Low energy effective theory

The low energy effective theory supports solitonic excitations which can be identified with the baryonic sector of the theory at non-zero chemical potential. In order to obtain classically stable configurations, it is necessary to include at least a four-derivative term (containing two temporal derivatives) in addition to the usual two-derivative term. Such a term is the Skyrme term ... 

It is also interesting to note that the explicit dependence on the quark chemical potential is communicated to the Goldstone excitations via the coefficients of the effective Lagrangian (see [31] for a review). For example is proportional to fj, in the high chemical potential limit and the low energy effective theory is a good expansion in the number of derivatives which allows to consistently incorporate in the theory the Wess-Zumino-Witten term [32] and its corrections. 

To construct the low energy effective theory of the fermionic system, we rewrite the fermion fields as... 

How it is that this GUT theory can be tested is a matter of some difficulty. It is still possible that low energy effects of a GUT may be detected. This was the hope for proton decay with the minimal 517(5) model. As there may be issues with chirality, or residual chirality in QCD it may be possible that GUTs can be experimentally tested. 

Our results are in agreement with direct numerical calculations for several corrections [9] (see Tables 3 and 4). The equation (12) can be used to estimate unknown corrections if we know the energy shift. Actually we put in Tables2 3 and 4 the uncertainty of the analytic results found in this way [4], However, one has to remember that the theory of the bound g factor is more complicated than the one for the Lamb shift and sometimes the bound anomaly can be more logarithmic. An example is the order a2(Za)4 the b term contains a logarithm of (Zot) and a non-analytic contribution due to low energy effects, while the contribution to the Lamb shift in this order has no logarithm and completely... 

At low temperature or energy, most degrees of freedom of quark matter are irrelevant due to Pauli blocking. Only quasi-quarks near the Fermi surface are excited. Therefore, relevant modes for quark matter are quasi-quarks near the Fermi surface and the physical properties of quark matter like the symmetry of the ground state are determined by those modes. High density effective theory (HDET) [7, 8] of QCD is an effective theory for such modes to describe the low-energy dynamics of quark matter. 

At low energy, the typical momentum transfer by quarks near the Fermi surface is much smaller than the Fermi momentum. Therefore, similarly to the heavy quark effective theory, we may decompose the momentum of quarks near the Fermi surface as... 

The reflectance, dielectric functions, and refractive indices, together with calculations based on the Drude theory, for the common metal aluminum are shown in Fig. 9.11. Aluminum is described well by the Drude theory except for the weak structure near 1.5 eV, which is caused by bound electrons. The parameters we have chosen to fit the reflectance data, hu>p = 15 eV and hy = 0.6 eV, are appreciably different from those used by Ehrenreich et al. (1963), hup = 12.7 eV and hy = 0.13 eV, to fit the low-energy (hu < 0.2 eV) reflectance of aluminum. This is probably caused by the effects of band transitions and the difference in electron scattering mechanisms at higher energies. The parameters we use reflect our interest in applying the Drude theory in the neighborhood of the plasma frequency. 

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