New principles for string/membrane unification

The target space theory of the N = (2,1) heterotic string may be interpreted as a theory of gravity coupled to matter in either 1 + 1 or 2 + 1 dimensions. Among the target space theories in 1 + 1 dimensions are the bosonic, type II, and heterotic string world-sheet field theories in a physical gauge. The (2 + 1)-dimensional version describes a consistent quantum theory of supermembranes in 10 + 1 dimensions. The unifying framework for all of these vacua is a theory of (2 + 2)-dimensional self-dual geometries embedded in 10 + 2 dimensions. There are also indications that the N = (2,1) string describes the strong-coupling dynamics of compactifications of critical string theories to two dimensions, and may lead to insights about the fundamental degrees of freedom of the theory.     

New infinite-dimensional hidden symmetries for the stationary axisymmetric Einstein－Maxwell equations with multiple Abelian gauge fields

By proposing a so-called extended hyperbolic complex (EHC) function method, an Ernst-like (p+2)×(p+2) matrix EHC potential is introduced for the stationary axisymmetric (SAS) Einstein－Maxwell theory with p Abelian gauge fields (EM-p theory, for short), then the field equations of the SAS EM-p theory are written as a so-called Hauser－Ernst-like self-dual relation for the EHC matrix potential. Two Hauser－Ernst-type EHC linear systems are established, based on which some new parametrized symmetry transformations for the SAS EM-p theory are explicitly constructed. These hidden symmetries are found to constitute an infinite-dimensional Lie algebra, which is the semidirect product of the Kac－Moody algebra su(p+1,1)\otimes R(t,t^{-1}) and Virasoro algebra (without centre charges). All of the SAS EM-p theories for p=0,1,2,… are treated in a unified formulation, p=0 and p=1 correspond, respectively, to the vacuum gravity and the Einstein－Maxwell cases.     

Effective field theory of a topological insulator and the Foldy–Wouthuysen transformation

Employing the Foldy–Wouthuysen transformation, it is demonstrated straightforwardly that the first and second Chern numbers are equal to the coefficients of the 2+1 and 4+1 dimensional Chern–Simons actions which are generated by the massive Dirac fermions coupled to the Abelian gauge fields. A topological insulator model in 2+1 dimensions is discussed and by means of a dimensional reduction approach the 1+1 dimensional descendant of the 2+1 dimensional Chern–Simons theory is presented. Field strength of the Berry gauge field corresponding to the 4+1 dimensional Dirac theory is explicitly derived through the Foldy–Wouthuysen transformation. Acquainted with it, the second Chern numbers are calculated for specific choices of the integration domain. A method is proposed to obtain 3+1 and 2+1 dimensional descendants of the effective field theory of the 4+1 dimensional time reversal invariant topological insulator theory. Inspired by the spin Hall effect in graphene, a hypothetical model of the time reversal invariant spin Hall insulator in 3+1 dimensions is proposed.     

Field theory in two-time physics with N=1 supersymmetry

We construct N=1 supersymmetric (SUSY) field theory in 4+2 dimensions compatible with the theoretical framework of two-time (2T) physics and its gauge symmetries. The fields are arranged into 4+2 dimensional chiral and vector supermultiplets, and their interactions are uniquely fixed by SUSY and 2T physics gauge symmetries. In a particular gauge the 4+2 theory reduces to ordinary supersymmetric field theory in 3+1 dimensions without any Kaluza-Klein remnants, but with some additional constraints in 3+1 dimensions of interesting phenomenological relevance. This construction is another significant step in the development of 2T physics as a structure that stands above 1T physics.     

Gauge and integrable theories in loop spaces

We propose an integral formulation of the equations of motion of a large class of field theories which leads in a quite natural and direct way to the construction of conservation laws. The approach is based on generalized non-abelian Stokes theorems for p-form connections, and its appropriate mathematical language is that of loop spaces. The equations of motion are written as the equality of a hyper-volume ordered integral to a hyper-surface ordered integral on the border of that hyper-volume. The approach applies to integrable field theories in (1+1) dimensions, Chern-Simons theories in (2+1) dimensions, and non-abelian gauge theories in (2+1) and (3+1) dimensions. The results presented in this paper are relevant for the understanding of global properties of those theories. As a special byproduct we solve a long standing problem in (3+1)-dimensional Yang-Mills theory, namely the construction of conserved charges, valid for any solution, which are invariant under arbitrary gauge transformations.     

ELECTRODYNAMICS OF A QUASI-(1+1)DIMENSIONAL ELECTRON GAS

A hydrodynamic model. is used to study the electrodynamics of a quasi-(1+1)-dimensional electron gas arranged in a periodic array and neutralized by rigid inert positive background The theory is applied to discuss a new model of quasi-(1+1)-dimensional electron gas with a complex unit cell and an analytical expression of the dispersion relation for this system is derived. The results are the same as. those der-ived caith the semi-classical theory dealing with collective excitations.     

