Oscillator model for particles underlying unitary symmetry
Oscillator model for particles underlying unitary symmetry
复制标题
酉对称性粒子的振荡器模型
DOI：
10.1007/bf02750221
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发表时间：
1964
期刊：
影响因子：
--
通讯作者：
T. Takabayasi
中科院分区：
文献类型：
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作者：
T. Takabayasi
1.为了对基本粒子的统一描述，YUKAWA很早就在双局域理论(1)的框架下提出了相对论性谐振子模型，该模型除了引入通常的外部坐标X~及其共轭动量分量P~外，还引入了内部时空坐标X~及其共轭动量P~。最近，他对这一理论作了新的发展（~），表明它可以暗示某些内部量子数，如同位旋。另一方面，提出了不同的粒子振子格式（~-5）来直接解释粒子的超多重结构和质量规律。特别是在参考文献（~）中指出，最初从Sakata模型(6)的观点提出的Ua对称性，可以用粒子的振荡模型来解释，并指出，根据这种模型，三维酉酉对称性运作的原因可以简单地理解为物理空间本身的维数的直接结果。通过结合两种观点，我们在本文中引入了基本假设（~）（r: 1,2,3）的存在，而不是一个单一的x~，即Yt~ KAWA的三个内部坐标向量x~，并表明这个扩展模型为Ua或SU对称性提供了新的基础，这种对称性最近在强相互作用粒子中越来越成功地被证明(6)。年代)。事实上，我们的理论为重子及其激发提供了一个统一的模型，因为属于各种可能的超多重态的所有重子态都可以被视为同一系统的不同振子能级，每个能级都由一组适当的量子数指定，其中包括通常的量子数。我们的模型的直接预测是具体的存在
1.-For a unified description of elementary particles YUKAWA was early led to a relativistic harmonic-oscillator model in the framework of bi-local theory (1), which introduces, besides the usual external co-ordinates X~ and their conjugate momentum components P~, the internal space-time co-ordinates x~ and their conjugates p~. Recently he made a new development of the theory (~) by showing that it could imply certain internal quantum number such as isospin. On the other hand different oscillator schemes for particles have been set forth (~-5) to directly account for supermultiplet structures and mass rules for particles. In particular in ref.(~) it was pointed out that the Ua symmetry, originally proposed from the standpoint of the Sakata model (6), could be interpreted in terms of an oscillator model for particles, and it Was remarked that the reason why the threedimensional unitary symmetry should operate could be trivially understood, according to this kind of model, as' the direct consequence of the dimensionality of the physical space itself.By combining both viewpoints we introduce in this note the basic assmnption (~)(r: 1, 2, 3) exist, instead of a single x~ that three internal co-ordinate vectors x~ of Yt~ KAWA, and show that this extended model provides a new basis underlying the Ua or SU a symmetry which has recently proved more and more successful for strongly interacting particles (6. s). Indeed our theory presents a unified model for baryons and their excitations since all baryonic states belonging to various possible supermultiplets can be regarded as different oscillator levels of that same system, each of which is specified by the set of appropriate quantum numbers that include the usual ones. The immediate prediction of our model is the existence of specific