Fermionic matter

We report on a new force that acts on cavities (literally empty regions of space) when they are immersed in a background of non-interacting fermionic matter fields. The interaction follows from the obstructions to the (quantum mechanical) motions of the fermions in the Fermi sea caused by the presence of bubbles or other (heavy) particles immersed in the latter, as, for example, nuclei in the neutron sea in the inner crust of a neutron star. 

This effect resembles the traditional Casimir effect, which describes the attraction between two parallel metallic mirrors in vacuum. Here, however, the fluctuating (bosonic) electromagnetic fields are replaced by fermionic matter fields. Furthermore, the Casimir energy is inferred from the geometry-dependent part of the density of states, and its sign is not fixed, but oscillates according to the relative arrangement and distances of the cavities. 

In the following we will consider the case of matter fields (non-relativistic fermions) located in the space between voids or cavities, such that the matter fields will build up a quantum pressure on the voids. Even if we assume that the matter fields are non-interacting, an effective interaction between the empty regions of space will still arise in the background of the fermionic matter fields, since the cavities - depending on their geometric arrangement - can shield the free movement of the matter modes. 

As simple example, let us consider a fermionic matter in 1+1 dimensions, where non-relativistic fermions are interacting with a gauge field A. The action is in general given as... 

The persistent correlation that recurs between number patterns and physical structures indicates a similarity between the structure of space-time and number. Like numbers and chiral growth, matter has a symmetry-related conjugate counterpart. The mystery about this antimatter is its whereabouts in the universe. By analogy with numbers, the two chiral forms of fermionic matter may be located on opposite sides of an achiral bosonic interface. In the case of numbers this interface is the complex plane, in the physical world it is the vacuum. An equivalent mapping has classical worlds located in the two surfaces and the quantum world, which requires complex formulation, in the interface. 

The last necessary ingredient toward a well-defined and consistent quantum field theory of radiation interacting with a fermionic matter field is the introduction of normal-ordered products of field operators. The necessity for this step is easily realized by consideration of the vacuum expectation value of Gauss law. 

Ceperley D M 1996 Path integral Monte Carlo for fermions Monte Carlo and Molecular Dynamics of Condensed Matter Systems vol 49, ed K Binder and E G Ciccotti (Bologna Italian Physical Society) pp 443-82... 

Stonier uses the example of a hole left behind in an atomic shell after it loses an electron. This hole constitutes a particulate form of information that Stonier calls an in/on, which he adds as a particulate manifestation of information to the two classes of particulate manifestations of matter and energy, namely fermions and bosons. See appendixes A and B in [ston90]. 

Note that the Casimir calculation under the presence of fermionic on-relativistic) matter fields simplifies enormously since the presence of the second scale, the chemical potential p,=h2k2F/2rn or the Fermi momentum kF, provides for a natural UV-cxAoii, Any = p, and kuv = kF- Therefore the Casimir energy for fermions between two impenetrable (parallel) planes at a distance L is simply given as... 

One of the most amazing phenomena in quantum many-particle systems is the formation of quantum condensates. Of particular interest are strongly coupled fermion systems where bound states arise. In the low-density limit, where even-number fermionic bound states can be considered as bosons, Bose-Einstein condensation is expected to occur at low temperatures. The solution of Eq. (6) with = 2/j, gives the onset of pairing, the solution of Eq. (7) with EinP = 4/i the onset of quartetting in (symmetric) nuclear matter. At present, condensates are investigated in systems where the cross-over from Bardeen-Cooper-Schrieffer (BCS) pairing to Bose-Einstein condensation (BEC) can be observed, see [11,12], In these papers, a two-particle state is treated in an uncorrelated medium. Some attempts have been made to include the interaction between correlated states, see [7,13]. 

The color superconducting DFS-phase, which is treated in a four-fermion contact interaction model, is preferred to the homogeneous 2SC state for asymmetries that are typical to matter under /1-equilibrium. 

The effect of thermal pion fluctuations on the specific heat and the neutrino emissivity of neutron stars was discussed in [27, 28] together with other in-medium effects, see also reviews [29, 30], Neutron pair breaking and formation (PBF) neutrino process on the neutral current was studied in [31, 32] for the hadron matter. Also ref. [32] added the proton PBF process in the hadron matter and correlation processes, and ref. [33] included quark PBF processes in quark matter. PBF processes were studied by two different methods with the help of Bogolubov transformation for the fermion wave function [31, 33] and within Schwinger-Kadanoff-Baym-Keldysh formalism for nonequilibrium normal and anomalous fermion Green functions [32, 28, 29],... 

First, there are constraints among the material quantities, which are rather straightforward for ideal quantum fluids. In case of interacting matter one can recall the self-consistent description of the interacting fermions in the 4 dimensional analogy [13], Second, the particle number density in the center, n(r = 0), is a free initial condition, as it was in the 4 dimensional case. Instead of density, we may use energy density, e(r = 0) = 0 as well. 

