Fermionic Structure Research Articles

An equivalence proof of the background gauge field quantization and the conventional one

The background gauge field quantization is a convenient tool for studying weakly interacting gauge and matter fields or analyzing anomalous current conservation in fermionic structures. This method is from the mid 1970’s, but it is only today that it received renewed interest for investigating nonperturbative evolution equations in Yang–Mills theory, as well as gauge field effective action formulations. We reviewed, to start with, the general formulation and assumptions about this method, and we pointed out some critical observations concerning it. In particular, we focus on some of the most common equivalence proofs presently known in the literature. We attempted to give a most convincing demonstration of this equivalence as it stands between the background gauge field scattering operator and the conventional one. The result shown here clearly indicates these methods are indeed physically equivalent. In proving that, we neglected all the infrared problems afflicting the pure Yang–Mills gauge theory; as a matter of fact, they appear to be a parallel, but nonintersecting problem with respect to the present one, i.e., to prove the equivalence.

Fermi-Bose transmutation for stringlike excitations of Maxwell-Higgs systems

We show that a closed Nielsen-Olesen string in the presence of a point scalar source exhibits the phenomenon of Fermi-Bose transmutation. This provides physical support to previous claims about transmutation between bosonic and fermionic one-dimensional structures in (3+1) dimensions. In order to render the computations mathematically rigorous we have resorted to an Euclidean lattice regularization.

Fermion mass prediction from infra-red fixed points

We argue that in a wide class of theories the fermion and soft supersymmetry breaking mass structure is largely determined by the infra-red fixed point structure of the theory lying beyond the standard model. We show how knowlege of the symmetries and multiplet content of this theory is sufficient to determine the infra-red structure, illustrating the idea for the case of a simple abelian family symetry. The resulting structure determines the fermion masses and mixing angles in terms of a restricted number of parameters.

Moduli and Kähler potential in fermionic strings.

We study the problem of identifying the moduli fields in fermionic four-dimensional string models. We deform a free-fermionic model by introducing exactly marginal operators in the form of Abelian Thirring interactions on the world-sheet, and show that their couplings correspond to the untwisted moduli fields. We study the consequences of this method for simple free-fermionic models which correspond to $Z_2\times Z_2$ orbifolds and obtain their moduli space and K\"ahler potential by symmetry arguments and by direct calculation of string scattering amplitudes. We then generalize our analysis to more complicated fermionic structures which arise in constructions of realistic models corresponding to asymmetric orbifolds, and obtain the moduli space and K\"ahler potential for this case. Finally we extend our analysis to the untwisted matter sector and derive expressions for the full K\"ahler potential to be used in phenomenological applications, and the target space duality transformations of the corresponding untwisted matter fields.

A New Way of Bosonic Structure of Fermions11The project supported by Grant LWTZ-1298 of Chinese Academy of Sciences

We propose a new approach to construct fermions in terms of usual bosons. The operator and normal product forms of the bosonic structure of fermions are obtained, and the extension of the method to many degrees of freedom and field theory is also given.

Naturalness of three generations in free fermionic Z2n

We study the construction of free fermionic spin structure models with [ital Z][sub 2][sup [ital n]][direct product][ital Z][sub 4] boundary-condition vectors. We argue that requiring chiral space-time fermions in the massless spectrum and the existence of a well-defined hidden gauge group severely constrain the allowed boundary-condition vectors. We show that the minimal way to obtain these requirements is given by a unique set of [ital Z][sub 2][sup 5] boundary-condition vectors. We classify the possible extensions to this basic set. We argue that a result of this fundamental set is that obtaining three generations in this construction is correlated with projecting out all the enhanced gauge symmetries which arise from nonzero vacuum expectation values of background fields. We propose that this correlation and the properties of the fundamental [ital Z][sub 2][sup 5] subset suggest that three generations is natural in this construction.

Fermionic structure of the magnon interaction vertex in quantum magnets

Fermionic structure of the spin-wave interaction vertex within the Hubbard-model representation of a quantum magnet is presented in a scheme that systematically preserves the spin-rotational symmetry and hence the Goldstone mode. We evaluate the diagrams contributing to the interaction vertex for the case of a quantum antiferromagnet in the strong-coupling limit. The exact cancellation of the leading-order contributions (of order U), as required by spin-rotational symmetry, is demonstrated.

On “Kerr‐Newman Metric and the Structure of Elementary Fermions” by Motz and Motz

On “Kerr‐Newman Metric and the Structure of Elementary Fermions” by Motz and Motz

LOGARITHMIC SCALING VIOLATION AND BOSE CONDENSATION IN ONE-MATRIX MODELS

In this paper, we are interested in studying critical behavior of Hermitian one-matrix models where the topological expansion for the free-energy develops a logarithmic singularity, Γ∝μ2 log μ+…. We consider models where the potential is of the type U(M)= t0V0(M)−tf log Vf(M). We show that, for tf>0, the model has an underlying fermionic structure. Continuing into the bosonic region where tf<0 allows the possibility of Bose condensation, which is shown to be responsible for a logarithmic scaling violation for the free energy.

TheC*-algebra of bosonic strings

We give a rigorous definition of Witten'sC*-string-algebra. To this end we present a new construction ofC*-algebras associated to special geometric situations (Kahler foliations) and generalize this later construction to the string case. Through this we get a natural geometrical interpretation of the string of semi-infinite forms as well as the fermionic algebra structure. Using the (non-commutative) geometric concepts for investigating the string algebra we get a natural Fredholm module representation of dimension 26+.

Polyakov's fermion-boson transmutation in 3+1 dimensions.

It is shown how a naive extension of Polyakov's construction to the (3+1)-dimensional case leads to transmutation between bosonic and fermionic one-dimensional structures.

