Oscillatory phenomena in cold matter with four-fermion interaction

The phase structure of the Nambu-Jona-Lasinio model in space-time with the topology R ³×S ¹ (spatial coordinate compactified) and chemical potential μ is investigated. Phase portraits of the model are constructed in the μλ plane (λ=1/L, where L is the size of the dimension S ¹) in the case with periodic boundary conditions. It is shown here for the first time that there exist in the model an infinite number of both chirally symmetric massless phases and asymmetric massive phases, between which (as a rule) transitions are second-order. Because of this phase structure, changes in the parameter λ induce oscillations in the particle density, fermion mass, and the critical curve on which chiral invariance is restored. Zh. éksp. Teor. Fiz. 114, 418–436 (August 1998)     

Phase structure of quark systems in models with four-fermion interaction

The features of a hot and dense gas of quarks that are considered as quasiparticles of a model Hamiltonian with four-fermion interaction are studied. Adapted to the Nambu-Jona-Lasinio model, this approach allows us to accommodate a phase transition similar to the nuclear liquid-gas one. Arguments are given in favor of the statement that a plausible scenario of (partial) chiral-symmetry restoration (even at zero temperature) in such a system could be a mixed phase of the vacuum and normal baryonic matter. The properties of the transition layer separating the two media in question are also discussed.     

Relativistic three-body recombination with the QED vacuum

Electron-positron pair annihilation into a single photon is studied when a second free electron is present. Focussing on the relativistic regime, we show that the photon emitted in the three-lepton interaction may exhibit distinct angular distributions and polarization properties. Moreover, the process can dominate over two-photon annihilation in relativistic electron-positron plasmas of few-MeV temperature. An analogy with three-body recombination of electrons with ions is drawn.     

Gravitational four-fermion interaction on the Planck scale

The four-fermion gravitational interaction is induced by torsion, and gets essential on the Planck scale. On this scale, the axial–axial contribution dominates strongly the discussed interaction. The energy–momentum tensor, generated by this contribution, is analyzed, as well as stability of the problem with respect to compression. The trace of this energy–momentum tensor can be negative.     

Investigating the QED vacuum with ultra-intense laser fields

In view of the increasingly stronger available laser fields it is becoming feasible to employ them to probe the nonlinear dielectric properties of the vacuum as predicted by quantum electrodynamics (QED) and to test QED in the presence of intense laser beams. First, we discuss vacuum-polarization effects that arise in the collision of a high-energy proton beam with a strong laser field. In addition, we investigate the process of light-by-light diffraction mediated by the virtual electron-positrons of the vacuum. A strong laser beam “diffracts” a probe laser field due to vacuum polarization effects, and changes its polarization. This change of the polarization is shown to be in principle measurable. Also, the possibility of generating harmonics by exploiting vacuum-polarization effects in the collision in vacuum of two ultra-strong laser beams is discussed. Moreover, when two strong parallel laser beams collide with a probe electromagnetic field, each photon of the probe may interact through the “polarized” quantum vacuum with the photons of the other two fields. Analogously to “ordinary” double-slit set-ups involving matter, the vacuum-scattered probe photons produce a diffraction pattern, which is the envisaged observable to measure the quantum interaction between the probe and strong field photons. We have shown that the diffraction pattern becomes visible in a few operating hours, if the strong fields have an intensity exceeding 10²⁴W/cm².     

QCD corrections to QED vacuum polarization

We compute QCD corrections to QED calculations for vacuum polarization in background magnetic fields. Formally, the diagram for virtual eē loops is identical to the one for virtual qq̄ loops. However, due to confinement, or to the growth of α_s as p² decreases, a direct calculation of the diagram is not allowed. At large p² we consider the virtual qq̄ diagram, in the intermediate region we discuss the role of the contribution of quark condensates 〈qq̄〉 and at the low-energy limit we consider the π⁰, as well as charged pion π⁺π^- loops. Although these effects seem to be out of the measurement accuracy of photon–photon laboratory experiments, they may be relevant for γ-ray burst propagation. In particular, for emissions from the center of the galaxy (8.5 kpc), we show that mixing between the neutral pseudo-scalar pion π₀ and photons renders a deviation from the power-law spectrum in the TeV range. For scalar quark condensates 〈qq̄〉 and virtual qq̄ loops are relevant only for very high radiation density ∼300 MeV/fm³ and very strong magnetic fields of order ∼10¹4 T. PACS 12.20.Ds; 14.40.-n; 12.38.Aw; 14.65.Bt     

Near QED regime of laser interaction with overdense plasmas

Interaction of laser plulses with intensities up to 10²⁵?W/cm² with overdense plasma targets is investigated via three-dimensional particle-in-cell simulations. At these intensities, radiation of electrons in the laser field becomes important. Electrons transfer a significant fraction of their energy to γ-photons and obtain strong feedbacks due to radiation reaction (RR) force. The RR effect on the distribution of laser energies among three main species: electrons, ions and photons is studied. The RR and electron-positron pair creation are implemented by a QED model. As the laser intensity inreases, the ratio of laser energy coupled to electrons drops while the one for γ-photons reaches up to 35%. Two distinctive plasma density regimes of the high-density carbon target and low-density solid hydrogen target are identified from the laser energy partitions and angular distributions of photons. The power-laws of absorption efficiency versus laser intensity and the transition of photon divergence are revealed. These show enhanced generation of γ-photon beams with improved collimation in the relativistically transparent regime. A new effect of transverse trapping of electrons inside the laser field caused by the RR force is observed: electrons can be unexpectedly confined by the intense laser field when the RR force is comparable to the Lorentz force. Finally, the RR effect and different regions of photon emission in laser-foil interactions are clarified.     

