Ultralocal spinor field models

Ultralocal spinor (fermion) field theories are distinguished by the independent temporal development of the field at each spacial point. For a wide class of models explicit operator constructions are given, in a positive definite Hilbert space, for the interacting field, the Hamiltonian, and several other operators. Not only do the fermion field operators fail to fulfill canonical anticommutation relations but associated ultralocal boson fields are required for their realization giving rise to both fermion and boson type excitations. Construction of the Hamiltonian from the field, as well as the transition from the interacting to the noninteracting theories entails various infinite renormalizations that are made explicit. The formulation and solution of these models is based solely on symmetry arguments and general principles, and makes no use whatsoever of cutoffs or perturbation theory.     

Density fluctuations in heavy fermion systems

We show explicitly that the hydrodynamic density modes of a heavy fermion system in the presence of long range Coulomb interactions can be reduced to those of an effective Hamiltonian used previously. Outside the hydrodynamic regime one finds acoustic plasmon (or zero sound) excitations as well as high energy plasmons. When the Fermi level intersects more than one heavy quasiparticle band, a situation which is expected to occur in most cases, then also a low-energy optical plasmon excitation should exist. The latter can be overdamped under special conditions.     

A Three Higgs Doublet Model for Fermion Masses

In this paper we propose a possible explanation to the Fermion mass hierarchy problem by fitting the type-II seesaw mechanism into the Higgs doublet sector, such that their vacuum expectation values are hierarchal. We extend the Standard Model with two extra Higgs doublets as well as a spontaneously broken U_X(1) gauge symmetry. All the fermion Yukawa couplings except that of the top quark are of O(10^-2) in our model. Constraints on the parameter space of the model from low energy processes are studied. Besides, the lightest one of the neutral fermion fields, which is introduced to cancel the anomalies of the U(1)_X gauge symmetry can be the cold dark matter candidate. We investigate its signature in the dark matter direct detection.     

Entanglement spectrum of non-Abelian anyons

Non-Abelian anyons can emerge as fractionalized excitations in two-dimensional systems with topological order. One important example is the Moore—Read fractional quantum Hall state. Its quasihole states are zero-energy eigenstates of a parent Hamiltonian, but its quasiparticle states are not. Both of them can be modeled on an equal footing using the bipartite composite fermion method. We study the entanglement spectrum of the cases with two or four non-Abelian anyons. The counting of levels in the entanglement spectrum can be understood using the edge theory of the Moore—Read state, which reflects the topological order of the system. It is shown that the fusion results of two non-Abelian anyons is determined by their distributions in the bipartite construction.     

Perfect Transfer of Many-Particle Quantum State via High-Dimensional Systems with Spectrum-Matched Symmetry

The quantum state transmission through the medium of high-dimensional many-particle system (boson or spinless fermion) is generally studied with a symmetry analysis. We discover that, if the spectrum of a Hamiltonian matches the symmetry of a fermion or boson system in a certain fashion, a perfect quantum state transfer can be implemented without any operation on the medium with pre-engineered nearest neighbor (NN). We also study a simple but realistic near half-filled tight-binding fermion system with uniform NN hopping integral. We show that an arbitrary many-particle state near the fermi surface can be perfectly transferred to its translational counterpart.     

Perfect Transfer of Many-Particle Quantum State via High-Dimensional Systems with Spectrum-Matched Symmetry

The quantum state transmission through the medium of high-dimensional many-particle system （boson or spinless fermion） is generally studied with a symmetry analysis. We discover that, if the spectrum of a Hamiltonian matches the symmetry of a fermion or boson system in a certain fashion, a perfect quantum state transfer can be implemented without any operation on the medium with pre-engineered nearest neighbor （NN）. We also study a simple but realistic near half-filled tight-bindlng fermion system wlth uniform NN hopping integral. We show that an arbitrary many-particle state near the fermi surface can be perfectly transferred to its translational counterpart.     

Fermion propagators on a four-dimensional random-block lattice

Fermion propagators, composite boson propagators and the fermion condensate are calculated numerically on the four-dimensional random-block lattice, respectively. The ensemble-averaged fermion propagator agrees with the continuum propagator for distances greater than three average lattice spacings. The results on the fermion condensate show that the chiral symmetry of the doubled modes is broken in the continuum limit. The Goldstone boson arising from the broken symmetry is revealed by examining the composite pseudo-scalar propagator. The doubled fermion and the Goldstone boson both acquire masses of the order of inverse lattice spacing and thus decouple from the theory in the continuum limit.     

On the correspondence between fermion and boson states and operators

Mapping of shell-model (fermion) Hamiltonians onto boson Hamiltonians which underly the interaction boson model ^1–5) is investigated. A simple correspondence is defined and a sufficient condition given for shell-model Hamiltonians to simply correspond to finite hermitian boson Hamiltonians. A special case is discussed where diagonalization of a shell-model Hamiltonian for valence protons and neutrons can be exactly carried out in an equivalent (but different) boson space. If, however, the proton Hamiltonian and neutron Hamiltonian are diagonal in the seniority scheme, mapping of fermion states onto orthogonal boson states cannot be a simple correspondence. In that case the boson quadrupole operators equivalent to fermion guadrupole operators cannot be single-boson operators but must be more complicated, ones.     

