Lattice simulations for light nuclei: Chiral effective field theory at leading order

We discuss lattice simulations of light nuclei at leading order in the chiral effective field theory. Using lattice pion fields and auxiliary fields, we include the physics of instantaneous one-pion exchange and the leading-order S-wave contact interactions. We also consider higher-derivative contact interactions which adjust the S-wave scattering amplitude at higher momenta. By construction our lattice path integral is positive definite in the limit of exact Wigner SU(4) symmetry for any even number of nucleons. This SU(4) positivity and the approximate SU(4) symmetry of the low-energy interactions play an important role in suppressing sign and phase oscillations in Monte Carlo simulations. We assess the computational scaling of the lattice algorithm for light nuclei with up to eight nucleons and analyze in detail calculations of the deuteron, triton, and helium-4.     

Unitary fermions and Lscher's formula on a crystal

We consider the low-energy particle-particle scattering properties in a periodic simple cubic crystal. In particular, we investigate the relation between the two-body scattering length and the energy shift experienced by the lowest-lying unbound state when this is placed in a periodic finite box. We introduce a continuum model for s-wave contact interactions that respects the symmetry of the Brillouin zone in its regularisation and renormalisation procedures, and corresponds to the nae continuum limit of the Hubbard model. The energy shifts are found to be identical to those obtained in the usual spherically symmetric renormalisation scheme upon resolving an important subtlety regarding the cutoff procedure. We then particularize to the Hubbard model, and find that for large finite lattices the results are identical to those obtained in the continuum limit. The results reported here are valid in the weak,intermediate and unitary limits. These may be used to significantly ease the extraction of scattering information, and therefore effective interactions in condensed matter systems in realistic periodic potentials. This can achieved via exact diagonalisation or Monte Carlo methods, without the need to solve challenging, genuine multichannel collisional problems with very restricted symmetry simplifications.     

Temperature-dependent orbital degree of freedom of a bilayer manganite by magnetic compton scattering

We have measured temperature-dependent magnetic Compton profiles (MCPs) from a single crystal of La1.2Sr1.8Mn2O7. The MCPs, which involved the scattering of circularly polarized x rays, are in general related to the momentum density of all the unpaired spins in the system. Nevertheless, we show that when the x-ray scattering vector lies along the [110] direction, the number of magnetic electrons of a specific symmetry, i.e., d electrons of x(2)-y(2) symmetry, yield a distinct signature in the MCP, allowing us to monitor substantial changes in the occupancy of the dx(2)(-y(2)) states over the investigated temperature range of 5-200 K. This study indicates that magnetic Compton scattering can provide a powerful window on the properties of specific magnetic electrons in complex materials.     

Nonperturbative, Unitary Quantum-Particle Scattering Amplitudes from Three-Particle Equations

We here use our nonperturbative, cluster decomposable relativistic scattering formalism to calculate photon–spinor scattering, including the related particle–antiparticle annihilation amplitude. We start from a three-body system in which the unitary pair interactions contain the kinematic possibility of single quantum exchange and the symmetry properties needed to identify and substitute antiparticles for particles. We extract from it a unitary two-particle amplitude for quantum–particle scattering. We verify that we have done this correctly by showing that our calculated photon–spinor amplitude reduces in the weak coupling limit to the usual lowest order, manifestly covariant (QED) result with the correct normalization. That we are able to successfully do this directly demonstrates that renormalizability need not be a fundamental requirement for all physically viable models.     

Collective features of gravitational light focusing

A distribution of matter described by a continuous density function of spherical symmetry is shown to behave as a stigmatic lens whose focal length and aberrations are calculated. We suggest that a statistically spherical cluster of stars has similar optical properties. The close ray — particle (star) interactions are described as scattering losses for the collective lens effect due to the averaged long range interactions.     

On relativistic approaches to the pion self-energy in nuclear matter

We argue that, in contrast to the non-relativistic approach, a relativistic evaluation of the nucleon-hole and delta-isobar-nucleon-hole contributions to the pion self-energy incorporates the s-wave scattering, whose magnitude within the RPA is in conflict with the near-threshold behavior imposed by chiral symmetry. As a result, a relativistic approach to the pion self-energy in isospin-symmetric nuclear matter, containing only these diagrams, does not satisfy the known experimental results on the near-threshold behavior of the -nucleon (forward) scattering amplitude.Received: 12 December 2003, Revised: 16 March 2004, Published online: 26 May 2004PACS: 24.10.Cn Many-body theory - 13.75.Cs Nucleon-nucleon interactions (including antinucleons, deuterons, etc.) - 21.65. + f Nuclear matter - 25.70.-z Low and intermediate energy heavy-ion reactions     

General laws of hadron scattering at very high energies

We review the general properties of particle scattering at extremely high energy and fixed momentum transfer, concentrating on features which can be derived from analyticity, crossing symmetry, unitarity and other general principles. The progress since 1973 is reported; it is pointed out that the rigorous approach yields fairly tight high-energy correlations between the phase and the modulus of the crossing-even as well as the crossing-odd forward scattering amplitude, without assuming any particular model of the interaction mechanism. The approach becomes particularly predictive when the formalism is supplemented by the phenomenological assumption that the total cross section rises unboundedly at high energies. Relation of the results to existing hadron-hadron scattering data and to future experiments is discussed.     

