On the boson mapping of fermion collective pairs

We study the problem of the mapping of fermion collective pairs onto particle-particle bosons and of different fermion operators (hamiltonian, one- and two-particle transfer operators) onto corresponding boson ones and we test the consequences of the truncation to lowest orders of these boson operators. We find that, although the lowest-order terms in the expansion of the operators in boson space lead to matrix elements between boson states which display the qualitative behaviour of the corresponding ones between fermion states, higher-order terms are required to get a quantitative agreement when a large number of particles are involved, as a direct consequence of the increased role of the Pauli principle.     

Fermion to boson mapping

The enveloping algebra, D_n, of fermions is extended on the lattice to include the discrete space invariance. This extended algebra, denoted X, has the space symmetry as a factor: X/D_n = space group.     

Spurious states in boson mapping

The possible occurrence of spurious states in boson mapping is discussed. By a concrete example it was found that the appearance of such states is a result of the choice of interactions.     

Dyson-type boson mapping and SU(6) boson model

The Dyson-type boson mapping is applied to realistic cases to show that it is a very promising method for describing nuclear collective motion. Eigenvectors are obtained in the corresponding hermitian boson theory from the results of right- and left-hand-side eigenvalue problems in the Dyson boson theory. The numerical results are compared with those of the SU(6) boson model and exact quasiparticle shell-model calculations within the multi-phonon subspace.     

Dyson boson mapping theory including ground-state correlation

Since the usual boson mapping methods are based on either Tamm-Dancoff phonons or bare fermion pairs, the ground-state correlation is not well taken into account by them. To improve this, we propose a new treatment of Dyson boson mapping based on a modification of the RPA phonon, which is used in the practical treatment of the self-consistent collective-coordinate (SCC) method. Applying this new method to a solvable SU(3) model and comparing the results with the exact solutions, we show that it is a good improvement of the usual Dyson boson mapping method. We also compare this method with the quantized first-order Dyson-type representation of the SCC method, which can be considered as another way to include the ground-state correlation in a boson mapping.     

New derivation of the seniority-scheme boson mapping of the shell model algebra

A new method is described for the derivation of the unitary boson mapping associated with a seniority shell-model basis. Surprisingly, the fundamental tool in the derivation is the generalized Dyson (non-hermitian) version of the Belyaev-Zelevinsky-Marshalek mapping, which bosonizes all the shell-model pairing and multipole degrees of freedom.     

On vector Goldstone boson

The possibility that higher dimensional field theories are broken spontaneously, through the usual Nambu-Goldstone mechanism, to 4-dimension is explored. As a consequence, vector Goldstone bosons can arise in this breaking of Lorentzian symmetry from higher dimension to 4-dimension. This can provide a simple mechanism for reduction to 4-dimension in theories with extra dimensions. Received: 3 January 2002 / Published online: 14 March 2003     

A generalized Schwinger boson mapping with a physical subspace

We investigate the existence of a physical subspace for generalized Schwinger boson mapping of SO(2n+1)⊃SO(2n) in view of previous observations by Marshalek and the recent construction of such a mapping and subspace for SO(8) by Kaup. It is shown that Kaup's construction can be attributed to the existence of a unique SO(8) automorphism. We proceed to construct a generalized Schwinger-type mapping for SO(2n+1)⊃SO(2n) which, in contrast to a similar attempt by Yamamura and Nishiyama, indeed has a corresponding physical subspace. This new mapping includes in the special case of SO(8) the mapping by Kaup which is equivalent to the one given by Yamamura and Nishiyama for n=4. Nevertheless, we indicate the limitations of the generalized Schwinger mapping regarding its applicability to situations where one seeks to establish a direct link between phenomenological boson models and an underlying fermion microscopy.     

Schwinger boson mapping of SO(8) fermion model

The Schwinger representation of the SO(8) fermion pair algebra in terms ofd and quasispin vector (u, s, v) bosons is used in deriving a microscopic boson coherent state having both particle-hole and pair excitations. The coherent state is the exact boson image of the HFB variational solution. We can study the shape phase transition and pairing behaviour of the nuclear ground states using the coherent states.     

