Abstract
Since it expresses a connection between the basic units of angular momentum /~ and electric charge e, the experimentally observed value of the fine-structure constant = eS/4~t~c may signify an underlying relationship between the associated groups for spatial rotations SOs and electromagnetic gauge transformations SOs. In the present letter, at tention is given to Haar-induced volumes of the fourand ten-dimensional envelopments #[SOs • SOs] and #[[S03] s • SOs]. I t is observed that if the lat ter volumes, denoted as V and V', are related to the radius a of SOs and the half-period b of SO s by the simple conditions in (12), then the fine-structure constant is required to have the theoretical value shown in (17). I t is customary to parametrize the SOs.group of proper rotations in physical Euclidean space in terms of r a real three-component vector defined through a sphere of radius z with antipodal surface points identified topologically: r ~-r for I~al = ~. For any SOs element the direction and magnitude (radians) of the rotation is given by the direction and magnitude of ~ . An elementary calculation yields the associated normalized Haar measure (1)
Published Version
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