Diagram technique for finding of vertex functions in the Landau theory of heteropolymer liquids

The problem on finding the coefficients of the Landau free energy expansion into the power series of parameter of order has been considered for solutions and melts of linear heteropolymers whose molecules comprise several types monomeric units arranged stochastically. The presence of such a quenched structural disorder places this problem outside the framework of the traditional statistical physics inviting for its solution special approaches. One of them, based on the replica concept and actively engaged in theoretical physics of disordered systems, has been invoked in this paper to derive expressions for the vertex functions in the Landau theory of heteropolymer liquids. An algorithm has been formulated which permits one resorting to the simple diagram technique to write down expressions for these functions of any order in terms of the statistical characteristics of chemical quenched structure of polymer molecules. Explicit expressions for the contributions to the Landau free energy up to the fourth degree of order parameters for polymer systems with an arbitrary structural disorder have been presented to illustrate this general algorithm. Its potentialities have been also exemplified for the melt of random m-component copolymer where exact analytical formulas for these contributions up to n=6 at an arbitrary m have been derived for the first time.     

Landau theory of relativistic Fermi liquids

A relativistic extension of the Landau Fermi liquid theory, applicable to the study of high density matter, is developed. Consequences of Lorentz invariance in the theory are explored. The formalism is illustrated by a study of relativistic Fermi systems weakly interacting via scalar and vector meson exchange. Second order exchange energies for both massless scalar and massless vector interactions are calculated in terms of Landau parameters on the Fermi surface. Zero sound and “color-plasma oscillations” are studied in quark matter with SU(3) color gluon coupling.     

Magnetic interactions in strongly correlated systems: Spin and orbital contributions

We present a technique to map an electronic model with local interactions (a generalized multi-orbital Hubbard model) onto an effective model of interacting classical spins, by requiring that the thermodynamic potentials associated to spin rotations in the two systems are equivalent up to second order in the rotation angles, when the electronic system is in a symmetry-broken phase. This allows to determine the parameters of relativistic and non-relativistic magnetic interactions in the effective spin model in terms of equilibrium Green’s functions of the electronic model. The Hamiltonian of the electronic system includes, in addition to the non-relativistic part, relativistic single-particle terms such as the Zeeman coupling to an external magnetic field, spin–orbit coupling, and arbitrary magnetic anisotropies; the orbital degrees of freedom of the electrons are explicitly taken into account. We determine the complete relativistic exchange tensors, accounting for anisotropic exchange, Dzyaloshinskii–Moriya interactions, as well as additional non-diagonal symmetric terms (which may include dipole–dipole interaction). The expressions of all these magnetic interactions are determined in a unified framework, including previously disregarded features such as the vertices of two-particle Green’s functions and non-local self-energies. We do not assume any smallness in spin–orbit coupling, so our treatment is in this sense exact. Finally, we show how to distinguish and address separately the spin, orbital and spin–orbital contributions to magnetism, providing expressions that can be computed within a tight-binding Dynamical Mean Field Theory.     

A microinstability code for a uniform magnetized plasma with an arbitrary distribution function

We have developed a very general computer code for studying microinstabilities in a uniform magnetized plasma. Employing a new algorithm to perform two-dimensional numerical integrals in the conductivity tensor, the code can handle an arbitrary distribution function given by either an analytical function or numerical values on a momentum space grid and solve the full dispersion relation for an arbitrary propagation angle in either a non-relativistic or relativistic plasma except for a highly relativistic plasma (energy 1 MeV). The results for cyclotron-maser instability and whistler-wave instability are presented to illustrate the validity of the method.     

Triviality of Quantum Electrodynamics Revisited

Quantum electrodynamics is often considered to be a trivial theory.This is based on a number of evidences,both numerical and analytical.One of the strong indications for triviality of QED is the existence of the Landau pole for the running coupling.We show that by treating QED as the leading order approximation of an effective field theory and including the next-to-leading order corrections,the Landau pole is removed.We also analyze the cutoff dependence of the bare coupling at two-loop order and conclude that the conjecture,that for reasons of self-consistency,QED needs to be trivial is a mere artefact of the leading order approximation to the corresponding effective field theory.     