On the free boson gas with spin

The generating functionals of the grand canonical and canonical thermodynamic equilibrium states of several models of free bosons with spin are calculated and the properties of the states discussed. In particular the distribution of condensate over the degenerate ground state is described, and it is shown that spinning bosons interacting with a magnetic field exhibit spontaneous magnetization at sufficiently low temperatures.     

On heavy Higgs boson production

We develop the technique for calculating interference effects in the effective-W boson method. We find that these effects produce a very large azimuthal asymmetry for single Higgs boson production, which could be used as identification of the process. We also find that the cross section of Higgs boson pair production strongly depends on Higgs self-interaction, and for non-standard models of Higgs bosons could be 5 or 10 times larger than in the case of the standard one.Laboratoire associé au Centre National de la Recherche Scientifique     

On the normal ordering of multi-mode boson operators

Combinatorial aspects of normal ordering for annihilation and creation operators of a multi-mode boson system are discussed. The modes are assumed to be coupled, since otherwise the problem of normal ordering is reduced to the cooresponding problem of the single-mode case. To describe the normal ordering in the multi-mode case, for each mode, a color is introduced, and colored contractions are considered. A depiction for colored contractions via colored linear representations is given. By analogy with the single-mode case, associated colored Stirling numbers are defined as coefficients appearing in the process of normal ordering for powers of the number operators. Several properties of these colored Stirling numbers are discussed.     

Vector boson decays of the Higgs boson

We derive the width of the Higgs boson into vector bosons. General formulas are derived both for the on–shell decay as well for the off–shell decays, and , where . For the off-shell decays the width of the decaying vector boson is properly included. The formulas are valid both for the Standard Model as well as for arbitrary extensions. As an example we study in detail the gauge-invariant effective Lagrangian models where we can have sizable enhancements over the Standard Model that could be observed at LEP. Received: 31 July 1998 / Revised version: 23 September 1998 / Published online: 6 November 1998     

On the zero mass boson in QCD2

The zero-mass boson in QCD₂ is shown to gain mass in the next to leading order in $\text{1}\text{N}$ expansion, in agreement with Coleman's Theorem.     

On generalized condensation in the free boson gas

We investigate the free boson gas with Dirichlet boundary conditions in d-dimensional Euclidean space. For d > 2 we find three types of condensation when the mean density ρ exceeds a critical value ρ_c, depending on how the bulk limit is taken.     

On the lattice approach to the maximum Higgs boson mass

If the triviality upper bound on the Higgs boson mass m_H occurs for strong self-coupling, inferring properties of the Higgs from the euclidean propagator is in principle theoretically difficult whether in coordinate or momentum space. In that case, common methods of identifying m_H in lattice field theory simulations may produce a value for which is at best distantly related to the true upper limit. We discuss some shortcomings and ambiguities of recent results suggesting that the maximum occurs for weak coupling and emphasize potential complications due to finite-size and non-Lorentz-invariant effects of the lattice. The situation is illustrated by reference to the behavior in an analytically soluble approximation based on a 1/N expansion.     

On the convergence of Marumori's boson expansion for pairing vibrations

It is demonstrated analytically for a two-level model with pairing force that Marumori's method converges rapidly if one uses the idea of pairing vibrations. The approximation of Sørensen and the broken-pair approximation are compared with Marumori's boson expansion.     

On the validity of ward identities

Ward identities for matrix elements of covariant two-point time-ordered operators in the presence of an arbitrary number of subtractions are investigated. Neither the existence of naiveT-products nor the existence of equal-time commutators between current densities will be assumed. It is shown by means of the Jost-Lehmann-Dyson representation thatT*-products can always be defined such that normal Ward identities with respect to one current are valid. The simultaneous validity of normal Ward identities with respect to two currents requires a relation between equal-time charge-current commutators.Our results show that the usual realization of current algebra in the form of Ward identities is possible even if subtractions are necessary. Some examples are discussed in detail.