Effective potential for the four-fermion interaction in topologically non-trivial spaces

We consider the influence of the space-time topology on the formation of a fermion condensate in a theory with a four-fermion interaction. We study the dependence of the behavior of the effective potential on the magnitude of the fermion condensate ¯ and find the dependence of the magnitude ¯ on the periodicity length of the wave functions in space-time with the topology R₁ × R₁ × S₁.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 5–8, March, 1988.     

Gravitational collapse with decaying vacuum energy

The effect of dark energy on the end state of spherical radiation collapse is considered within the context of the cosmic censorship hypothesis. It is found that it is possible to have both black holes as well as naked singularities.     

Dynamical dark energy with a constant vacuum energy density

We present a holographic dark-energy model in which the Newton constant GN$G_N$ scales in such a way as to render the vacuum energy density a true constant. Nevertheless, the model acts as a dynamical dark-energy model since the scaling of GN$G_N$ goes at the expense of deviation of concentration of dark-matter particles from its canonical form and/or of promotion of their mass to a time-dependent quantity, thereby making the effective equation of state (EOS) variable and different from −1 at the present epoch. Thus the model has a potential to naturally underpin Dirac's suggestion for explaining the large-number hypothesis, which demands a dynamical GN$G_N$ along with the creation of matter in the universe. We show that with the aid of observational bounds on the variation of the gravitational coupling, the effective-field theory IR cutoff can be strongly restricted, being always closer to the future event horizon than to the Hubble distance. As for the observational side, the effective EOS restricted by observation can be made arbitrary close to −1, and therefore the present model can be considered as a “minimal” dynamical dark-energy scenario. In addition, for nonzero but small curvature (|Ω_k0|?0.003)$(|{\Omega }_{k0}|?0.003)$, the model easily accommodates a transition across the phantom line for redshifts z?0.2$z?0.2$, as mildly favored by the data. A thermodynamic aspect of the scenario is also discussed.     

Weak four-fermion interaction in terms of SU(3) invariants. II

A lepton octet is constructed by analogy with the baryon octet by the substitution p⁺N ₁e⁺,⁺₁ é⁺,^-₂^-, ^- N ₂^-, where ₁, ₂,N ₁,N ₂ are arbitrary constants. The neutral components are replaced by a linear sum of the electron and muon neutrinos with arbitrary coefficients. The constants are determined from the system of general conditions (normalization, absence of crossed terms of the type ( etc.). As a result, the lepton octet is determined to within a single constant, and this is shown to be identical with the Cabibbo angle. Calculations are also made of the weak decays of baryons of the octet in the case of both charged and neutral currents. In the case of charged currents, the results agree with Cabibbo's theory. Calculations are also made of the lepton-lepton weak interactions and the ratios of the corresponding constants are determined. The ratios are in qualitative agreement with the existing experimental data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 51–56, January, 1976.     

Confinement and vacuum structure in compact QED on the lattice

Using an effective action and assuming that the physical ground state has no structure, we demonstrate that the spectrum of the compact U(1) gauge model has massless (vector and scalar) bosons.     

Composite antisymmetric-tensor Nambu-Goldstone bosons in a four-fermion interaction model and the Higgs mechanism

Starting from the Fierz transform of the two-flavour 't Hooft interaction (a four-fermion Lagrangian with antisymmetric Lorentz tensor interaction terms augmented by an NJL type Lorentz scalar interaction responsible for dynamical symmetry breaking and quark mass generation), we show that: (1) antisymmetric tensor Nambu-Goldstone bosons appear provided that the scalar and tensor couplings stand in the proportion of two to one, which ratio appears naturally in the Fierz transform of the two-flavour 't Hooft interaction; (2) non-Abelian vector gauge bosons coupled to this system acquire a non-zero mass. Axial-vector fields do not mix with antisymmetric tensor fields, so there is no mass shift there. Received: 3 September 1999 / Revised Version: 3 November 1999 / Published online: 6 April 2000     

Uncertainties in the hadronic contribution to the QED vacuum polarization

We describe an updated evaluation of the hadronic contribution to the QED vacuum polarization. It is obtained from a dispersion integral over the measured cross section ofe ⁺ e ^?→hadrons.     

The vacuum and lightcone quantization of interaction Hamiltonians

Let denote the conformally invariant neutral free scalar field on ×S ⁿ. The naive lightcone Hamiltonian for a ^p interaction is given by c^p, where C denotes a lightcone in ×S ⁿ, and the Wick power is relative to the free vacuum. We show that this sesquilinear form annihilates the free vacuum if n3 is odd, p>2, and p(n–1)0 mod 4.