Self-consistent hartree description of finite nuclei in a relativistic quantum field theory

Relativistic Hartree equations for spherical nuclei are derived from a relativistic nuclear quantum field theory using a coordinate-space Green function approach. The renormalizable field theory lagrangian includes the interaction of nucleons with σ, ω, ρ and π mesons and the photon. The Hartree equations represent the “mean-field” approximation for a finite nuclear system. Coupling constants and the σ-meson mass are determined from the properties of nuclear matter and the rms charge radius in ⁴⁰Ca, and pionic contributions are absent for static, closed-shell nuclei. Calculated charge densities, neutron densities, rms radii, and single-nucleon energy levels throughout the periodic table are compared with data and with results of non-relativistic calculations. Relativistic Hartree results agree with experiment at a level comparable to that of the most sophisticated non-relativistic calculations to date. It is shown that the Lorentz covariance of the relativistic formalism leads naturally to density-dependent interactions between nucleons. Furthermore, non-relativistic reduction reveals non-central and non-local aspects inherent in the Hartree formalism. The success of this simple relativistic Hartree approach is attributed to these features of the interaction.     

Revisiting radiative decays of $$1^{+-}$$ heavy quarkonia in the covariant light-front approach

We revisit the calculation of the width for the radiative decay of a \(1^{+-}\) heavy \(Q \bar{Q}\) meson via the channel \(1^{+-} \rightarrow 0^{-+} +\gamma \) in the covariant light-front quark model. We carry out the reduction of the light-front amplitude in the non-relativistic limit, explicitly computing the leading and next-to-leading order relativistic corrections. This shows the consistency of the light-front approach with the non-relativistic formula for this electric dipole transition. Furthermore, the theoretical uncertainty in the predicted width is studied as a function of the inputs for the heavy-quark mass and wave function structure parameter. We analyze the specific decays \(h_{\mathrm{c}}(1P) \rightarrow \eta _{\mathrm{c}}(1S) + \gamma \) and \(h_{\mathrm{b}}(1P) \rightarrow \eta _{\mathrm{b}}(1S) + \gamma \). We compare our results with experimental data and with other theoretical predictions from calculations based on non-relativistic models and their extensions to include relativistic effects, finding reasonable agreement.     

Giant monopole and quadrupole states in the relativistic σ-ω model

Giant monopole and quadrupole states in the relativistic σ-ω model are studied with use of a local Lorentz boost and scaling method. In assuming nuclear matter, those excitation energies are expressed in a simple way in terms of the relativistic Landau parameters, and the expressions are formally very similar to nonrelativistic ones. In the σ-ω model, however, the values of the Landau parameters themselves are dominated by relativistic effects. Unlike the restoring forces depending on the Landau parameters, the mass parameters of these states are little affected by relativity.     

Electronuclear sum rules

Generalized sum rules are derived by integrating the electromagnetic structure functions along lines of constant ratio of momentum and energy transfer. For non-relativistic systems these sum rules are related to the conventional photonuclear sum rules by a scaling transformation. The generalized sum rules are connected with the absorptive part of the forward scattering amplitude of virtual photons. The analytic structure of the scattering amplitudes and the possible existence of dispersion relations have been investigated in schematic relativistic and non-relativistic models. While for the non-relativistic case analyticity does not hold, the relativistic scattering amplitude is analytical for time-like (but not for space-like) photons and relations similar to the Gell-Mann-Goldberger-Thirring sum rule exist.     

Quasiparticle relativistic G-matrix interaction

A quasiparticle G-matrix interaction has been constructed from a three-dimensional integral equation which is a relativistic generalization of the conventional non-relativistic Bethe-Goldstone equation. Relativistic dynamical effects have been discussed by comparing the relativistic and the conventional non-relativistic G-matrices. The Landau theory and, in particular, the quasi-particle current have also been discussed within the present relativistic formulation.

