Construction of topological defect networks with complex scalar fields

This work deals with the construction of networks of topological defects in models described by a single complex scalar field. We take advantage of the deformation procedure recently used to describe kinklike defects in order to build networks of topological defects, which appear from complex field models with potentials that engender a finite number of isolated minima, both in the case where the minima present discrete symmetry, and in the non-symmetric case. We show that the presence of symmetry guide us to the construction of regular networks, while the non-symmetric case gives rise to irregular networks which spread throughout the complex field space. We also discuss bifurcation, a phenomenon that appear in the non-symmetric case, but is washed out by the deformation procedure used in the present work.     

A bosonic representation of the twisted string emission vertex

We present an explicit construction of the twist fields which create states in the twisted sectors of the Hilbert space in twisted bosonic string models. Such vertex operators have a complicated structure, which intertwines between the various sectors in the theory, and therefore represents a bosonic analogue of the fermion emission vertex which intertwines between the two sectors of the spinning string.     

Preferred shapes and modes of internal motion in a system of four identical fermions

The 0⁺ and 0^– states of a model fermion system with symmetric and antisymmetric spatial permutation symmetry have been investigated. The pairwise interaction adopted has a repulsive core and an attractive tail. Evidences on the preferred shapes and on modes of internal motions have been extracted from the wave functions. A comparison is made among the states having even or odd parity and being symmetric or antisymmetric. It is found that the symmetry plays an essential role in determining the microscopic structures.Supported by the National Educational Committee of the People's Republic of China     

Relativistic bound-state equations for fermions with instantaneous interactions

In thispaper three types of relativistic bound-state equations for a fermion pair with instantaneous interaction are studied, viz., the instantaneous Bethe-Salpeter equation, the quasi-potential equation, and the two-particle Dirac equation. General forms for the equations describing bound states with arbitrary spin, parity, and charge parity are derived. For the special case of spinless states bound by interactions with a Coulomb-type potential the properties of the ground-state solutions of the three equations are investigated both analytically and numerically. The coupling-constant spectrum turns out to depend strongly on the spinor structure of the fermion interaction. If the latter is chosen such that the nonrelativistic limits of the equations coincide, an analogous spectrum is found for the instantaneous Bethe-Salpeter and the quasi-potential equations, whereas the two-particle Dirac equation yields qualitatively different results.     

Possible boson-fermion symmetry in79Kr

The main features of the U(6∥12) boson-fermion symmetry of O(6) type are examined; the fermion occupies j=1/2, 3/2, 5/2 degenerate states. The scheme is applied to the negative parity states of⁷⁹Kr.     

Five- and six-body resonances tied to an Efimov trimer

We explore the properties of weakly bound bosonic states in the strongly interacting regime. Combining a correlated-Gaussian basis set expansion with a complex-scaling method, we extract the energies and structural properties of bosonic cluster states with N ≤ 6 for different two-body potentials. The identification of five- and six-body resonances attached to the first-excited-Efimov trimer provides strong support to the premise of Efimov universality in bosonic systems. Our study also reveals a rich structure of bosonic cluster states. Besides the lowest cluster states that behave as bosonic droplets, we identify cluster states weakly bound to one or two atoms forming effective cluster-atom dimers and cluster-atom-atom "trimers." The experimental signatures of these cluster states are discussed.     

Ward-Takahashi Identities and Mass Spectra in (2+1) Dimensional SU(2) Four-fermi Model

Ward-Takahashi identities with composite fields are utilized to inverstigate (2+1) dimensional model with SU(2) four-fermion couplings.When SU(2) chiral symmetry is both explicitly and dynamically broken,fermion mass is dynamically generated and mass spectra of the bound states are obtained The properties of vector and axial-vector currents are discussed.It turns out that the bound state π_α acquires a mass and the axial-vector current is partially conserved,and the Goldberger-Treimab relation is approximately valid in the case of small fermion current masses.     

Spontaneous Symmetry Breaking of a Hyperbolic Sigma Model in Three Dimensions

Non-linear sigma models that arise from the supersymmetric approach to disordered electron systems contain a non-compact bosonic sector. We study the model with target space H², the two-hyperboloid with isometry group SU(1,1), and prove that in three dimensions moments of the fields are finite in the thermodynamic limit. Thus the non-compact symmetry SU(1,1) is spontaneously broken. The bound on moments is compatible with the presence of extended states.Dedicated to Freeman Dyson on the Occasion of his eightieth birthdayAcknowledgement T. Spencer would like to thank M. Disertori, K. Gawedzki, G. Papanicolau and S.R.S. Varadhan for helpful comments.     

BOND STRUCTURE AND ELECTRON STATES OF CHARGED C60

In the alkali-metal doped C₆₀, the charge transfer induces the distortion of the bond structure and forms the self-trapping electronic bound states. Our theory manifests: 1, the charge transfer reduces the symmetry of C₆₀ from I_h to D_5d. 2, Both the bond distortion and the self-trapping states possess layer structures and are localized in the equatorial area. 3, The carbon atoms in charged C₆₀ are divided into eight layers with an inversion center, then there exist four nonequivalent groups of carbon atoms. It makes the NMR line split into a fine structure with strength ratio 1:1:2:2. 4, The charged C₆₀ has two self-trapping bound states, one is 0.06eV above HOMO with odd parity and the other is 0.05 eV below LUMO with even parity.     

An introduction to quantum order, string-net condensation, and emergence of light and fermions

We review some recent work on new states of matter. Those states cannot be described by symmetry breaking and hence contain a new kind of order—quantum order. Some quantum orders are shown to be closely related to string-net condensations. Those quantum orders lead to an emergence of gauge bosons and fermions from pure bosonic models.     

