Electroweak theory electrodynamics

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. 

Both A(3> and B(3> are longitudinally directed and are nonzero in the vacuum. Both A(3> and B(3> are phaseless, but propagate with the radiation [47-62] and with their (1) and (2) counterparts. The radiated vector potential A<3 does not give rise to a photon on the low-energy scale, because it has no phase with which to construct annihilation and creation operators. On the high-energy scale, there is a superheavy photon [44] present from electroweak theory with an SU(2)x SU(2) symmetry. The existence of such a superheavy photon has been inferred empirically [44], However, the radiated vector potential A<3) is not zero in 0(3) electrodynamics from first principles, which, as shown in this section, are supported empirically with precision. 

Therefore, the empirical and theoretical evidence for the superiority of an 0(3) invariant over a U(l) invariant electrodynamics is overwhelming. It is clear that the process of development can be continued, for example, in quantum electrodynamics, electroweak theory, and grand unified theory, and the ontology of these developments can also be studied in parallel. 

What has been presented is an outline of an SU(2) x SU(2) electroweak theory that can give rise to the non-Abelian 0(3)b theory of quantum electrodynamics on the physical vacuum. The details of the fermions and their masses has yet to be worked through, as well as the mass of the A boson. This vector boson as well as the additional fermions should be observable within the 10-Tev range of energy. This may be accessible by the CERN Large Hadron Collider in the near future. 

As in the case of the electromagnetic self-mass, the implied dynamical mass increment is infinite unless perturbation-theory sums are truncated by a renormalization cutoff procedure. In analogy to electrodynamics, each fermion field acquires an incremental dynamical mass through interaction with the gauge field. This implies in electroweak theory that neutrinos must acquire such a dynamical mass from their interaction with the SUIT) gauge field. For a renormalized Dirac fermion in an externally determined SUIT) gauge field, the Lagrangian density is... 

The principal purpose here has been to demonstrate what sort of electroweak interaction physics may be required for the existence of an 0(3)b theory of quantum electrodynamics on the low-energy physical vacuum. This demonstrates that an extended standard model of electroweak interactions can support such a theory with the addition of new physics at high energy. 

In particular, the consideration of relativistic and QED effects of electronic systems (i.e. free electrons, electronic ions, atoms or molecules) in strong external electromagnetic fields provides various appropriate scenarios for sensitive tests of our understanding of the underlying interactions. Theories of fundamental interactions, such as quantum electrodynamics (QED) or the standard model of electroweak interactions can be tested conclusively by studying QED radiative corrections and parity-violating effects (PNC) in the presence of strong fields. 

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