Bose-Einstein-condensed gases with arbitrary strong interactions

Bose-condensed gases are considered with an effective interaction strength varying in the whole range of the values between zero and infinity. The consideration is based on the usage of a representative statistical ensemble for Bose systems with broken global gauge symmetry. Practical calculations are illustrated for a uniform Bose gas at zero temperature, employing a self-consistent mean-field theory, which is both conserving and gapless.Comment: Latex file, 23 pages, 4 figure

Non-perturbative solutions in the electro-weak theory with tˉt\bar t t condensate and the tt-quark mass

We apply Bogoliubov compensation principle to the gauge electro-weak interaction to demonstrate a spontaneous generation of anomalous three-boson gauge invariant effective interaction. The non-trivial solution of compensation equations uniquely defines the form-factor of the anomalous interaction and parameters of the theory including value of gauge electro-weak coupling $g(M_W^2)$ in satisfactory agreement with its experimental value. A possibility of spontaneous generation of effective four-fermion interaction of heavy quarks is also demonstrated. This interaction defines an equation for a scalar bound state of heavy quarks which serve as a substitute for the elementary scalar Higgs doublet. As a result we calculate the $t$-quark mass $m_t\,=\,177\,GeV$ in satisfactory agreement with the experimental value. The results strongly support idea of $\bar t\,t$ condensate as a source of the electro-weak symmetry breaking.Comment: 16 pages, 5 figures. arXiv admin note: substantial overlap with arXiv:1103.395

CDF Wjj anomaly as a non-perturbative effect of the electro-weak interaction

The recently reported CDF excess at $120\,-\, 160\,GeV$ in invariant mass distribution of jet pairs accompanying $W$-boson is tentatively interpreted as a bound state of two $W$ decaying to quark-anti-quark pair. Non-perturbative effects of EW interaction obtained by application of Bogoliubov compensation approach lead to such bound state due to existence of anomalous three-boson gauge-invariant effective interaction. The application of this scheme gives satisfactory agreement with existing data without any adjusting parameter but the bound state mass $145\,GeV$.Comment: 5 pages, 2 figure

BCS approximation to the effective vector vertex of superfluid fermions

We examine the effective interaction of nonrelativistic fermions with an external vector field in superfluid systems. In contrast to the complicated vertex equation, usually used in this case, we apply the approach which does not employ an explicit form of the pairing interaction. This allows to obtain a simple analytic expression for the vertex function only in terms of the order parameter and other macroscopic parameters of the system. We use this effective vertex to analyze the linear response function of the superfluid medium at finite temperatures. At the time-like momentum transfer, the imaginary part of the response function is found to be proportional to the fourth power of small Fermi velocity, i.e. the energy losses through vector currents are strongly suppressed. As an application, we calculate the neutrino energy losses through neutral weak currents caused by the pair recombination in the superfluid neutron matter at temperatures lower than the critical one for S-wave pairing. This approach confirms a strong suppression of the neutrino energy losses as predicted in Ref.[4].Comment: 19 pages, no figure

Coupling running through the Looking-Glass of dimensional Reduction

The dimensional reduction, in a form of transition from four to two dimensions, was used in the 90s in a context of HE Regge scattering. Recently, it got a new impetus in quantum gravity where it opens the way to renormalizability and finite short-distance behavior. We consider a QFT model $g\,\varphi^4\,$ with running coupling defined in both the two domains of different dimensionality; the \gbar(Q^2)\, evolutions being duly conjugated at the reduction scale $\,Q\sim M.$ Beyond this scale, in the deep UV 2-dim region, the running coupling does not increase any more. Instead, it {\it slightly decreases} and tends to a finite value \gbar_2(\infty) \,< \, \gbar_2(M^2)\, from above. As a result, the global evolution picture looks quite peculiar and can propose a base for the modified scenario of gauge couplings behavior with UV fixed points provided by dimensional reduction instead of leptoquarks.Comment: 8 pages, 4 figures,Version to match the one which (besides the Appendix) will appear in "Particles and Nuclei (PEPAN), Letters", v.7, No 6(162) 2010 pp 625-631. Slightly edited, one more reference and related numerical estimate adde

String Picture of Bose-Einstein Condensation

A nonrelativistic Bose gas is represented as a grand-canonical ensemble of fluctuating closed spacetime strings of arbitrary shape and length. The loops are characterized by their string tension and the number of times they wind around the imaginary time axis. At the temperature where Bose-Einstein condensation sets in, the string tension, being determined by the chemical potential, vanishes, the system becomes critical, and the strings proliferate. A comparison with Feynman's description in terms of rings of cyclicly permuted bosons shows that the winding number of a loop corresponds to the number of particles contained in a ring.Comment: 13 pages, 6 figures; references adde

Analyticity of the Scattering Amplitude, Causality and High-Energy Bounds in Quantum Field Theory on Noncommutative Space-Time

In the framework of quantum field theory (QFT) on noncommutative (NC) space-time with the symmetry group $O(1,1)\times SO(2)$, we prove that the Jost-Lehmann-Dyson representation, based on the causality condition taken in connection with this symmetry, leads to the mere impossibility of drawing any conclusion on the analyticity of the $2\to 2$-scattering amplitude in $\cos\Theta$, $\Theta$ being the scattering angle. Discussions on the possible ways of obtaining high-energy bounds analogous to the Froissart-Martin bound on the total cross-section are also presented.Comment: 25 page

Bogoliubov theory of Feshbach molecules in the BEC-BCS crossover

We present the Bogoliubov theory for the Bose-Einstein condensation of Feshbach molecules in a balanced Fermi mixture. Because the Bogoliubov theory includes (Gaussian) fluctuations, we can in this manner accurately incorporate both the two-body and many-body aspects of the BEC-BCS crossover that occurs near a Feshbach resonance. We apply the theory in particular to the very broad Feshbach resonance in atomic Li-6 at a magnetic field of B_0 = 834 G and find good agreement with experiments in that case. The BEC-BCS crossover for more narrow Feshbach resonances is also discussed.Comment: 13 pages of RevTex and 12 Figures. Submitted for publication in Physical review

Exactness of the Bogoliubov approximation in random external potentials

We investigate the validity of the Bogoliubov c-number approximation in the case of interacting Bose-gas in a \textit{homogeneous random} media. To take into account the possible occurence of type III generalized Bose-Einstein condensation (i.e. the occurrence of condensation in an infinitesimal band of low kinetic energy modes without macroscopic occupation of any of them) we generalize the c-number substitution procedure to this band of modes with low momentum. We show that, as in the case of the one-mode condensation for translation-invariant interacting systems, this procedure has no effect on the exact value of the pressure in the thermodynamic limit, assuming that the c-numbers are chosen according to a suitable variational principle. We then discuss the relation between these c-numbers and the (total) density of the condensate