Weak theory

As this concerns the nature of non-Abelian electrodynamics, we will pursue the matter of a GUT that incorporates non-Abelian electrodynamics. This GUT will be an 50(10) theory as outlined above. We have that an extended electro-weak theory that encompasses non-Abelian electrodynamics is spin(4) = 51/(2) x 517(2). This in turn can be embedded into a larger 50(10) algebra with spin(6) = 517(4). 50(10) may be decomposed into 517(2) x 517(2) x 517(4). This permits the embedding of the extended electro weak theory with 517(4), which may contain the nuclear interactions as 517(4) 51/(3) x 1/(1). In the following paragraphs we will discuss the nature of this gauge theory and illustrate some basic results and predictions on how nature should appear. We will also discuss the nature of fermion fields in an 517(2) x 51/(2) x 51/(4) theory. 

Another way to manage experimentally the problem of the unknown term is to use another kind of theory. The usual theory in the case of simple atoms (we call it strong theory) give us some values, while in case of the g factor it must be useful even to fix a form of the theoretical expression (we call this option weak theory). When one knows part of the theoretical terms and a form of other terms, it is possible try to measure the unknown coefficients. The only unknown term which is important for carbon and ions with Z around 6 is of order (Za)Am/M. One can take an advantage of the weak theory approach and measure the coefficient of this term by studying with the oxygen ion. 

Note that n — N/2 corresponds to the independent particle model analogous to the celebrated Hartree-Fock equations in atomic and molecular physics. We also observe that the fundamental interaction mentioned above is unitarily connected with the electromagnetic interactions between the particle m0 and the antiparticle —m0. Since we do not make any distinctions between the Klein-Gordon and the Dirac equation, we are not able here to integrate the electro-weak theory although in principle this should be possible. 

The weak interaction, some lO times weaker than the electrom neUc interaction, occurs between "leptons and in the decay of hadrons. It is responsible for the "beta decay of particles and nuclei. In the current model, the weak interaction is visualized as a force mediated by the exchange of virtual particles, called intermediate vector bosons. The weak interactions are described by "electro-weak theory, which unifies them with the electromagnetic interactions. 

As mentioned in the introduction to Parts A and B, new experimental methods have enriched and advanced the field of atomic spectroscopy to such a degree that it serves not only as a source of atomic structure data but also as a test ground for fundamental atomic theories based upon the framework of quantum mechanics and quantum electrodynamics. However, modem laser and photon correlation techniques have also been applied successfully to probe beyond the traditional quantum mechanical and quantum electrodynamical theories into nuclear stracture theories, electro-weak theories, and the growing field of local realistic theories versus quantum theories. 

M.C. Noecker, B.P. Masterson, C.E. Wieman Precision measurement of parity nonconservation in atomic cesium A low-energy test of the electro-weak theory. Phys. Rev. Lett. 61, 310 (1988)... 

Perturbation theory is a natural tool for the description of intemioleciilar forces because they are relatively weak. If the interactmg molecules (A and B) are far enough apart, then the theory becomes relatively simple because tlie overlap between the wavefiinctions of the two molecules can be neglected. This is called the polarization approximation. Such a theory was first fomuilated by London [3, 4], and then refomuilated by several others [5, 6 and 7]. 

Levelt Sengers J M H 1999 Mean-field theories, their weaknesses and strength Fluid Phase Equilibria 158-160 3-17... 

Gilbert R G, Luther K and Troe J 1983 Theory of thermal unimolecular reactions in the fall-off range. II. Weak collision rate constants Ber. Bunsenges. Phys. Chem. 87 169-77... 

A good example is the spectnun of naphthalene. The two lowest excited states have 62 and synnnetries and are allowed for one-photon transitions. A weak transition to one of these is observable in die two-photon spectnun [33], presumably made allowed by vibronic effects. Much stronger two-photon transitions are observable at somewhat higher energies to a and an A state lying quite close to the energies predicted by theory many years earlier [34]. 

Figure B3.6.5. Phase diagram of a ternary polymer blend consisting of two homopolymers, A and B, and a synnnetric AB diblock copolymer as calculated by self-consistent field theory. All species have the same chain length A and the figure displays a cut tlirough the phase prism at%N= 11 (which corresponds to weak segregation). The phase diagram contains two homopolymer-rich phases A and B, a synnnetric lamellar phase L and asynnnetric lamellar phases, which are rich in the A component or rich in the B component ig, respectively. From Janert and Schick [68].

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