Quantum fields are considered as generators of infinite-dimensional Clifford algebra $\mathrm{\text{Cl}}(\infty )$, which can be either orthogonal (in the case of fermions) or symplectic (in the case of bosons). A generic quantum state can be expressed as a superposition of the basis elements of $\mathrm{\text{Cl}}(\infty )$, with the superposition coefficients being multiparticle complex-valued wavefunctions. The basis elements, that are products of the generators of $\mathrm{\text{Cl}}(\infty )$ in the Witt basis, act as creation and annihilation operators. They create positive and negative energy states that include the bare and the Dirac vacuum as special cases. It is shown that the nonvanishing electric charge arises from an extra dimension or from doubling the number of creation and annihilation operators, which brings an extra imaginary unit $ī$ into the description. A further extension is to consider $ī$ as one of the quaternionic imaginary units and consider a generic state as having values in the quaternionic algebra or, equivalently, in the complexified two-dimensional Clifford algebra, $\mathrm{\text{Cl}}(2)\otimes C$. It contains two distinct fundamental representations of $\mathrm{\text{SU}}(2)$, one associated with the weak isospin doublet $({\nu }_e,e^{-})$ and the other one with the doublet of new leptons, denoted by $({𝜖}^{+},{\nu }_{𝜖})$, that together with the new quarks $(u^{\prime },d^{\prime })$ can be identified with dark matter.

量子场被认为是无限维克利福德代数的生成器$\mathrm{\text{氯}}(\infty )$，它可以是正交的（在费米子的情况下）或辛的（在玻色子的情况下）。一个通用的量子态可以表示为基本元素的叠加$\mathrm{\text{氯}}(\infty )$，叠加系数是多粒子复值波函数。基本元素，即生成器的乘积$\mathrm{\text{氯}}(\infty )$在 Witt 基础上，充当创造和湮灭算子。它们产生正能量和负能量状态，包括作为特例的裸真空和狄拉克真空。结果表明，不消失的电荷来自一个额外的维度，或者来自于创造和湮灭算子数量的两倍，这带来了一个额外的虚单位$\mathrm{一世}$进入描述。进一步的扩展是考虑$\mathrm{一世}$作为四元数虚数单位之一，并将一般状态视为在四元数代数中具有值，或者等效地在复二维 Clifford 代数中具有值，$\mathrm{\text{氯}}(2)\otimes C$. 它包含两个不同的基本表示$\mathrm{\text{苏}}(2)$，一个与弱同位旋双峰相关$({\nu }_e,e^{-})$另一个带有新轻子的双峰，表示为$({𝜖}^{+},{\nu }_{𝜖})$，与新夸克一起$({你}^{\text{'}},d^{\text{'}})$可以与暗物质鉴别。