BRST invariant formulation of spontaneously broken gauge theory in generalized differential geometry

Noncommutative geometry(NCG) on the discrete space successfully reproduces the Higgs mechanism of the spontaneously broken gauge theory, in which the Higgs boson field is regarded as a kind of gauge field on the discrete space. We could construct the generalized differential geometry(GDG) on the discrete space $M_4\times Z_N$ which is very close to NCG in case of $M_4\times Z_2$. GDG is a direct generalization of the differential geometry on the ordinary manifold into the discrete one. In this paper, we attempt to construct the BRST invariant formulation of spontaneously broken gauge theory based on GDG and obtain the BRST invariant Lagrangian with the t'Hooft-Feynman gauge fixing term.Comment: 15 page

Modified Reconstruction of Standard Model in Non-Commutative Differential Geometry

Sogami recently proposed the new idea to express Higgs particle as a kind of gauge particle by prescribing the generalized covariant derivative with gauge and Higgs fields operating on quark and lepton fields. The field strengths for both the gauge and Higgs fields are defined by the commutators of the covariant derivative by which he could obtain the Yang-Mills Higgs Lagrangian in the standard model. Inspired by Sogami's work, we present a modification of our previous scheme to formulate the spontaneously broken gauge theory in non-commutative geometry on the discrete space; Minkowski space multiplied by two points space by introducing the generation mixing matrix in operation of the generalized derivative on the more fundamental fields a_i(x,y) which compose the gauge and Higgs fields. The standard model is reconstructed according to the modified scheme, which does not yields not only any special relations between the particle masses but also the special restriction on the Higgs potential.Comment: 21 page

Microcomputer system for medium-sized and experimental finite element analysis

The development of a microcomputer system is described. A series of finite element analysis programs are evaluated in terms of their cost effective application within the microcomputer system. It is shown that the system is practically maintenance free and can be sustained by individual laboratories of standard scale in the educational or academic environment

The vibrational predissociation spectroscopy of hydrogen cluster ions

The first infrared spectra of protonated hydrogen clusters in the gas phase have been observed. Predissociation spectra were taken with a tandem mass spectrometer: mass selected hydrogen cluster ions were irradiated inside a rf ion trap by a tunable infrared laser, and the fragment ions created by photodissociation of the clusters were mass selected and detected. Spectra for each product channel were measured by counting fragment ions as a function of laser frequency. Low resolution spectra (Deltanu=10 cm^−1) in the region from 3800 to 4200 cm^−1 were observed for the ions H + 5, H + 7, and H + 9 at 3910, 3980, and 4020 cm−1, respectively. A band was also observed for H + 5 at 3532 cm^−1. No rotational structure was resolved. The frequencies of the band maxima agree well with the frequencies predicted by previous ab initio calculations for the highest modes

BRST invariant Lagrangian of spontaneously broken gauge theories in noncommutative geometry

The quantization of spontaneously broken gauge theories in noncommutative geometry(NCG) has been sought for some time, because quantization is crucial for making the NCG approach a reliable and physically acceptable theory. Lee, Hwang and Ne'eman recently succeeded in realizing the BRST quantization of gauge theories in NCG in the matrix derivative approach proposed by Coquereaux et al. The present author has proposed a characteristic formulation to reconstruct a gauge theory in NCG on the discrete space $M_4\times Z_{_N}$. Since this formulation is a generalization of the differential geometry on the ordinary manifold to that on the discrete manifold, it is more familiar than other approaches. In this paper, we show that within our formulation we can obtain the BRST invariant Lagrangian in the same way as Lee, Hwang and Ne'eman and apply it to the SU(2)$\times$U(1) gauge theory.Comment: RevTeX, page