From BCS theory it is known, that in order to form Cooper pairs at T = 0 in a dense Fermi system, the difference in the chemical potentials of the Fermions to be paired should not exceed the size of the gap. As previous calculations within this type of models have shown [24], there is a critical chemical potential for the occurrence of quark matter pf > 300 MeV and values of the gap in the region A < 150 MeV have been found. Therefore it is natural to consider the problem of the color superconducting (2SC) phase with the assumption, that quark matter is symmetric or very close to being symmetric (pu pd). 

Chemistry is the central science in the sense that it provides the tie between physics on the one hand and biology on the other. The world of physics, seen broadly, covers a wide spectrum. In general, the concerns of physics focus on entities smaller or larger than those of direct interest to chemistry. At the micro level physics unravels the mysteries of the elementary particles, known generally as fermions, which constimte all ordinary matter. Fermions include the quarks and their antiparticles, the antiquarks. There are six kinds of quarks, known as top, bottom, strange, charm,... 

From the thermodynamic standpoint, the basic components of stars can be considered as photons, ions and electrons. The material particle gas (fermions) and the photon gas (bosons) react differently under compression and expansion. Put n photons and n material particles into a box. Let R be the size of the box (i.e. a characteristic dimension or scale factor). The relation between temperature and size is TR = constant for the photons and TR = constant for the particles. This difference of behaviour is very important in the Big Bang theory, for these equations show quite unmistakably that matter cools more quickly than radiation under the effects of expansion. Hence, a universe whose energy density is dominated by radiation cannot remain this way for long, in fact, no longer than 1 million years. 

Due to Heisenberg s uncertainty and Pauli s exclusion principles, the properties of a multifermionic system correspond to fermions being grouped into shells and subshells. The shell structure of the one-particle energy spectrum generates so-called shell effects, at different hierarchical levels (nuclei, atoms, molecules, condensed matter) [1-3]. 

Here, we should mention that there exists an extensive discussion in the literature on the capabilities of spin-DFT regarding, for instance, the question whether the Kohn-Sham spin density has to be equal to the spin density of the fully interacting system of electrons (and in the case of open-shell singlet broken-symmetry (BS) determinants (see below) for binuclear transition-metal clusters this is certainly not the case see Ref. (33) for a more detailed discussion). But the situation is much more subtle and one may basically set up the variational procedure in a Kohn-Sham framework such that the spin density of the Kohn-Sham system of noninteracting fermions represents the true spin density. However, the frame of this review is not sufficient to present all details on this matter (34,35). 

The subject of 0(3) electrodynamics was initiated through the inference of the Bl]> field [11] from the inverse Faraday effect (IFF), which is the magnetization of matter using circularly polarized radiation [11-20]. The phenomenon of radiatively induced fermion resonance (RFR) was first inferred [15] as the resonance equivalent of the IFE. In this section, these two interrelated effects are reviewed and developed using 0(3) electrodynamics. The IFE has been observed several times empirically [15], and the term responsible for RFR was first observed empirically as a magnetization by van der Ziel et al. [37] as being proportional to the conjugate product x A multiplied by the Pauli matrix... 

The experimental or empirical demonstration of RFR is a logical consequence of the detection of a term proportional to by van der Ziel et al. [37], and some experimental details are suggested here. It would be necessary to work initially on the interaction of a fermion beam with an electromagnetic beam. All levels of one fermion theory given in this section could then be tested under conditions that most closely approximate the theory. A successful demonstration of RFR would require careful engineering in the matter of beam interaction. The IFE has been demonstrated at 3.0 GHz by Deschamps et al. [75], and this experiment provides clues as to how to go about detecting RFR. It seems that the simplest demonstration is autoresonance, where the circularly polarized pump frequency (to) is adjusted to be the same as the RFR frequency (a)res) ... 

Just to whet your appetite matter consists of fermions bound together by bosons. 

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. 

Lieb, E. H. and Thirring, W. E. Bound for the kinetic energy of fermions which proves the stability of matter, Phys.Rev.Lett., 35 (1975) 687-689. 

The model which we have developed is called the Fermion Dynamical Symmetry Model (FDSM)11 which is the subject matter of two recent preprints. The FDSM begins with a shell model Hamiltonian in one major valence shell. 

Bernabei, R., et al. 2003. Dark matter search, Riv. Nuovo Cim. 26, 1 Binetruy, P, Girardi, G., Salati, P. 1984. Constraints On A System Of Two Neutral Fermions From Cosmology, Nucl. Phys. B237, 285 Birrell, N. D. Davies, P. C. W., 1982. Quantum Fields in Curved Space (Cambridge Cambridge UniversityPress)... 

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