An interacting boson model description of octupole states in nucleic

The IBM-1 + f-boson model is described and systematically applied to the nuclei 154Sm, 156Gd, 158Gd, 158Dy, 162Dy, 168Er, 172Yb, 178Hf, and 182W. Reasonable agreement with available energies and B( E3) transition rates is obtained in all cases except 162Dy, which has the anomalous octupole band order K π = 2 −, 0 −, 1 −. This energy ordering of K − bands cannot be obtained within the present model. The parameter trends show considerable variation, indicating that the underlying fermionic subshell structure is very important in octupole states.

Electronic structure and magnetic properties of heavy fermions

The electronic structure of some heave fermions, especially UPt3 and CeCu6, is derived experimentally. Quasiparticle bands of meV width are found near the Fermi energy. The magnetic susceptibility is calculated as a Pauli susceptibility of heavy quasiparticles, and an excellent agreement with the measurement is obtained. The saturation magnetization of UPt3 is found experimentally and theoretically to be 1μB per uranium atom.

Fermions and octonions

We analyse further the algebraic structure of dependent fermions, namely ones interrelated by the vertex operator construction. They are associated with special sorts of lattice systems which are introduced and discussed. The explicit evaluation of the relevant cocycles leads to the result that the operator product expansion of the fermions is related in a precise way to one or another of the division algebras given by complex numbers, quaternions or octonions. The latter case is seen to be realised in the light cone formalism of superstring theory.

Constraints on a vector coupling to baryon number from the Eötvös experiment.

We point out that the deviations \ensuremath{\Delta}\ensuremath{\kappa} in the E\otv\os experiment do not correlate with the lepton and the neutron number of the used materials. As a consequence of these facts if the hypothetical ``fifth force'' is associated with a new U(1) gauge symmetry there must be new fermions in the extended model or this symmetry does not respect the family structure of the low-energy fermions.

Damping width of double resonances

Damping width of the double giant dipole resonance of 136Xe excited in relativistic heavy ion collisions is calculated by diagonalizing a microscopic Hamiltonian in a basis containing one-, two- and three-phonon states. The coupling between these states is determined making use of the fermion structure of the phonons. The resulting width of the double giant dipole resonance is close to \(\left( {3_1^ + } \right)\) times the width of the single giant dipole resonance.

Fermion representation of the three-dimensional Ising model

The construction of the sign factor ensuring the cancellation of self-intersecting two-dimensional surfaces in the partition function of the three-dimensional Ising model is reviewed. It is shown that the three-dimensional Ising model is exactly equivalent to a model of surfaces with fermionic structure on them. In the naive continuum limit the action of the resulting string theory is defined by the Dirac action induced on a two-dimensional surface.

Construction of fermionic string models in four dimensions

The construction of four-dimensional closed fermionic string models is discussed. The approach is based on a fermionic formulation of all internal (i.e. toroidally compactified) coordinates. Modular invariance, world sheet supersymmetry, (super)conformal invariance and proper space-time spin-statistics impose stringent constraints on the model building. Using these constraints on the boundary conditions (spin structure) of the world sheet fermions, we obtain a simple set of rules for constructing ultraviolet-finite closed fermionic string models. For a large subclass of these models, this “spin structure” construction can be related to bosonic constructions via the fermionic charge lattice. These charge lattices are odd lorentzian self-dual lattices shifted by a fixed vector and form a nontrivial generalization of the lorentzian self-dual even-integer lattices considered by Narian. In particular, four-dimensional models with N = 4, N = 2, and N = 1 supersymmetry as well as non-supersymmetric tachyon-free chiral models can easily be construted. Some models may be interpreted as charge lattices moded by discrete symmetries - in particular Z 2 type orbifolds. String interactions and other related issues are also discussed.

A model for the structure of point-like fermions: Qualitative features and physical description

A model for the structure of point-like fermions as tightly bound composite states is described. The model is based upon the premise that electromagnetism is the only fundamental interaction. The fundamental entity of the model is an object called the vorton. Vortons are semiclassical monopole configurations of electromagnetic charge and field, constructed to satisfy Maxwell's equations. Vortons carry topological charge and one unit each of two different kinds of angular momenta, and are placed in magnetically bound pair states having angular momentum l=1/2. The topological charge prevents the mutual annihilation of the vorton pair. The helicity eigenstates of the vortons' intrinsic angular momenta form the basis for a set of internal quantum numbers for the pair which distinguish the different (point-like) pair states. Sixteen fourcomponent spinor states, eight leptonic and eight hadronic, are obtained. Eleven of these are identified with the quantum numbers of the experimentally known particles: e, ve, μ, vμ, τ, vτ; p, n, Λ, Λc, and b. Thus one new heavy lepton with its neutrino and three new quark states are predicted. Some possibilities for the extension of this model are discussed.

Fermion-monopole system reexamined. II

Following a preceding paper, we reexamine the interaction of magnetic monopoles (dyons) with Dirac particles. For an infinitely heavy SU(2) dyon with one isodoublet fermion, we show that the vacuum angle in the original theory may be incorporated as a boundary condition in an effective one-particle Hamiltonian, which allows us to determine the charge distribution and the fermionic structure of the stable dyons. The resulting boundary conditions turn out to be Abelian and charge conserving, in contrast to that of previous authors. In particular, the dyon degree of freedom is essentially frozen, and there is no charge-exchange scattering off the dyon. With a Dirac mass term for the fermion, we also find that the ground state is twofold degenerate, owing to a spontaneous breakdown of fermion-number conjugation. For a Higgs mass, we find that the conjugation symmetry is unbroken, as in the original analysis of Jackiw and Rebbi. However, because of the changed boundary condition, the characteristic zero mode ceases to exist, and the ground state is nondegenerate with zero fermion number.