On Fermion Grading Symmetry for Quasi-Local Systems

We discuss fermion grading symmetry for quasi-local systems with graded commutation relations. We introduce a criterion of spontaneously symmetry breaking (SSB) for general quasi-local systems. It is formulated based on the idea that each pair of distinct phases (appeared in spontaneous symmetry breaking) should be disjoint not only for the total system but also for every complementary outside system of a local region specified by the given quasi-local structure. Under a completely model independent setting, we show the absence of SSB for fermion grading symmetry in the above sense. We obtain some structural results for equilibrium states of lattice systems. If there would exist an even KMS state for some even dynamics that is decomposed into noneven KMS states, then those noneven states inevitably violate our local thermal stability condition.     

Polaron, molecule and pairing in one-dimensional spin-1/2 Fermi gas with an attractive Delta-function interaction

Using solutions of the discrete Bethe ansatz equations, we study in detail the quantum impurity problem of a spin-down fermion immersed into a fully ploarized spin-up Fermi sea with weak attraction. We prove that this impurity fermion in the one-dimensional (1D) fermionic medium behaves like a polaron for weak attraction. However, as the attraction grows, the spin-down fermion binds with one spin-up fermion from the fully-polarized medium to form a tightly bound molecule. Thus it is seen that the system undergos a crossover from a mean field polaron-like nature into a mixture of excess fermions and a bosonic molecule as the attraction changes from weak attraction into strong attraction. This polaron-molecule crossover is universal in 1D many-body systems of interacting fermions. In a thermodynamic limit, we further study the relationship between the Fredholm equations for the 1D spin-1/2 Fermi gas with weakly repulsive and attractive delta-function interactions.     

Bosonic zero modes in discretized light-cone field theory

It is shown that for theories with bosonic fields a constrained zero mode is a necessary ingredient for a consistent discretized light-cone quantization (DLCQ). Inclusion of this zero mode is shown to remove a non-covariant, quadratically divergent contribution to the fermion self-energy in 3+1 dimensional Yukawa theory which would otherwise be present. It is further shown to result in a fully consistent set of Heisenberg equations. The possibility of maintaining parity in DLCQ is discussed.     

Top quark mass in exophobic Pati-Salam heterotic string model

We analyse the phenomenology of an exemplary exophobic Pati-Salam heterotic string vacuum, in which no exotic fractionally charged states exist in the massless string spectrum. Our model also contains the Higgs representations that are needed to break the gauge symmetry to that of the Standard Model and to generate fermion masses at the electroweak scale. We show that the requirement of a leading mass term for the heavy generation, which is not degenerate with the mass terms of the lighter generations, places an additional strong constraint on the viability of the models. In many models a top quark Yukawa may not exist at all, whereas in others two or more generations may obtain a mass term at leading order. In our exemplary model a mass term at leading order exist only for one family. Additionally, we demonstrate the existence of supersymmetric F- and D-flat directions that give heavy mass to all the colour triplets beyond those of the Standard Model and leave one pair of electroweak Higgs doublets light. Hence, below the Pati-Salam breaking scale, the matter states in our model that are charged under the observable gauge symmetries, consist solely of those of the Minimal Supersymmetric Standard Model.     

Superfluidity near phase separation in Bose-Fermi mixtures

We study the transition to fermion pair superfluidity in a mixture of interacting bosonic and fermionic atoms. The fermion interaction induced by the bosons and the dynamical screening of the condensate phonons due to fermions are included using the nonperturbative Hamiltonian flow equations. We determine the bosonic spectrum near the transition towards phase separation and find that the superfluid transition temperature may be increased substantially due to phonon damping.     

A grand unification of flavour with testable predictions

We present a grand unification of flavour based on the group O (14) = SO(14) ? K'. The novel feature of this model is that the discrete symmetry K' is not the internal parity. This implies a fermion assignment different from the usual O(14) with important consequences on the low energy phenomenology. One new fermion family with V - A weak interactions and four new families with V + A character are predicted, with masses less than 250 GeV. The cosmological bound on light neutrino species forces us to keep an SU(2) family group acting on the V + A families unbroken until low energy. Depending on the hierarchy pattern, either we recover the standard model predictions or a new scenario emerges with substantial departures in the neutral current phenomenology.     

Integrable quantum field theories and conformal field theories from lattice models in the light-cone approach

The light-cone lattice approach to two-dimensional quantum field theories is generalized to a large class of vertex models with any number of possible states per link and any simple Lie group of symmetry. Starting from a given lattice model, different scaling limits are defined leading to conformal field theories or to massive integrable quantum field theories, for which the lattice hamiltonian, momentum and currents are constructed. For a large set of models, the complete mass spectrum is also exhibited. Our approach applies equally well to chiral fermionic theories (like the chiral Gross-Neveu) and to bosonic models like the principal chiral model.     

高阶微商系统中正则Ward恒等式和Abel规范理论中动力学质量的产生

基于含复合场的正则Ward恒等式，研究了含高阶微商的Abel理论中动力学规范对称破缺.得到了包括费米子和束缚态的质量谱.讨论了高阶微商项的影响. 关键词： 正则Ward恒等式 约束 动力学对称破缺 Abel规范理论     

Finite-size effects on a lattice calculation

We study in this Letter the finite-size effects of a non-periodic lattice on a lattice calculation. To this end we use a finite lattice equipped with a central difference derivative with homogeneous boundary conditions to calculate the bosonic mass associated to the Schwinger model. We found that the homogeneous boundary conditions produce absence of fermion doubling and chiral invariance, but we also found that in the continuum limit this lattice model does not yield the correct value of the boson mass as other models do. We discuss the reasons for this and, as a result, the matrix which cause the fermion doubling problem is identified.