abstract

The Gibbs-Heaviside vector algebra is widely used in problems pertaining to three dimensional Euclidean space. In this paper we introduce a remarkably similar complex three dimensional vector algebra for use in four dimensional spacetime. A complex vector has the geometric interpretation of a bivector in spacetime.

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Following an extension of the Utiyama and Kibble method, gravitational fields are introduced as gauge fields. The gauge group is the GL(4,R) which is derived from the group of general coordinate transformations. This group corresponds to a metric affine geometry. The equations of fields follow from a Lagrangian containing linear and quadratic invariants constructed from the gauge field tensor and an additional scalar field. Certain constraints lead to a hierarchy of gauge gravitational theories including the Einstein or U\(_4\) theory as the most direct case.

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We analyse classical gauge potentials generated by static external sources coupled to gauge invariant, nonlocal operators. For the gauge invariant operators involving fermions we find two sharply distinct cases. In the first one, the external source decouples from Yang–Mills equations what leads to zero gauge potentials. The other one is found to be inconsistent with classical Yang–Mills equations. We consider also nonlocal, gauge invariant operators without fermions. We argue that there exists a possibility that the corresponding classical gauge field configuration is that of the closed magnetic flux tube with quantized energy.

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Physics below 300 GeV is termed infrared, and physics above 1 TeV is called ultraviolet. Some aspects of the relation between these two regions are discussed. It is argued that the symmetries of the infrared must be symmetries in the ultraviolet. Furthermore, naturalness within the context of the standard model is considered. It is concluded that there is either a threshold in the TeV region, or alternatively a certain mass formula holds. This formula, when true, might be indicative for an underlying supersymmetry.

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We reanalyze the probabilistic description of inelastic hadron–nucleus and nucleus–nucleus collisions with diffractive channels present. We give several formulae which may he useful in analyzing data on multiparticle production in high energy nuclear scattering.

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The binding energy of the \({\mit \Lambda }\) particle in nuclear matter, \(B_{\mit \Lambda }\), is calculated for a number of central hard core \({\mit \Lambda }\)N potentials and for the OMY6 NN potential. Firstly, the Jastrow method in the Fermi-hypernetted-chain (FITINC) approximation is applied. Secondly, the Brueckner reaction method is used. The FHNC results for \(B_{\mit \Lambda }\) are much bigger than the reaction-matrix matrix results. Possible sources of this discrepancy are discussed.

abstract

The 120, 145 and 172.5 MeV \(\alpha \)-particle beams from JULIC were used to measure differential cross sections for elastic scattering on \(^{12}\)C, \(^{24}\)Mg and \(^{27}\)Al in the angular range from about 5\(^{\circ }\) to 70\(^{\circ }\) (c.m. system). The angular distributions were analysed extensively in terms of the optical model using a variety of potential forms. Apart from the parametrized forms of potential, as Woods–Saxon (WS) or rather (WS)\(^{\nu }\), also a model independent representation of potential (spline potential) was employed. The analysis based on the parametrized forms of the potential provided the possibility to find best fit parameter sets, which were then examined on their uniqueness and energy dependence. It has been of special interest to gain information on the radial shape of the potential.