Regular Magnetic Monopole from Generalized ’t Hooft Tensor

It is well known that ’t Hooft--Polykov magnetic monopole regularly realizes the Dirac magnetic monopole in terms of a two-rank tensor, i.e. the so-called ’t Hooft tensor in three-dimensional space, which has been generalized to all even rank ones. We propose an arbitrary odd rank ’t Hooft tensor, which universally determines the quantized low-energy boundaries of the even dimensional Georgi--Glashow models under asymptotic conditions. Furthermore, the dual magnetic monopole theory is built up in terms of the Ф-mapping theory.