Scattering and infinite dimensional symmetry schemes

We examine the recently proposed non-trivial binding of the Poincare group with internal symmetry groups, which leads to mass splitting without symmetry breaking, from the point of view of scattering. We give a very general realization of the corresponding infinite dimensional Lie algebra in the Fok space of asymptotic states built from two scalar nucleons. Assuming that the algebra describes the exact symmetry of theS-matrix we conclude that no elastic NN scattering exists.The author is indebted to Professor V. Votruba and Dr. J. Formánek for many stimulating discussions.     

Strong quadrupole interaction of light with molecules and its manifestation in surface-enhanced hyper-Raman scattering spectra

The possibility of the giant enhancement of hyper-Raman scattering by molecules adsorbed on rough metal surfaces is demonstrated. The theory is based on the qualitative consideration of electromagnetic field enhancement near some model rough surfaces and individual irregularities, as well as on the quantum-mechanical features of dipole and quadrupole interactions of light with molecules (as in the theory of surface-enhanced Raman scattering), proposed by the author. A consideration of symmetric molecules makes it possible to obtain selection rules for surface-enhanced hyper-Raman scattering (SEHRS) spectra and establish such a regularity as the occurrence of strong forbidden lines (which are due to totally symmetric vibrations); these lines are transformed according to unitary irreducible representation in molecules with the symmetry groups C _nh , D, and higher. An analysis of the data in the literature for trans-1,2-bis (4-pyridyl)ethylene and pyridine molecules shows that their spectra can be explained in terms of the dipole-quadrupole theory of SEHRS. At the same time, the analysis of the SEHRS spectra of pyrazine revealed the presence of strong forbidden bands due to totally symmetric vibrations. This finding substantiated the proposed theory, which makes it possible to interpret the entire spectrum in detail. These results are in good agreement with the general mechanism of the optical effects enhanced by molecules adsorbed on metal surfaces, which was developed by the author.     

Entropy and global Markov properties

We extend, refine and give simple proofs of some recent results on the validity of global Markov properties for classical spin systems. One of the new results is that there is a global Markov property that is satisfied by equilibrium states in general. The proof of this establishes formulas for the entropy and free energy that show that these quantities are, ford-dimensional systems, given in terms of (d–1)-dimensional systems. Furthermore, we show that global Markov properties imply the absence of some types of symmetry breaking.Research supported by NSF Grants DMS 85-12505 and SMR 86-12369     

Star-triangle relation for a three-dimensional model

The solvablesl(n)-chiral Potts model can be interpreted as a three-dimensional lattice model with local interactions. To within a minor modification of the boundary conditions it is an Ising-type model on the body-centered cubic lattice with two- and three-spin interactions. The corresponding local Boltzmann weights obey a number of simple relations, including a restricted star-triangle relation, which is a modified version of the well-known star-triangle relation appearing in two-dimensional models. We show that these relations lead to remarkable symmetry properties of the Boltzmann weight function of an elementary cube of the lattice, related to the spatial symmetry group of the cubic lattice. These symmetry properties allow one to prove the commutativity of the row-to-row transfer matrices, bypassing the tetrahedron relation. The partition function per site for the infinite lattice is calculated exactly.On leave of absence from the Institute for High Energy Physics, Protvino, Moscow Region, 142284, Russia.     

Asymptotic Scaling in a Model Class of Anomalous Reaction-Diffusion Equations

Abstract

We analyze asymptotic scaling properties of a model class of anomalous reaction-diffusion (ARD) equations. Numerical experiments show that solutions to these have, for large t, well defined scaling properties. We suggest a general framework to analyze asymptotic symmetry properties; this provides an analytical explanation of the observed asymptotic scaling properties for the considered ARD equations.     

Unitarity structure of scattering amplitudes

As a first step towards constructing scattering amplitudes satisfying unitarity, analyticity and crossing symmetry, we derive a linear non-singular integral equation for the total scattering amplitude which is equivalent to the unitarity condition. For this purpose we use the partial-waveN/D representation (with inelasticity) and the convolution theorem for Legendre transforms. We also discuss briefly the choice of two functionsN(s, cos Θ),C(s, cos Θ) which determine the unitary scattering amplitude through the integral equation. These functions may hopefully be chosen so that the analyticity and crossing symmetry requirements are satisfied.

     

The off-shell electromagnetic T-matrix: momentum-dependent scattering from spherical inclusions with both dielectric and magnetic contrasts

The momentum- and frequency-dependent T-matrix operator for the scattering of electromagnetic waves by a dielectric/conducting and para- or diamagnetic sphere is derived as a Mie-type series, and presented in a compact form emphasizing various symmetry properties, notably the unitarity identity. This result extends to magnetic properties one previously obtained for purely dielectric contrasts by other authors. Several situations useful to spatially-dispersive effective-medium approximations to one-body order are examined. Partial summation of the Mie series is achieved in the case of elastic scattering.     

