Quark fields

This Eq. (32) provides the representation of detB as a path integral over Nf constituent quark fields ipf(x)... 

To identify the modes near the Fermi surface, we expand the quark field as (z) = Ee , (5)... 

Here To = y 11/ is proportional to the unit matrix in flavor space. The quark field ip now contains a third component in flavor space, the strange quark, and consequently the mass matrix rh, see Eq. (4), is equally enlarged by the current strange quark mass, ms, which can in general be different from up and down quark masses. This interaction consists of a U(3)l x U(3)ft-syrnmetric 4-point interaction and a 7 Hooft-type 6-point interaction which breaks the UA (1) symmetry. 

Using the mean-field approximation (MFA) with the DCDW configuration, we introduce a new quark field tl>w by the Weinberg transformation [29],... 

In order to perform the functional integrations over the quark fields q and q we use the formalism of bosonisation which is based on the Hubbard-Stratono-vich transformation of the four-fermion interaction. The resulting transformed partition function in terms of bosonic variables will be considered in the mean-field approximation... 

Since the atomic nucleus consists of nucleons which themselves consist of quarks, in principle the wavefunction of the quarks within the nucleons is required in order to determine appropriate equivalent potentials for the interactions between an electron and the nucleons within the nucleus. The models currently available for the calculation of the substructure of the nucleons, however, allow only for an approximate description of the wavefunctions of the quarks (see for instance [74] for a comparison of a few of these models). One may on the other hand introduce nucleon field operators, which replace the quark field operators in the scattering matrix element (equation (66)), and relate the corresponding vector and axial coupling coefficients in the resulting equivalent potential to empirical data. 

The most natural way to enlarge C to include hadrons is to extend the gauge invariance plus spontaneous symmetry breaking prescription to include quark fields q = (u, d, s) in an analogous fashion to the leptons but taking account of the Cabibbo mixing of d and s. 

In this approach V has appeared as a consequence of transforming to quark fields which have definite mass. 

In the SM all hadronic currents are expressed in terms of quark fields f x) where / labels the fiavour. As in Sections 1.2, 16.8 and 18.1, we often require the forward matrix elements of these currents taken between nucleon states. We shall use the quark-parton model to evaluate these in the firame S°°. 

Despite the successes, even with its generalizations, difficulties in thermal field theory remain to be overcome in order to deal with experimental and theoretical demands. In fact, numerous studies, in particular using quantum chromodynamics (A. Smilga, 2001), have been carried out in an attempt to understand, for instance, the quark-gluon plasma at finite temperature and in this common effort, some underlying aspects have been identified. For example, the coupling constants for 7r,a,w and p mesons decrease to zero at a certain critical temperature, which are, respectively, given by = 360 MeV, Tj = 95... 

It is interesting to note that we have calculated the casimir pressure at finite temperature for parallel plates, a square wave-guide and a cubic box. For a fermion field in a cubic box with an edge of 1.0 fm, which is of the order of the nuclear dimensions, the critical temperature is 100 MeV. Such a result will have implications for confinement of quarks in nucleons. However such an analysis will require a realistic calculation, a spherical geometry, with full account of color and flavor degrees of freedom of quarks and gluons. 

Abstract. Low-momentum quark determinant and effective action in the presence of current quark mass and external flavor fields is derived. The results of the calculations of various correlators are briefly presented. We conclude that, this approach is a reliable tool for the hadron physics, especially including strange quarks. 

In the present work we refine the calculations Diow and derive the QCD low-energy effective action not only with an account of current quark masses but also other external V = v + 075 + s + >75 fields, where v = a = 7v and a are vector and axial fields, s... 

A- Also we define quark propagator in the field of single instanton A and external fields V ... 

The main assumption of previous works (D. Diakonov et.al., 1986 D.I. Diakonov et.al., 1996) (see also review (T. Schafer et.al., 1998)) was that at very small m the quark propagator in the single instanton field A may t>e approximated as ... 

We see that B is the extension of Lee-Bardeen s matrix B, taking into account the presence of the external fields V and with an account of the quark current mass m without making expansion over current mass m and also extended to a few flavors case. 

If we had turned off the external fields V and expanded over m keeping only 0(m) term we would have obtained the same quark determinant Detiow given by (C. Lee et.al., 1979). 

In Eq. (37) soft external and a fields, carrying momentum q p l. were assumed. Then, they are present inside of the form-factor F in above mentioned form. If v, a external fields are flavor matrices then form-factor F also becomes matrix Nf x Nf. So, we get the partition function Z[m,V], where W are multi-quark interaction terms in the presence of current quark mass m and external fields V. 

Thus we have treated the chaotic dynamics of the quarkonium in a time periodic field. Using the Chirikov s resonance overlap criterion we obtain estimates for the critical value of the external field strength at which chaotization of the quarkonium motion will occur. The experimental realization of the quarkonium motion under time periodic perturbation could be performed in several cases in laser driven mesons and in quarkonia in the hadronic or quark-gluon matter. 

Sedrakian, D. M., Blaschke, D. (2002). Magnetic field of a neutron star with color superconducting quark matter core. Astrofiz., 45 203-212. 

Neutron stars (NSs) are perhaps the most interesting astronomical objects from the physical point of view. They are associated with a variety of extreme phenomena and matter states for example, magnetic fields beyond the QED vacuum pair-creation limit, supranuclear densities, superfluidity, superconductivity, exotic condensates and deconfined quark matter, etc. 

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