As an example of application, the quasiparticle relativistic G-matrix interaction has been used in the RPA calculation which includes 2p-2h processes.     

Ground-state energy of dilute neutron matter at next-to-leading order in lattice chiral effective field theory

We present lattice calculations for the ground-state energy of dilute neutron matter at next-to-leading order in chiral effective field theory. This study follows a series of recent papers on low-energy nuclear physics using chiral effective field theory on the lattice. In this work we introduce an improved spin- and isospin-projected leading-order action which allows for a perturbative treatment of corrections at next-to-leading order and smaller estimated errors. Using auxiliary fields and Euclidean-time projection Monte Carlo, we compute the ground state of 8, 12, and 16 neutrons in a periodic cube, covering a density range from 2% to 10% of normal nuclear density.     

Green's function formalism and quantum correction for finite-temperature baryon matter

A relativistic temperature Green's function formalism is used to find the one-loop quantum correction for infinite baryon matter with scalar and vector interactions. Effects on the equation of state and the baryon effective mass are analyzed.     

1/N expansion and the correlation energy of nuclear matter in the relativistic σω model

We propose the 1/N expansion method, where N can be identified with 2 due to the isospin SU(2), as a systematic expansion scheme for the relativistic meson-nucleon many-body theory. We derive a general formula for the computation of the effective action in the σω model based on the 1/N expansion, utilizing the functional integral method. In this scheme the leading contribution coincides with the familiar Hartree approximation. The elimination of the Landau ghost from the meson propagators in the subgraphs, which appears to be essential for our formulation, is also established.

As an application we compute the energy density of nuclear matter beyond the Hartree approximation including the next-to-leading order contributions in the 1/N expansion. In this order, one should include the ring energy contribution as a correlation energy addition to the exchange energy contribution. We find that we can describe the nuclear matter saturation properties without drastic changes of the overall physical picture which emerged in the Hartree approximation. The important role of the repulsive contribution due to the vacuum polarization effects in the ring energy is emphasized.     

Graphene-like physics in optical lattices

Graphene has attracted enormous attention over the past years in condensed matter physics. The most interesting feature of graphene is that its low-energy excitations are relativistic Dirac fermions. Such feature is the origin of many topological properties in graphene-like physics. On the other hand, ultracold quantum gas trapped in an optical lattice has become a unique setting for quantum simulation of condensed matter physics. Here, we mainly review our recent work on quantum simulation of graphene-like physics with ultracold atoms trapped in a honeycomb or square optical lattice, including the simulation of Dirac fermions and quantum Hall effect with and without Landau levels. We also present the related experimental advances.     

Mapping Between Charge-Dyon and Position-Dependent Mass Systems

The primary purpose of this work is to reproduce the scenario composed of a charge-dyon system utilizing position-dependent effective mass (PDM) background in the non-relativistic and in the relativistic regimes. In the non-relativistic case we substitute the exact charge-dyon eigenfunction into PDM Schr?dinger equation, in the Zhu-Kroemer parametrization, and then solve it for the mass distribution considering $M=M(r)$. Analogously, in the relativistic case we study the Klein-Gordon equation for a position-dependent mass, and in this case, we are able to analytically solve the equation for $M=M(r,\theta)$.     

Perturbations of unitary representations of the Galilei group: Mass operators with continuous spectra

We present a systematic procedure for constructing mass operators with continuous spectra for a system of particles in a manner consistent with Galilean relativity. These mass operators can be used to construct what may be called point-form Galilean dynamics. As in the relativistic case introduced by Dirac, the point-form dynamics for the Galilean case is characterized by both the Hamiltonian and momenta being altered by interactions. An interesting property of such perturbative terms to the Hamiltonian and momentum operators is that, while having well-defined transformation properties under the Galilei group, they also satisfy Maxwell’s equations. This result is an alternative to the well-known Feynman-Dyson derivation of Maxwell’s equations from non-relativistic quantum physics.