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Register a new userBeyond the Schwinger boson representation of the su(2)-algebra. I -- New boson representation based on the su(1,1)-algebra and its related problems with application
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With the use of two kinds of boson operators, a new boson representation of the su(2)-algebra is proposed. The basic idea comes from the pseudo su(1,1)-algebra recently given by the present authors. It forms a striking contrast to the Schwinger boson representation of the su(2)-algebra which is also based on two kinds of bosons. This representation may be suitable for describing time-dependence of the system interacting with the external environment in the framework of the thermo field dynamics formalism, i.e., the phase space doubling. Further, several deformations related to the su(2)-algebra in this boson representation are discussed. On the basis of these deformed algebra, various types of time-evolution of a simple boson system are investigated.
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New boson representation of the su(2)-algebra proposed by the present authors for describing the damped and amplified oscillator is examined in the Lipkin model as one of simple many-fermion models. This boson representation is expressed in terms of two kinds of bosons with a certain positive parameter. In order to describe the case of any fermion number, third boson is introduced. Through this examination, it is concluded that this representation is well workable for the boson realization of the Lipkin model in any fermion number.
The su(2)-algebraic model interacting with an environment is investigated from a viewpoint of treating the dissipative system. By using the time-dependent variational approach with a coherent state and with the help of the canonicity condition, the time-evolution of this quantum many-body system is described in terms of the canonical equations of motion in the classical mechanics. Then, it is shown that the su(1,1)-algebra plays an essential role to deal with this model. An exact solution with appropriate initial conditions is obtained by means of Jacobis elliptic function. The implication to the dissipative process is discussed.
We study a possibility of the Higgs boson, which consists of an SU(2) doublet and a septet. The vacuum expectation value of a septet with hypercharge Y=2 is known to preserve the electroweak rho parameter unity at the tree level. Therefore, the septet can give significant contribution to the electroweak symmetry breaking. Due to the mixing with the septet, the gauge coupling of the standard-model-like Higgs boson is larger than that in the standard model. We show the sizable VEV of the Higgs septet can be allowed under the constraint from the electroweak precision data. The signal strengths of the Higgs boson for the diphoton and a pair of weak gauge boson decay channels at the LHC are enhanced, while those for the fermonic decay modes are suppressed. The mass of additional neutral Higgs boson is also bounded by the current LHC data for the standard model Higgs boson. We discussed the phenomenology of the multiply charged Higgs bosons, which come from the septet.
An orthogonal basis of the Hilbert space for the quantum spin chain associated with the su(3) algebra is introduced. Such kind of basis could be treated as a nested generalization of separation of variables (SoV) basis for high-rank quantum integrable models. It is found that all the monodromy-matrix elements acting on a basis vector take simple forms. With the help of the basis, we construct eigenstates of the su(3) inhomogeneous spin torus (the trigonometric su(3) spin chain with antiperiodic boundary condition) from its spectrum obtained via the off-diagonal Bethe Ansatz (ODBA). Based on small sites (i.e. N=2) check, it is conjectured that the homogeneous limit of the eigenstates exists, which gives rise to the corresponding eigenstates of the homogenous model.
Let ${cal Z}$ be the Jiang-Su algebra and ${cal K}$ the C*-algebra of compact operators on an infinite dimensional separable Hilbert space. We prove that the corona algebra $M({cal Z}otimes {cal K})/{cal Z}otimes {cal K}$ has real rank zero. We actually prove a more general result.
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