论文标题
了解克利福德和格拉斯曼空间中费米子的第二次量化 - 第二次量化的新方法，第二部分
Understanding the second quantization of fermions in Clifford and in Grassmann space -- New way of second quantization of fermions, Part II
论文作者
论文摘要
我们在第二部分中介绍了内部对费尔米的自由度的描述，通过奇怪的代数元素的奇数产品的叠加，即$γ^a $'s或$ \tildeγ^a $'s $'s的奇怪性确定创造的固定空间和eNterized formion fiens a fermion Fields y $ d $ d $ d $ d $ d $ d $ d in vermientions of the of the of the vermentions in vermion nim in-nim dim-d。由Grassmann代数元素$θ^a $'和$ \ frac {\ partial} {\ partialθ_a} $。我们讨论：{\ bf i。}两种奇数Clifford代数的属性，形成了两个独立的空间，两者都用$θ^{a} $的Grassmann代数表达，又可以表达出$θ^{a} $和$ \ frac {\ frac {\ partial} {\ partial} {\ partial timialθ_= a} a} $'s。 {\ bf ii。}两种奇怪的克利福德对象之一的冻结过程，使剩下的克利福德对象在有限的基础基础量的张张量中确定其奇怪性，而有限的基础数量的无限数量和无限量的量子和否定的量子数量：跨性别的量子，否定了量子的量子，并实现了量子数量，并实现了量的量子数量：真空状态，以及整个希尔伯特空间，由无限数量的空和占用的单个费米态的“ slater决定因素”的总和。 {\ bf iii。} dirac假定的第二个量化费米与我们克利福德代数创建和歼灭操作员之后的关系之间的关系，这为dirac假设提供了解释。
We present in Part II the description of the internal degrees of freedom of fermions by the superposition of odd products of the Clifford algebra elements, either $γ^a$'s or $\tildeγ^a$'s, which determine with their oddness the anticommuting properties of the creation and annihilation operators of the second quantized fermion fields in even $d$-dimensional space-time, as we do in Part I of this paper by the Grassmann algebra elements $θ^a$'s and $\frac{\partial}{\partial θ_a}$'s. We discuss: {\bf i.} The properties of the two kinds of the odd Clifford algebras, forming two independent spaces, both expressible with the Grassmann algebra of $θ^{a}$'s and $\frac{\partial}{\partial θ_{a}}$'s. {\bf ii.} The freezing out procedure of one of the two kinds of the odd Clifford objects, enabling that the remaining Clifford objects determine with their oddness in the tensor products of the finite number of the Clifford basis vectors and the infinite number of momentum basis, the creation and annihilation operators carrying the family quantum numbers and fulfilling the anticommutation relations of the second quantized fermions: on the vacuum state, and on the whole Hilbert space defined by the sum of infinite number of "Slater determinants" of empty and occupied single fermion states. {\bf iii.} The relation between the second quantized fermions as postulated by Dirac and the ones following from our Clifford algebra creation and annihilation operators, what offers the explanation for the Dirac postulates.