THE TWO-BOSON SCATTERING PHASE SHIFTS IN THE GENERAL φ6 THEORY WITH THE GAUSSIAN WAVE-FUNCTIONAL APPROACH

The two-particle scattering phase shifts with a λφ⁴ +ξφ⁶ interaction are com-puted in (1 + 1) and (2 + 1) dimensions using the Gaussian wave-functional approach.Through numerical analysis, we give the phase-shift curves with respect to the scat-tering energy for most cases of this theory. In (1 + 1) and (2 + 1 ) dimensions, for the symmetry vacuum the phase shifts are positive or negative depending on the signs of the renormalized parameter, while for the asymmetric vacuum the phase shifts are negative.     

Dynamical breaking of supersymmetry

General conditions for dynamical supersymmetry breaking are discussed. Very small effects that would usually be ignored, such as instantons of a grand unified theory, might break supersymmetry at a low energy scale. Examples are given (in 0 + 1 and 2 + 1 dimensions) in which dynamical supersymmetry breaking occurs. Difficulties that confront such a program in four dimensions are described.     

TDDFT study on the excited‐state hydrogen bonding of N‐(2‐hydroxyethyl)‐1,8‐naphthalimide and N‐(3‐hydroxyethyl)‐1,8‐naphthalimide in methanol solution

The time‐dependent density functional theory method was performed to investigate the excited‐state hydrogen‐bonding dynamics of N‐(2‐hydroxyethyl)‐1,8‐naphthalimide (2a) and N‐(3‐hydroxyethyl)‐1,8‐naphthalimide (3a) in methanol (meoh) solution. The ground and excited‐state geometry optimizations, electronic excitation energies, and corresponding oscillation strengths of the low‐lying electronically excited states for the complexes 2a + 2meoh and 3a + 2meoh as well as their monomers 2a and 3a were calculated by density functional theory and time‐dependent density functional theory methods, respectively. We demonstrated that the three intermolecular hydrogen bonds of 2a + 2meoh and 3a + 2meoh are strengthened after excitation to the S₁ state, and thus induce electronic spectral redshift. Moreover, the electronic excitation energies of the hydrogen‐bonded complexes in S₁ state are correspondingly decreased compared with those of their corresponding monomer 2a and 3a. In addition, the intramolecular charge transfer of the S₁ state for complexes 2a + 2meoh and 3a + 2meoh were theoretically investigated by analysis of molecular orbital. Copyright © 2014 John Wiley & Sons, Ltd.     

液氦温度(4.2K)下LaOBr:Ce3+,Tb3+粉末的电子顺磁共振研究

本文研究了LaOBr:Ce+3,Tb3+粉末在液氦温度(4.2K)下的电子顺磁共振,并且进行了晶体场理论计算,理论与实验结果符合得较好,这表明Ce,Tb离子取代了基质中La离子形成发光中心。     

Progress in lattice gauge theory

Two topics of lattice gauge theory are reviewed. They include string tension and β-function calculations by strong coupling Hamiltonian methods for SU(3) gauge fields in 3 + 1 dimensions, and a 1/N-expansion for discrete gauge and spin systems in all dimensions. The SU(3) calculations give solid evidence for the coexistence of quark confinement and asymptotic freedom in the renormalized continuum limit of the lattice theory. The crossover between weak and strong coupling behavior in the theory is seen to be a weak coupling but non-perturbative effect. Quantitative relationships between perturbative and non-perturbative renormalization schemes are obtained for the O(N) nonlinear sigma models in 1 + 1 dimensions as well as the range theory in 3 + 1 dimensions. Analysis of the strong coupling expansion of the β-function for gauge fields suggests that it has cuts in the complex 1/g²-plane. A toy model of such a cut structure which naturally explains the abruptness of the theory's crossover from weak to strong coupling is presented. The relation of these cuts to other approaches to gauge field dynamics is discussed briefly.The dynamics underlying first order phase transitions in a wide class of lattice gauge theories is exposed by considering a class of models-P(N) gauge theories - which are soluble in the N → ∞ limit and have non-trivial phase diagrams. The first order character of the phase transitions in Potts spin systems for N #62; 4 in 1 + 1 dimensions is explained in simple terms which generalizes to P(N) gauge systems in higher dimensions. The phase diagram of Ising lattice gauge theory coupled to matter fields is obtained in a $\text{1}\text{N}$ expansion. A one-plaquette model (1 time-0 space dimensions) with a first-order phase transitions in the N → ∞ limit is discussed.     

The model for self-dual chiral bosons as a Hodge theory

We consider (1+1) dimensional theory for a single self-dual chiral boson as a classical model for gauge theory. Using the Batalin–Fradkin–Vilkovisky (BFV) technique, the nilpotent BRST and anti-BRST symmetry transformations for this theory have been studied. In this model other forms of nilpotent symmetry transformations like co-BRST and anti-co-BRST, which leave the gauge-fixing part of the action invariant, are also explored. We show that the nilpotent charges for these symmetry transformations satisfy the algebra of the de Rham cohomological operators in differential geometry. The Hodge decomposition theorem on compact manifold is also studied in the context of conserved charges.     