Disordered d-wave superconductors with interactions

We study the localization properties of disordered d-wave superconductors by means of the fermionic replica trick method. We derive the effective non-linear σ-model describing the diffusive modes related to spin transport which we analyze by the Wilson–Polyakov renormalization group. A lot of different symmetry classes are considered within the same framework. According to the presence or the absence of certain symmetries, we provide a detailed classification for the behavior of some physical quantities, like the density of states, the spin and the quasiparticle charge conductivities. Following the original Finkel'stein approach, we finally extend the effective functional method to include residual quasiparticle interactions, at all orders in the scattering amplitudes. We consider both the superconducting and the normal phase, with and without chiral symmetry, which occurs in the so-called two-sublattice models.     

Electroweak Processes in Few-Nucleon Systems

 After a brief introduction into the basic ingredients of electroweak theory as a spontaneously broken local, non-Abelian gauge symmetry, the general properties of the electromagnetic current and two-photon operators are discussed. In particular, the consequences of gauge invariance and the resulting low-energy theorems are reviewed. The multipole decomposition of the current operators and the general Siegert theorem are presented. The specific forms of vector and axial one-nucleon currents are given, together with lowest-order π- meson exchange and isobar currents as well as meson production currents. A brief overview is given on the most important one- and two-boson processes. Electron scattering in the one-boson approximation is then considered in greater detail. Formal expressions of the cross section for inclusive and exclusive processes are given, including parity-violating contributions from γ-Z interference as well as from parity-violating components in the hadronic wave function. Specific electromagnetic reactions on the deuteron are then discussed with respect to the influence of meson exchange currents, isobar configurations in the deuteron ground state, relativistic contributions and the role of π-meson retardation. Furthermore, recent results on coherent and incoherent π- and η-photoproduction are presented as well as a discussion of the Gerasimov-Drell-Hearn sum rule and the effect of a parity-violating deuteron component on inclusive electron scattering off the deuteron for quasifree kinematics. The review closes with a summary and a brief outlook.     

The Bethe-Salpeter equation for spin-1 particles

We develop here the general treatment of the Bethe—Salpeter equation for the bound state of two spin-l particles interacting through an electromagnetic interaction. The treatment here, which can be generalized to strong interactions, combines the two-component approach utilized previously by the author in conjunction with spontaneous symmetry breaking. This is done by using a Lagrangian having SU(2)×U(1) symmetry (without fermions) and then choosing the ′t Hooft gauge. In this way, a renormalizable theory for the interaction of two spin-l particles via an electromagnetic interaction is ensured.     

Short-Range Repulsion and Broken Chiral Symmetry in Low-Energy Scattering

This paper is an essentially modified version of the chapter “Short-range repulsion” from the English edition [1] of the book “Dispersion theories of strong interactions at low-energies” (in the Russian edition [1] this chapter is absent). Unlike the English version, we have employed the concept of chiral symmetry and ist consequences for the low-energy characteristics of strong interactions as boundary conditions on the solution of dispersion equations. The introduction of the short-range repulsion “potentials” into the low-energy equations for lower partial waves makes it possible to eliminate the main difficulties of the purely elastic low-energy (Pele) approximation. There is then a possibility in principle of obtaining solutions with small s-wave scattering lengths and broad resonances. The use of threshold conditions resulting from chiral symmetry allows us (under certain additional conditions) to express the main resonance scattering parameters in terms of the pion decay characteristics. Formulas are presented, by means of one of which the ϱ meson mass m_ϱ is expressed in terms of the pion mass μ and the decay constant ƒ_π from the PCAC condition (Eq. (5.26) and the other (Eq. (5.27)) expresses the ϱ meson width Γ via μƒ_π and m_π and is a generalization of the well-known KSFR relation taking into account unitarity corrections. Similar results have been obtained for the Δ₃₃ resonance in pion-nucleon scattering. Thus, using the broken chiral symmetry approximation and unitarity dispersion equations for low-energy ππ and πN scattering we have obtained masses, life-time and coupling constants for p-wave resonances by specifying only the pion and nucleon masses, their life-times and the Fermi coupling constant. Reported at the Conference on the High Energy Physics in the Institute for Theoretical Physics, Kiev, the Ukrainian SSR, October 1969.     

Time reversal symmetry in light scattering by excitations in a film

We present a general symmetry argument for light scattering by excitations in an insulator film. The analysis holds for bulk continuum, guided and surface excitations.The main results represent a simplification of the theory and a better understanding for the time reversal properties of the system. Those properties hold both for forward and backward scatering, and are independent of the substrate upon which the film is deposited. We show that the asymmetry in the shape of the cross-section which is common to many experimental situations is in fact a consequence of the time reversal properties of the system.     

Localized retarded modes in a ferromagnetic slab

General results are given for Green functions, mode frequencies and light scattering cross section for retarded modes in a ferromagnetic slab. These results hold for a more general geometry than the Voigt's one. We show that they fulfill very general symmetry requirements.