Quark spin

Of course, realistically, in addition to the spin of the electrons, the complexity origin of the magnetic spin can be from the motion of either electrons or nuclei, where the spin torque combinations totally can be treated by the equations of motion of angular momentums augmented by the ad hoc nuclear spin or more fundamentally the quark spin with the non-Abelian gauge, which were all formulated in the preceding papers. ... 

The classic example is the N resonance A(1238) with spin and isospin It thus requires all quark spins and isospins pointing in the same direction, and is completely symmetric, e.g. u u u where... 

Our example deals with quarks of the third color in a phase composed only of up and down quarks. As only quarks of a single color are involved, the pairing must take place in a channel which is symmetric in color. Assuming s-wave condensation in an isospin-singlet channel, a possible candidate is a spin-1 condensate [8], We consider the condensate... 

Our analysis is, however, not complete in any respect. For instance, as the large difference in Fermi momenta renders the BCS-type condensation in the classical 2SC phase difficult, it seems to be worthwhile to consider other possibilities. Among others we thereby think of a crystalline phase, deformed Fermi surfaces [32, 35], spin-1 pairing [20] or the gapless 2SC [33, 34] or CFL phase [60], We conclude that whether quark matter exists in hybrid or... 

CSC) is complete in the sense that the diquark condensation produces a gap for quarks of all three colors and flavors. The values of the gap are of the same order of magnitude for 2SC and CFL phases, whereas relations between critical temperature and the gap might be different, Tc 0.57A for 2SC and Tc OJA for CFL phase [9], There are also another possibilities, e.g., of pairing in the spin-one channel, for which the pairing gap proves to be small A < 1 MeV, see [9],... 

In our scenario, we consider a purely hadronic star whose central pressure is increasing due to spin-down or due to mass accretion, e.g., from the material left by the supernova explosion (fallback disc), from a companion star or from the interstellar medium. As the central pressure exceeds the threshold value Pq at static transition point, a virtual drop of quark matter in the Q -phase can be formed in the central region of the star. As soon as a real drop of Q -matter is formed, it will grow very rapidly and the original Hadronic Star will be converted to and Hybrid Star or to a Strange Star, depending on the detail of... 

To summarize, in the present scenario pure hadronic stars having a central pressure larger than the static transition pressure for the formation of the Q -phase are metastable to the decay (conversion) to a more compact stellar configuration in which deconfined quark matter is present (i. e., HyS or SS). These metastable HS have a mean-life time which is related to the nucleation time to form the first critical-size drop of deconfined matter in their interior (the actual mean-life time of the HS will depend on the mass accretion or on the spin-down rate which modifies the nucleation time via an explicit time dependence of the stellar central pressure). We define as critical mass Mcr of the metastable HS, the value of the gravitational mass for which the nucleation time is equal to one year Mcr = Miis t = lyr). Pure hadronic stars with Mh > Mcr are very unlikely to be observed. Mcr plays the role of an effective maximum mass for the hadronic branch of compact stars. While the Oppenheimer-Volkov maximum mass Mhs,max (Oppenheimer Volkov 1939) is determined by the overall stiffness of the EOS for hadronic matter, the value of Mcr will depend in addition on the bulk properties of the EOS for quark matter and on the properties at the interface between the confined and deconfined phases of matter (e.g., the surface tension a). 

A brief review of the complexities to which the quark theory is addressed is in order. Particles which can interact via the strong nuclear force arc called hadrons. Hadrons can be divided into two main classes—the mesous (with baryon number zero) and the baryons (with nonzero baryon number). Within each of the classes there are small subclasses. The subclass of baryons which has been known ihe longest consists of those particles with spin j and even parity. The members of this class are the proton, the neutron, the A0 hyperon, the three hyperons and the two 3 hyperons. There are no baryons with spin 4 and even parity (or, to the usual notation, Jp = i+). The next family of baryons has ten members, each with Jp = l+. The mesons can be grouped into similar families. One of the first successes of the quark model was to explain just why there should be eight baryons with Jp = 1, ten with 1, etc., and why the various members of these families have the particular quantum numbers observed. 

The initial quark model was formulated to explain the diversity of the hadrons and not to explicitly describe the internal structure of any particle. It was inevitable, however, that with further research there w as a tendency to identify new findings with the hypothetical quarks. A number ofproperties of the partons, such as their intrinsic spin angular momentum, have been measured and have proved to be consistent with the predictions of the quark model. 

As well as binding three quarks (antiquarks) together to make baryons (anti-baryons), the nuclear or strong interaction can bind a quark and an antiquark to form unstable particles called mesons (q, q). The it+ and it- mesons (ud, du) are of special importance in nuclear science. The quark/antiquark pairs in the it mesons couple to have zero spin, and thus these mesons are bosons. In fact, all mesons have integer spins and are thus bosons. 

The basic building blocks of the theory are Heisenberg operators (x) which create and destroy respectively, particles of type m at the space-time point x = x, (x. For the purposes of chemistry we can take the index nzs>e for electrons and a for nuclei only. Of course when energies are much larger than chemical energies, nuclei appear to be composite particles, and we must then introduce fields for their constituents (quarks, rishons). We shall not make any explicit reference to the spins carried by these fields beyond noting that odd-integral spins require fermi statistics, so that for fermi fields we have canonical anticommutation relations (CARS)... 

This technique becomes problematic when the particles touch—for example, for the constituents of atomic nuclei. Already, spin forced us to consider quantization without potentials. Many other strange quantum numbers have been posited, with no help from continuum mathematics. Perturbation expansions become funny, since the interaction is no longer smaller than some overriding field. Nucleon-nucleon potentials are discussed in terms of pion exchange, and may also be discussed in terms of quark-gluon interactions. 

The three quark color states are restricted to the color singlet, 1=1, which together with the fermion antisymmetry principle leads to requirement that the flavor-ordinary spin space must be totally symmetric i. e., I I I I This, in turn, leads to the following relationships between the flavor space and the ordinary spin space ... 

Particles with antisymmetric wave function are called fermions - they have to obey the Pauli exclusion principle. Apart from the familiar electron, proton and neutron, these include the neutrinos, the quarks (from which protons and neutrons are made), as well as some atoms like helium-3. All fermions possess "half-integer spin", meaning that they possess an intrinsic angular momentum whose value is hbar = li/2 pi (Planck s constant divided by 27i) times a half-integer (1/2, 3/2, 5/2, etc ). In the theory of quantum mechanics, fermions are described by "antisymmetric states", which are explained in greater detail in the article on identical particles. 

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