Extracting excitations from model state entanglement

We extend the concept of an entanglement spectrum from the geometrical to the particle bipartite partition. We apply this to several fractional quantum Hall wave functions on both sphere and torus geometries to show that this new type of entanglement spectra completely reveals the physics of bulk quasihole excitations. While this is easily understood when a local Hamiltonian for the model state exists, we show that the quasihole wave functions are encoded within the model state even when such a Hamiltonian is not known. As a nontrivial example, we look at Jain's composite fermion states and obtain their quasiholes directly from the model state wave function. We reach similar conclusions for wave functions described by Jack polynomials.     

原子核费密多体系统平均场近似的推广

本文应用先前得到的序参量——统计格林函数耦合方程组,对于原子核多费密子体系,系统地导出了它的平均场近似,Hartree-Fock近似和无规相位近似。并求出了相应近似下系统热力学势的明显表达式。本文的讨论也适用于处于平衡或非平衡定常态的其他多体系统。 关键词：     

Quantum States of a Neutral Massive Fermion with an Anomalous Magnetic Moment in an External Electric Field

The quantum dynamics of a nonrelativistic neutral massive fermion with an anomalous magnetic moment (AMM) is examined in the external electric field of an infinitely long thin homogeneously charged thread in the plane with a normal directed along the thread. The Hamiltonian of the Dirac–Pauli equation for a neutral fermion with AMM is essentially singular in the considered external field and requires a supplementary extension of the definition in order for it to be treated as a self-adjoint quantum-mechanical operator. All one-parameter self-adjoint extensions of the Hamiltonian of the Dirac–Pauli equation in the considered external field are found in the nonrelativistic approximation. The corresponding Hilbert space of squareintegrable functions, including a singularity point of the Hamiltonian, is specified for each self-adjoint extension of the Hamiltonian. The wave functions of free and bound states, as well as discrete energy levels, are determined by the self-adjoint extension method and their correspondence with similar quantities obtained by the physical regularization procedure is discussed. It is shown that energy levels of bound states are simple poles of the scattering amplitude, which should be extended in definition by introducing the self-adjoint extension parameter into it. Expressions for the scattering amplitude and cross-section, depending on the orientation of the initial-state spin of fermion, are obtained.     

Impurity non-preserving 3-point correlators of BMN operators from PP-wave holography II: Fermionic excitations

The holographic principle in the PP-wave limit proposed in our previous works is further confirmed by studying impurity non-preserving processes which contain a fermionic BMN operator with one scalar and one fermion impurities. We show that the previously proposed duality relation between the matrix elements of the three point interaction Hamiltonian in the holographic string field theory and the OPE coefficients in super-Yang–Mills theory holds to the leading order in the large μ limit. Operator mixing is required to obtain the BMN operator of definite conformal dimension which corresponds to the string state with one scalar and one fermion excitations. The mixing term plays a crucial role for our duality relation to be valid. Our results, combined with those in the previous papers, provide a positive support that our duality relation holds for the general process regardless of the kind of impurities and of whether impurities conserve or not.     

Field theory of collective excitations; I. A soluble model

Collective fields are introduced into fermion Lagrangians and graphical rules for a joint treatment of both types of excitations are derived via Feynman path integrals. For the soluble degenerate-shell model with pairing forces used in nuclear and many-body physics the exact collective action is exhibited.     

Schwinger-Dyson equation for massless vector theory and the absence of a fermion pole

The Schwinger-Dyson equation of the fermion propagator in the massless vector theory is discussed. It is found that the Baker-Johnson-Willey solution in lowest approximation is in fact a confining solution: the Fermion propagator has no pole or cut in the time-like region. Discussions of homogeneous and inhomogeneous equations with momentum integration cut-off are also given in some detail.     

Yang-Mills potentials and the van der Waals force between hadrons

The colour-induced magnetic dipole interaction between hadrons is discussed. Fermion motion in a gauge field obtained by solving the classical Yang-Mills equations is considered. It is shown that the spectrum of stationary fermion states is discrete and bound states are colourless. The long range asymptotic behaviour of the gauge potential results in the van der Waals interaction of hadrons.     

Hamiltonian models of interacting fermion fields in quantum field theory

We consider Hamiltonian models representing an arbitrary number of spin 1 / 2 fermion quantum fields interacting through arbitrary processes of creation or annihilation of particles. The fields may be massive or massless. The interaction form factors are supposed to satisfy some regularity conditions in both position and momentum space. Without any restriction on the strength of the interaction, we prove that the Hamiltonian identifies to a self-adjoint operator on a tensor product of antisymmetric Fock spaces and we establish the existence of a ground state. Our results rely on new interpolated \(N_\tau \) estimates. They apply to models arising from the Fermi theory of weak interactions, with ultraviolet and spatial cutoffs.