Bosons and fermions are two different classes of particles in quantum field theory. Bosons are particles that obey Bose-Einstein statistics, while fermions obey Fermi-Dirac statistics. The concept of virtual particles arises in the framework of quantum field theory, where particles and their interactions are described in terms of virtual particle exchanges.
In quantum field theory, interactions between particles are described by the exchange of virtual particles. These virtual particles are not directly observable, but they mediate the forces between particles. For example, in electromagnetic interactions, photons are the virtual particles that mediate the electromagnetic force between charged particles.
In the case of bosons, such as gauge bosons like photons or W and Z bosons in the electroweak theory, they can have fermionic virtual particles associated with them. These fermionic virtual particles are not actual particles but arise as mathematical constructs within the framework of perturbation theory. They are introduced to account for the interactions between bosons and fermions and to ensure the consistency of the theory.
Regarding the excitation in U(1) and its relation to excitation in SU(2), it's important to note that U(1) and SU(2) are different gauge symmetries in the framework of gauge theory, specifically in the electroweak theory. The electroweak theory unifies the electromagnetic force (described by U(1)) and the weak nuclear force (described by SU(2)) into a single electroweak force.
In this theory, the excitation of one gauge symmetry, such as U(1), can cause an excitation in the other gauge symmetry, SU(2), through a process known as symmetry breaking. Symmetry breaking occurs when the underlying symmetries of a system are not manifested in the observed phenomena. This can happen through the Higgs mechanism, where a scalar field called the Higgs field acquires a non-zero vacuum expectation value, breaking the electroweak symmetry.
The Higgs mechanism leads to the generation of masses for the W and Z bosons and also introduces new particles called Higgs bosons. This process of symmetry breaking causes the excitation of both U(1) and SU(2) and is essential for understanding the electroweak interactions in particle physics.
It's worth noting that the detailed mathematical and theoretical aspects of these phenomena are complex and require a deeper study of quantum field theory and gauge theories.