Aspects of affine Toda field theory

Several of the recently discovered classical and quantum features of affine Toda field theory are briefly reviewed, with particular emphasis on the Lie algebraic structure of masses, conserved quantities and S-matrices.     

Three approaches to classical thermal field theory

In this paper we study three different functional approaches to classical thermal field theory, which turn out to be the classical counterparts of three well-known different formulations of quantum thermal field theory: the closed-time path (CTP) formalism, the thermofield dynamics (TFD) and the Matsubara approach.     

Quasiparticle excitations in relativistic quantum field theory

We analyze the particle-like excitations arising in relativistic field theories in states different than the vacuum. The basic properties characterizing the quasiparticle propagation are studied using two different complementary methods. First we introduce a frequency-based approach, wherein the quasiparticle properties are deduced from the spectral analysis of the two-point propagators. Second, we put forward a real-time approach, wherein the quantum state corresponding to the quasiparticle excitation is explicitly constructed, and the time-evolution is followed. Both methods lead to the same result: the energy and decay rate of the quasiparticles are determined by the real and imaginary parts of the retarded self-energy, respectively. Both approaches are compared, on the one hand, with the standard field-theoretic analysis of particles in the vacuum and, on the other hand, with the mean-field-based techniques in general backgrounds.     

Properties and structure of N=Z nuclei within relativistic mean field theory

The axially deformed relativistic mean field theory with the force NLSH has been performed in the blocked BCS approximation to investigate the properties and structure of N=Z nuclei from Z=20 to Z=48.Some ground state quantities such as binding energies, quadrupole deformations, one/two-nucleon separation energies, root-mean-square (rms) radii of charge and neutron, and shell gaps have been calculated.The results suggest that large deformations can be found in medium-heavy nuclei with N=Z=38-42.The charge and neutron rms radii increase rapidly beyond the magic number N=Z=28 until Z=42 with increasing nucleon number, which is similar to isotope shift, yet beyond Z=42, they decrease dramatically as the structure changes greatly from Z=42 to Z=43.The evolution of shell gaps with proton number Z can be clearly observed.Besides the appearance of possible new shell closures, some conventional shell closures have been found to disappear in some region.In addition, we found that the Coulomb interaction is not strong enough to breakdown the shell structure of protons in the current region.     

Properties and structure of N=Z nuclei within relativistic mean field theory

The axially deformed relativistic mean field theory with the force NLSH has been performed in the blocked BCS approximation to investigate the properties and structure of N=Z nuclei from Z=20 to Z=48. Some ground state quantities such as binding energies, quadrupole deformations, one/two-nucleon separation energies, root-mean-square （rms） radii of charge and neutron, and shell gaps have been calculated. The results suggest that large deformations can be found in medium-heavy nuclei with N=Z=38-42. The charge and neutron rms radii increase rapidly beyond the magic number N=Z=28 until Z=42 with increasing nucleon number, which is similar to isotope shift, yet beyond Z=42, they decrease dramatically as the structure changes greatly from Z=42 to Z=43. The evolution of shell gaps with proton number Z can be clearly observed. Besides the appearance of possible new shell closures, some conventional shell closures have been found to disappear in some region. In addition, we found that the Coulomb interaction is not strong enough to breakdown the shell structure of protons in the current region.     

The role of type III factors in quantum field theory

One of von Neumann's motivations for developing the theory of operator algebras and his and Murray's 1936 classification of factors was the question of possible decompositions of quantum systems into independent parts. For quantum systems with a finite number of degrees of freedom the simplest possibility, i.e. factors of type I in the terminology of Murray and von Neumann, are perfectly adequate. In relativistic quantum field theory (RQFT), on the other hand, factors of type III occur naturally. The same holds true in quantum statistical mechanics of infinite systems. In this brief review some physical consequences of the type III property of the von Neumann algebras corresponding to localized observables in RQFT and their difference from the type I case will be discussed. The cumulative effort of many people over more than 30 years has established a remarkable uniqueness result: The local algebras in RQFT are generically isomorphic to the unique, hyperfinite type III, factor in Connes' classification of 1973. Specific theories are characterized by the net structure of the collection of these isomorphic algebras for different space-time regions, i.e. the way they are embedded into each other     

量子场论方法在电子与分子碰撞中的应用

这是一种利用量子场论所进行的探究性的研究方法,在文章中,我们设 计了一种新的较为简单的电子-原子碰撞模型,将量子场论方法与光学势方法中的可加性规 则结合起来.利用这种模型,我们计算了e-H,e-He和e-Li的微分碰撞截面,获得了较满意的 结果.     

Localization in algebraic field theory

The algebra of observables has two distinct local structures. The first, derived from the localization of measurements, gives rise to an additive net structure. The second, derived from the support properties of infinitestimal operations, gives rise to a sheaf structure. It is also shown how an additive net of field algebras acted on by a compact gauge group of the first kind generates an additive net of observable algebras.     

Two problems in thermal field theory

In this talk, I review recent progress made in two areas of thermal field theory. In particular, I discuss various approaches for the calculation of the quark gluon plasma thermodynamical properties, and the problem of its photon production rate.     

