• Volume 4, Issue 3

March 1975,   pages  105-152

• Theψ-particles in an SU4 scheme with anomalous currents

The recently discovered narrow peaks (theψ-particles) in e+e system at 3.105 and 3.695 GeV are interpreted as hadrons in a broken SU4 symmetry scheme. A new additional additive quantum number, parachargeZ, is combined with the usual SU3 quantum numbers in the group SU4. Theψ (3.1) is assigned to a near ideally mixed151 multiplet of vector mesons (containing theρ) as theI=Y=0, charge conjugationC=−combination ofZ=±1.members. Theψ (3.7) is assigned correspondingly to another mixed151 multiplet containing theρ′ (1600). The hadronic electromagnetic interactions are modified by the addition of (non-minimal) anomalous pieces that can changeZ. The decays of theψ-particles are discussed. New enlarged SU4 multiplets of other hadrons are proposed. Tests of our scheme are put forward. The most crucial test will be the observation of two rather broad resonances in e+ e collisions with masses around 4.2 GeV and 5.1 GeV. Another prediction is the presence of energetic photons in the decays of theψ-particles. Important results concerning the recently observed phenomena in the process e+e→hadrons follow in this scheme.

• Response of a two-level system to a sequence of N radiation pulses

A general expression has been obtained for the polarisation of an assembly of two-level systems irradiated by a sequence of N radiation pulses. The times and amplitudes of the echo-polarisation have been obtained. The method is an extension of the T-matrix method for the exact solution of the problem of interaction of radiation with two-level systems. The number of polarisation echoes is 3N−1N. The echo times are given by$$t' = (1 + a)t_N + (b - a)t_{N - 1} + (c - b)t_{N - 2} + \cdots + (q - p)t_1$$ wheretk are the pulse times anda, b, c take on values 1, 0, − 1. From the general expression the amplitudes of echoes due to sequences of 2, 3 and 4 pulses are obtained as special cases. Distinct echo sequences determined by time relations among the incident pulses are discussed. The echo sequences exhibit interesting features which are of significance in the application of the phenomenon in holophony, etc.

• Some results in the theory of interacting electron systems

The expressions for the longitudinal dielectric function, spin and orbital susceptibilities in the static, long wavelength limit are evaluated by solving the corresponding linearized vertex functions exactly in this limit. The plasma dispersion relation to leading order in the long wave limit is similarly obtained. These are compared with the corresponding results obtained previoulsy by us by a variational solution to the same vertex equations. It is established that the variational method gives the exact results in the static, zero wave vector limit, involving the proper renormalizations. The plasma dispersion relation is found to be the same as in the exact calculation whereas the coefficient of q2 in the static density correlation function has an important additional contribution to the variational result. Applications of these results are briefly discussed.

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