在数学几何学与物理中，旋量是复矢量空间中的的元素。旋量乃自旋群的表象，类似于欧几里得空间中的矢量以及更广义的张量，当欧几里得空间进行无限小旋转时，旋量做相应的线性转换。当如此一系列这样的小旋转组合成一定量的旋转时，这些旋量转换的次序会造成不同的组合旋转结果，与矢量或张量的情形不同。当空间从0°开始，旋转了完整的一圈（360°），旋量发生了正负号**（见图），这个特征即是旋量最大的特点。在一给定维度下，需要旋量才能完整地描述旋转，如此引入了额外数量的维度。

在闵考斯基空间的情形，也可以定义出相似的旋量，其中狭义相对论的劳仑兹转换扮演旋转的角色。旋量最先是由埃利·嘉当于1913年引入几何学。在1920年代，物理学家发现若要描述电子及其他次原子粒子的内禀角动量或自旋，旋量为不可或缺的角色。旋量群为所有旋转相关的旋量所构成的群，其二重覆叠了旋转群，因为每个完整旋转结果皆有两种不同但等效的旋转方式。

In geometry and physics, spinors are elements of a (complex) vector space that can be associated with Euclidean space. Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a slight (infinitesimal) rotation. When a sequence of such small rotations is composed (integrated) to form an overall final rotation, however, the resulting spinor transformation depends on which sequence of small rotations was used, unlike for vectors and tensors. A spinor transforms to its negative when the space is rotated through a complete turn from 0° to 360° (see picture), and it is this property that characterizes spinors. It is also possible to associate a substantially similar notion of spinor to Minkowski space in which case the Lorentz transformations of special relativity play the role of rotations. Spinors were introduced in geometry by Élie Cartan in 1913. In the 1920s physicists discovered that spinors are essential to describe the intrinsic angular momentum, or "spin", of the electron and other subatomic particles.