On goldstone fermions
On goldstone fermions
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关于戈德斯通费米子
DOI：
10.1016/0370-2693(74)90637-6
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发表时间：
1974
影响因子：
4.4
通讯作者：
J. Strathdee
中科院分区：
文献类型：
--
作者：
A. Salam;J. Strathdee
在最近的两篇论文 [1, 2] 中，Wess 和 Zumino 将双模型理论的超规范对称性推广到了 4 维时空场。超规范对称性最不寻常的特征是它们将费米子与玻色子结合在同一多重态中。这意味着产生这些对称性的一些守恒电流必须是费米子电流。对于洛伦兹群，这些电流 J 将像矢量和狄拉克旋量的乘积一样进行变换。它们的分量是自旋 1/2 和 3/2 的混合。 μας 超规范对称性的酉不可约表示 [3] 由三个量子数表征：质量 M、“自旋”J 和宇称 n。如果 M 不为零，则（自旋）奇偶校验内容为 (J)"、Jin、J-in 和 (J+ 1)"。如果M= 0，则螺旋度含量为J、J+和-J,−(J+})。这篇文章的目的是考虑如果真空是简并的，即不是超规范单线态，会发生什么。很自然地，一方面，先前不可约多重态中的大规模简并性将会解除，另一方面，戈德斯通现象也会出现。事实上，直接的含义是系统必须包含自旋 1/2 的零质量费米子，因为以下一般论点。无穷小的超规范变换 € 在狄拉克旋量场 Vɑ› 上的作用正式表示为
In two recent papers [1, 2] Wess and Zumino have generalized the super-gauge symmetry of dual model theory to apply to fields in 4-dimensional space-time. The most unusual feature of super-gauge symmetries is that they combine fermions with bosons in the same multiplet. This means that some of the conserved currents which generate these symmetries must be fermionic. With respect to the Lorentz group, these currents, J, will transform like the product of a vector and a Dirac spinor. Their components are a mixture of spins 1/2 and 3/2. μαςThe unitary irreducible representations [3] of the super-gauge symmetry are characterized by three quantum numbers: the mass M," spin" J, and parity n. If M is non-vanishing, then the (spin) parity content is (J)", Jin, J-in and (J+ 1)". If M= 0, then the helicity content is J, J+ and-J,−(J+}). The purpose of this note is tò consider what happens if the vacuum is degenerate, ie not a supergauge singlet. It is natural to expect, on the one hand, a lifting of the mass degeneracy in the previously irreducible multiplets and, on the other, a Goldstone phenomenon. In fact, the immediate implication would be that the system must contain a zero-mass fermion of spin 1/2 because of the following general argument. The action of an infinitesimal super-gauge transformation,€, on the Dirac spinor field, Vɑ› is expressed formally by