MAGNETIC MONOPOLES IN UNIFIED GAUGE THEORIES

MAGNETIC MONOPOLES IN UNIFIED GAUGE THEORIES

1974 | G. 't HOOFT
In unified gauge theories where the electromagnetic group U(1) is a subgroup of a larger compact group like SU(2) or SU(3), magnetic monopoles can be created as regular solutions of the field equations. Their mass is calculable and of order 137 times the mass of a typical vector boson, $ M_W $. The paper discusses the existence of magnetic monopoles in non-Abelian gauge theories, where the Higgs field is not aligned with the z-axis but instead rotated. This leads to a non-trivial solution of the field equations, resulting in a stable magnetic monopole at the origin. The monopole has a total magnetic flux of $ 4\pi/e $, satisfying Schwinger's condition $ eg = 1 $. The model uses a Lagrangian with a compact covering group, such as SO(3), and considers the Georgi-Glashow model, where the monopole mass is approximately 137 times $ M_W $. In the Weinberg-Salam model, the monopole mass would be 137 times the mass of a superheavy vector boson. The monopole mass is calculated using dimensionless parameters and is found to be nearly independent of the parameter $ \beta $, varying from 1.1 to 1.44. The paper concludes that magnetic monopoles are possible in these theories, and their properties are predictable and calculable. The monopole mass is high, which may explain the lack of experimental evidence so far. In the Georgi-Glashow model, monopoles do not obey Schwinger's condition but only Dirac's condition $ qg = 1/2 $. In other models, the monopole quantum may be a multiple of the Dirac value. The paper also notes that the theory avoids the need for Dirac's string and that quantum corrections to the solution are expected to be calculable.In unified gauge theories where the electromagnetic group U(1) is a subgroup of a larger compact group like SU(2) or SU(3), magnetic monopoles can be created as regular solutions of the field equations. Their mass is calculable and of order 137 times the mass of a typical vector boson, $ M_W $. The paper discusses the existence of magnetic monopoles in non-Abelian gauge theories, where the Higgs field is not aligned with the z-axis but instead rotated. This leads to a non-trivial solution of the field equations, resulting in a stable magnetic monopole at the origin. The monopole has a total magnetic flux of $ 4\pi/e $, satisfying Schwinger's condition $ eg = 1 $. The model uses a Lagrangian with a compact covering group, such as SO(3), and considers the Georgi-Glashow model, where the monopole mass is approximately 137 times $ M_W $. In the Weinberg-Salam model, the monopole mass would be 137 times the mass of a superheavy vector boson. The monopole mass is calculated using dimensionless parameters and is found to be nearly independent of the parameter $ \beta $, varying from 1.1 to 1.44. The paper concludes that magnetic monopoles are possible in these theories, and their properties are predictable and calculable. The monopole mass is high, which may explain the lack of experimental evidence so far. In the Georgi-Glashow model, monopoles do not obey Schwinger's condition but only Dirac's condition $ qg = 1/2 $. In other models, the monopole quantum may be a multiple of the Dirac value. The paper also notes that the theory avoids the need for Dirac's string and that quantum corrections to the solution are expected to be calculable.
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