The Higgs field is a fundamental field in particle physics that interacts with elementary particles to give them mass. The expectation value of the Higgs field, also known as the vacuum expectation value (VEV), plays a crucial role in the theory of electroweak symmetry breaking.
An electric field, on the other hand, arises from the presence of electric charges and is described by the electromagnetic field. It interacts with charged particles and can exert forces on them.
In the Standard Model of particle physics, the Higgs field and the electromagnetic field are distinct and independent of each other. The presence of an electric field, by itself, does not directly affect the expectation value of the Higgs field.
However, in the presence of high-energy or extreme conditions, such as those found in the early universe or in certain high-energy experiments, the behavior of the Higgs field and its expectation value can be influenced by other fields and interactions. In such cases, the dynamics of the Higgs field may be affected indirectly by the presence of strong electromagnetic fields or other forces.
For example, in the early universe, during the process of electroweak symmetry breaking, the Higgs field undergoes a phase transition that separates the electroweak symmetry phase from the broken symmetry phase. In this phase transition, the Higgs field's expectation value changes from zero to a non-zero value, giving mass to the elementary particles. The dynamics of this phase transition can be influenced by the presence of various fields, including the electromagnetic field.
In summary, while the presence of an electric field by itself does not directly affect the expectation value of the Higgs field, under certain extreme conditions or in the context of specific interactions, the behavior of the Higgs field and its expectation value can be influenced by other fields, including the electromagnetic field.