At the same time, classical gauge theory admits comprehensive geometric formulation where gauge fields are represented by connections on principal bundles. In this framework, spontaneous symmetry breaking is characterized as a reduction of the structure group G of a principal bundle P → → X to its closed subgroup H . By the well-known theorem, such a reduction takes place if and only if there exists a global section h of the quotient bundle P / H → → X . This section is treated as a classical Higgs field.