Boson Realization Research Articles

Oscillator-like coherent states of an asymmetric top

A transformation from the Euler angles to the Cayley-Klein variables is used to obtain the Schwinger boson realization of the angular momentum algebra suitable for a triaxial top. A set of wave packets for the top are then constructed in exact analogy with the oscillator coherent states. These coherent states of the top are shown to be a generalization of those defined by other authors.

Real and complex boson expansions in even-even deformed nuclei

Analysis of real and complex boson expansions of the Kishimoto-Tamura type is performed in a deformed basis in order to allow a further study of the anharmonicities of vibrations in deformed nuclei. It is shown that complex solutions cannot be found in the cases where no real one exits.

Infrared problem and boson suppression in massless Abelian gauge theory

The vacuum polarization effects lead to a complete shielding of the charge and to a suppression of real boson excitations in massless Abelian gauge theory. Nevertheless, fermions interact by means of neutral vector currents. It is concluded that charged massless fermions cannot exist.

Algebraic identities among U (n) infinitesimal generators

Some algebraic identities among infinitesimal generators of the n−dimensional unitary group U (n) have been found. They satisfy a simple quadratic equation for degenerate representations. A generalization of Holstein−Primakoff boson realization for the U (n) group is also given.

Casimir operators of complementary unitary groups

A relationship between all the generalized Casimir operators of complementary unitary groups is derived, both in the fermion and boson realizations of the corresponding Lie algebras. It is shown that the number of independent Casimir operators of unitary groups reduces essentially to half the number for self−conjugate irreducible representations.

Boson realization of the unitary symplectic group

A realization of the Lie algebra of the unitary symplectic group is proposed in terms of boson operators. The existence of a noncompact orthogonal group, complementary to the symplectic one, is shown. The highest weight polynomial of an irreducible representation of the latter group is constructed with the help of the former.

Complex Regge poles

The practical consequences of introducing conjugate complex pairs of Regge poles, in place of the usual real boson Regge poles, are considered. A range of properties are discussed systematically.

On Possible Anomalous Interaction of Muon

In order to introduce a mechanism to induce the extraordinary muon mass in compar­ ison with the electron mass, interactions with derivative coupling between muon and a hypo­ thetical neutral vector boson are proposed. The muon self-energy and the muon anomalous magnetic moment (a.m.m.) arising from this interaction are calculated in the self-consistent method. The parameters involved are then investigated to see whether a large muon self­ energy is compatible with its anomalous magnetic moment. The allowed upper limit for the ratio of the coupling constant and the vector boson mass is obtained within the experimental uncertainty and the theoretical value of the muon a.m.m. In these interactions, the hypo­ thetical neutral vector boson appears only in the intermediate state and no real neutral boson is created. In the high energy processes, the muon pair production by muon is proportional to the fourth power of the transferred momentum. Further, the recently discover~d possible anomalous properties of high energy muon can be explained by this model.

On the application of non-equilibrium statistical mechanics to quantum field theory

The class of problems which belong to Heitler's general theory of damping phenomena may be reformulated in a new way using the recent development of non-equilibrium statistical mechanics. As examples cross sections of Møller scattering through a real boson and as well as higher order contribution to the life time of an unstable fermion are indicated.

Absorption of neutrinos in the coulomb field of the nuclei

The cross sections of high energy neutrinos are calculated for the absorption in the Coulomb-field of atomic nuclei, giving another neutrino and two charged leptons. The cases of the local Fermi interaction and the case of the indirect weak interaction (transmitted by a boson field with heavy quanta) are discussed separately. The probability of the emission of a real heavy boson is also determined.

Selection Rules Implied byCPInvariance

Some consequences of the rigorous invariance under the product of charge conjugation and reflection are discussed. The restrictions on the interactions of real boson fields with one spinor field, and of complex boson fields with charge symmetric spinor fields are derived and compared with the restrictions implied by invariance under the separate operations. Two selection rules for transitions among such boson fields are given. Some possible applications to known particles are mentioned.

On quantum field theory. II: Non-perturbative equations and methods

The evaluation of an element of theU-matrix between arbitrary initial and final states is reduced to that of a kernel, whose form depends only upon the number of particles involved and is given explicity as a perturbative expansion. Kernels are shown to satisfy systems of «branching equations», which hold independently of perturbation methods and can be taken as the axiomatic foundation of the theory, Lorentz covariance being manifest. Complete systems of such equations are given for the kernels and their derivatives with respect to the interaction strength λ: all other conceivable equations among kernels are necessarily deducible from them. All kernels corresponding to processes involving real bosons can be obtained, with simple integrations, from the kernels for purely fermionic processes; the branching equations for these are also explicity given and suffice to define the theory. A kernel, with its first and second λ-derivatives, satisfies a single integral relation. A variety of approximation methods are immediately deducible from the branching equations; they, while extending and generalizing the known ones, always permit, at least in principle, tests of convergence. Questions of renormalization, existence of solutions, etc., will be studied in the sequel to this paper.