Electroweak

The Hamiltonian considered above, which connmites with E, involves the electromagnetic forces between the nuclei and electrons. However, there is another force between particles, the weak interaction force, that is not invariant to inversion. The weak charged current mteraction force is responsible for the beta decay of nuclei, and the related weak neutral current interaction force has an effect in atomic and molecular systems. If we include this force between the nuclei and electrons in the molecular Hamiltonian (as we should because of electroweak unification) then the Hamiltonian will not conuuiite with , and states of opposite parity will be mixed. However, the effect of the weak neutral current interaction force is mcredibly small (and it is a very short range force), although its effect has been detected in extremely precise experiments on atoms (see, for... 

Except for a couple of rather extreme areas (like the combination of general relativity and quantum mechanics, or the unification of the strong and gravitational forces with the electroweak interaction), we believe that all the fundamental physics is known. The only problem is that the real world contains so many (different) components interacting by complicated potentials that a detailed description is impossible. 

Symmetry breaking associated with chiral phenomena is a theme that recurs across the sciences—from the intricacies of the electroweak interaction and nuclear decay [1-3] to the environmentally influenced dimorphic chiral structures of microscopic planktonic foraminifera [4, 5], and the genetically controlled preferential coiling direction seen in the shells of snail populations [6, 7]. 

It is well recognized that heavy atoms and heavy polar diatomic molecules are very promising candidates in the experimental search for permanent EDMs arising from the violation of P and T. The search for nonzero P,T-odd effects in these systems with the presently accessible level of experimental sensitivity would indicate the presence of new physics beyond the SM of electroweak and strong interactions [9], which is certainly of fundamental importance. Despite the well known drawbacks and unresolved problems of the SM, there are no experimental data available that would be in direct contradiction with this theory. In turn, some popular extensions of the SM, which allow one to overcome its disadvantages, are not yet confirmed experimentally [8, 10]. 

Now, let us consider the divergence of axial currents in HDET, which is related to the axial anomaly and also to how the quark matter responds to external axial-current sources like electroweak probes. 

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... 

Tranter, G. E., MacDermott, A. J., Overill, R. E., and Speers, P. (1992). Computational studies of the electroweak origin of biomolecular handedness in natural sugars. Proc. Royal Soc., London A, 436, 603-15. 

Whilst this demonstrates that calculations using the methods of this paper may prove very useful in studies of molecules containing only low-Z atoms, a major objective has been to study systems containing heavier atoms. So far, only a limited number of molecular calculations have been carried out with BERTHA at the DHF level, mainly in connection with studies of hyperfine and PT-odd effects in heavy polar molecules such as YbF [33] and TIF [13]. The reader is referred to the literature for an assessment of these calculations and for technical details on the construction of basis sets which must not only describe molecular bonding properly but also give a good representation of spinors close to the heavy nuclei to handle the short-range electron-nuclear electroweak interactions. 

This mathematical model is only fitting as long as atomic nuclei can be considered achiral. In fact, this is not true because of the electroweak interaction. The consequence is an energy difference of enantiomers on the order of 10 17 J/ mol. For an excellent account of these recent insights see S. Mason, Chem. Soc. Rev. 17, 347-359 (1988). 

Electroweak Processes in External Electromagnetic Fields By A. Kuznetsov and N. Mikheev 2003. 24 figs., XII, 136 pages... 

Precision Electroweak Physics at Electron-Positron Colliders By S. Roth 2007. 107 figs., X, 174 pages... 

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. 

The prediction of a heavy boson has received preliminary empirical support [92,96] from an anomaly in Z decay widths that points toward the existence of Z bosons with a mass of 812 GeV 1 33j [92,96] within the SO(l) grand unified field model, and a Higgs mechanism of 145 GeV4gj3. This suggests that a new massive neutral boson has been detected. Analysis of the hadronic peak cross sections obtained at LEP [96] implies a small amount of missing invisible width in Z decays. The effective number of massless neutrinos is 2.985 0.008, which is below the prediction of 3 by the standard model of electroweak interactions. The weak charge Qw in atomic parity violation can be interpreted as a measurement of the S parameter. This indicates a new Qw = 72.06 0.44, which is found to be above the standard model pre-... 

---