0 electroweak theory

With the exception of recent extensions to electroweak theory [1] chemistry deals exclusively with electromagnetic interactions. The starting point for a quantum theory to describe these interactions is the Lagrangian formalism since it allows the correct identification of conjugated momenta appearing in the Hamiltonian [2]. Full-fledged quantum electrodynamics (QED) is based on a Lagrangian of the form... 

A simple example in classical electrodynamics of what is now known as gauge invariance was introduced by Heaviside [3,4], who reduced the original electrodynamical equations of Maxwell to their present form. Therefore, these equations are more properly known as the Maxwell-Heaviside equations and, in the terminology of contemporary gauge field theory, are identifiable as U(l) Yang-Mills equations [15]. The subj ect of this chapter is 0(3) Yang-Mills gauge theory applied to electrodynamics and electroweak theory. 

The extension of U(l) x SU(2) electroweak theory to SU(2) x SU(2) elec-troweak theory succeeds in describing the empirically measured masses of the weakly interacting vector bosons, and predicts a novel massive boson that was been detected in 1999 [92]. The SU(2) x SU(2) theory is developed initially with one Higgs field for both parts of the twisted bundle [93], and is further developed later in this section. 

The 0 3 connection has a chiral component that seems to imply that Ti v has a chiral component, or is mixed with the chiral component of the other SU(2) chiral field of the electroweak theory. This is what happens to SU(2) electromagnetism at very high energies. It becomes very similar in formal structure to the theory of weak interactions and has implications for the theory of leptons. The electromagnetic interaction acts on a doublet that can be treated as an element of a Fermi doublet of charged leptons and their neutrinos in the SU(2) theory of the weak interaction. 

Therefore the electroweak theory is chiral at high energies, but is vector and chiral in separate sectors on the physical vacuum of low energies. The high-energy chiral field combines with the other chiral field in the twisted bundle to produce a vector field plus a broken chiral field at low energy. There are independent fields that are decoupled on the physical vacuum at low energies. 

The second Higgs field acts in such a way that if the vacuum expectation value is zero, ( ) = 0, then the symmetry breaking mechanism effectively collapses to the Higgs mechanism of the standard SU(2) x U(l) electroweak theory. The result is a vector electromagnetic gauge theory 0(3)/> and a broken chiral SU(2) weak interaction theory. The mass of the vector boson sector is in the A(3) boson plus the W and Z° particles. 

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