The simplest black holes

A relativistic gravitational theory in (1 + 1) dimensions is presented which exhibits many of the qualitative features of (3 + 1)-dimensional general relativity. The field equations are simple enough for undergraduates to solve yet rich enough in structure to form a useful pedagogical example for exploring the qualitative features of relativistic gravitation. Black hole solutions to the field equations of the theory are derived and its relationship to Newtonian gravity is discussed in detail.     

Spherically symmetric classical solutions in SU(2) gauge theory with a Higgs field

A consistent ansatz for time dependent classical solutions in an SU(2) gauge theory with a doublet Higgs field is presented. The (3+1)-dimensional field equations are reduced to those of an effective (1+1)-dimensional theory. This ansatz describes solutions which travel between topologically distinct classical vacua of the non-abelian gauge theory. The real time version of these solutions describes the creation and decay of the unstable static “sphaleron”, the imaginary time version describes a euclidean instanton.     

Quantum Double Actions on Operator Algebras and Orbifold Quantum Field Theories

Starting from a local quantum field theory with an unbroken compact symmetry group G in 1+1-dimensional spacetime we construct disorder fields implementing gauge transformations on the fields (order variables) localized in a wedge region. Enlarging the local algebras by these disorder fields we obtain a nonlocal field theory, the fixpoint algebras of which under the appropriately extended action of the group G are shown to satisfy Haag duality in every simple sector. The specifically 1+1 dimensional phenomenon of violation of Haag duality of fixpoint nets is thereby clarified. In the case of a finite group G the extended theory is acted upon in a completely canonical way by the quantum double D(G) and satisfies R-matrix commutation relations as well as a Verlinde algebra. Furthermore, our methods are suitable for a concise and transparent approach to bosonization. The main technical ingredient is a strengthened version of the split property which is expected to hold in all reasonable massive theories. In the appendices (part of) the results are extended to arbitrary locally compact groups and our methods are adapted to chiral theories on the circle. Received: 4 September 1996 / Accepted: 6 May 1997     

The gauge boson sector ofU(1) lattice theories

We examine theU(1) Hamiltonian lattice gauge theory in (2+1) and (3+1) dimensions. We set up a differential eigenvalue equation for the energy levels of the system, valid for all values of the coupling parameter. We show how the standard strong coupling results are retrieved, and also present a weak coupling solution which exhibits (unconfined) transverse photons as the phonons of the lattice. The lattice approach is thus seen to be appropriate for non-confining as well as for confining systems.     

An improved guided random walk algorithm for quantum field theory computations

We introduce an improved guided random walk algorithm for evaluating vacuum matrix elements in hamiltonian field theories. This algorithm does not require the creation of absorption of walks, unlike related random walk techniques which have appeared in the literature. Applications to a scalar field theory in (1 + 1) dimensions and to an abelian gauge theory in (3 + 1) dimensions are described. The algorithm appears to be very fast; we have used it to generate independent abelian gauge field configurations on an 8³ spatial lattice at a rate of about one per IBM 3081 CPU second.     

ADM-like Hamiltonian formulation of gravity in the teleparallel geometry

We present a new Hamiltonian formulation of the teleparallel equivalent of general relativity (TEGR) meant to serve as the departure point for canonical quantization of the theory. TEGR is considered here as a theory of a cotetrad field on a spacetime. The Hamiltonian formulation is derived by means of an ADM-like $3+1$ decomposition of the field and without any gauge fixing. A complete set of constraints on the phase space and their algebra are presented. The formulation is described in terms of differential forms.     

(2+1)-dimensional dissipation nonlinear Schrödinger equation for envelope Rossby solitary waves and chirp effect

In the past few decades, the (1+1)-dimensional nonlinear Schrödinger (NLS) equation had been derived for envelope Rossby solitary waves in a line by employing the perturbation expansion method. But, with the development of theory, we note that the (1+1)-dimensional model cannot reflect the evolution of envelope Rossby solitary waves in a plane. In this paper, by constructing a new (2+1)-dimensional multiscale transform, we derive the (2+1)-dimensional dissipation nonlinear Schrödinger equation (DNLS) to describe envelope Rossby solitary waves under the influence of dissipation which propagate in a plane. Especially, the previous researches about envelope Rossby solitary waves were established in the zonal area and could not be applied directly to the spherical earth, while we adopt the plane polar coordinate and overcome the problem. By theoretical analyses, the conservation laws of (2+1)-dimensional envelope Rossby solitary waves as well as their variation under the influence of dissipation are studied. Finally, the one-soliton and two-soliton solutions of the (2+1)-dimensional NLS equation are obtained with the Hirota method. Based on these solutions, by virtue of the chirp concept from fiber soliton communication, the chirp effect of envelope Rossby solitary waves is discussed, and the related impact factors of the chirp effect are given.