Diagrammar in classical scalar field theory

In this paper we analyze perturbatively a g?⁴classical field theory with and without temperature. In order to do that, we make use of a path-integral approach developed some time ago for classical theories. It turns out that the diagrams appearing at the classical level are many more than at the quantum level due to the presence of extra auxiliary fields in the classical formalism. We shall show that a universal supersymmetry present in the classical path-integral mentioned above is responsible for the cancelation of various diagrams. The same supersymmetry allows the introduction of super-fields and super-diagrams which considerably simplify the calculations and make the classical perturbative calculations almost “identical” formally to the quantum ones. Using the super-diagrams technique, we develop the classical perturbation theory up to third order. We conclude the paper with a perturbative check of the fluctuation-dissipation theorem.     

Incompressible turbulence as non-local field theory

It is well-known that incompressible turbulence is non-local in real space because sound speed is infinite in incompressible fluids. The equation in Fourier space indicates that it is non-local in Fourier space as well. However, the shell-to-shell energy transfer is local. Contrast this with Burgers equation which is local in real space. Note that the sound speed in Burgers equation is zero. In our presentation we will contrast these two equations using non-local field theory. Energy spectrum and renormalized parameters will be discussed.     

Classical and quantum theory of the massive spin-two field

In this paper, we review classical and quantum field theory of massive non-interacting spin-two fields. We derive the equations of motion and Fierz–Pauli constraints via three different methods: the eigenvalue equations for the Casimir invariants of the Poincaré group, a Lagrangian approach, and a covariant Hamilton formalism. We also present the conserved quantities, the solution of the equations of motion in terms of polarization tensors, and the tree-level propagator. We then discuss canonical quantization by postulating commutation relations for creation and annihilation operators. We express the energy, momentum, and spin operators in terms of the former. As an application, quark–antiquark currents for tensor mesons are presented. In particular, the current for tensor mesons with quantum numbers J^PC=2⁻⁺$J^{PC}=2^{-+}$ is, to our knowledge, given here for the first time.     

Classical field theory with fermions

Classical field theory simulations have been essential for our understanding of non-equilibrium phenomena in particle physics. In this talk we discuss the possible extension of the bosonic classical field theory simulations to include fermions. In principle we use the inhomogeneous mean field approximation as introduced by Aarts and Smit. But in practice we turn from their deterministic technique to a stochastic approach. We represent the fermion field as an ensemble of pairs of spinor fields, dubbed male and female. These c-number fields solve the classical Dirac equation. Our improved algorithm enables the extension of the originally 1+1 dimensional analyses and is suitable for large-scale inhomogeneous settings, like defect networks.     

Double field formulation of Yang-Mills theory

Based on our previous work on the differential geometry for the closed string double field theory, we construct a Yang-Mills action which is covariant under O(D,D) T-duality rotation and invariant under three-types of gauge transformations: non-Abelian Yang-Mills, diffeomorphism and one-form gauge symmetries. In double field formulation, in a manifestly covariant manner our action couples a single O(D,D) vector potential to the closed string double field theory. In terms of undoubled component fields, it couples a usual Yang-Mills gauge field to an additional one-form field and also to the closed string background fields which consist of a dilaton, graviton and a two-form gauge field. Our resulting action resembles a twisted Yang-Mills action.     

The dirac-schwinger covariance condition in classical field theory

A straightforward derivation of the Dirac-Schwinger covariance condition is given within the framework of classical field theory. The crucial role of the energy continuity equation in the derivation is pointed out. The origin of higher order derivatives of delta function is traced to the presence of higher order derivatives of canonical coordinates and momenta in the energy density functional.     

Topological representations of quantum groups and conformal field theory

These are three introductory lectures on the relation between representations of affine Kac-Moody algebras, homology of configuration spaces with local coefficient systems, and quantum groups. The first lecture contains background on highest weight representations of affine Kac-Moody algebras. In the second lecture, conformal blocks, the Friedan-Shenker connection and the Knizhnik-Zamolodchikov (KZ) equation are reviewed. In the third lecture, the case of sl_z is studied in more detail. Integral representations of solutions of the KZ equation are derived, and recent results, obtained in collaboration with C. Wieczerkowski, on the relation between integration cycles and representations of U_q (sl₂) are explained.     

Feynman diagrams to three loops in three-dimensional field theory

The two-point integrals contributing to the self-energy of a particle in a three-dimensional quantum field theory are calculated to two-loop order in perturbation theory as well as the vacuum ones contributing to the effective potential to three-loop order. For almost every integral an expression in terms of elementary and dilogarithm functions is obtained. For two integrals, the master integral and the Mercedes integral, a one-dimensional integral representation is obtained with an integrand consisting only of elementary functions. The results are applied to a scalar λφ⁴ theory.     

Ising-like field theory

A field theory model onR ² in which the basic fields are Ising spins instead of Gaussian spins is examined. Using statistical mechanics techniques we discuss the ultraviolet and the infrared problems. In particular we discuss a technique yielding the asymptotic expansion in of the ground state energy, as 0, without using the cluster expansion.Supported in part by Consiglio Nazionale delle Ricerche.