The phase structure of Einstein–Cartan theory

In the Einstein–Cartan theory of torsion-free gravity coupling to massless fermions, the four-fermion interaction is induced and its strength is a function of the gravitational and gauge couplings, as well as the Immirzi parameter. We study the dynamics of the four-fermion interaction to determine whether effective bilinear terms of massive fermion fields are generated. Calculating one-particle-irreducible two-point functions of fermion fields, we identify three different phases and two critical points for phase transitions characterized by the strength of four-fermion interaction: (1) chiral symmetric phase for massive fermions in strong coupling regime; (2) chiral symmetric broken phase for massive fermions in intermediate coupling regime; (3) chiral symmetric phase for massless fermions in weak coupling regime. We discuss the scaling-invariant region for an effective theory of massive fermions coupled to torsion-free gravity in the low-energy limit.     

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.     

Gravitational interaction in a model of nonlinear spinor theory with derivatives of the fundamental fields

To eliminate the difficulties that arise when particles of high spin (J 2) are treated in nonlinear spinor field theory, it is proposed to include terms with derivatives of the fundamental fields in the self-interaction Lagrangian of the subparticles. It is shown that with this generalization the four-fermion model of nonlinear spinor theory describes the gravitational interaction of subparticles in the approximation of single-graviton exchange. A relation between the gravitational constant and the parameters of the model is found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 79–85, August, 1977.I thank D. D. Ivanenko for a helpful discussion of this work.     

Tests of the standard model and constraints on new physics from measurements of fermion-pair production at 189 GeV at LEP

Cross-sections and angular distributions for hadronic and lepton pair final states in collisions at a centre-of-mass energy near 189 GeV, measured with the OPAL detector at LEP, are presented and compared with the predictions of the Standard Model. The results are used to measure the energy dependence of the electromagnetic coupling constant , and to place limits on new physics as described by four-fermion contact interactions or by the exchange of a new heavy particle such as a sneutrino in supersymmetric theories with R-parity violation. A search for the indirect effects of the gravitational interaction in extra dimensions on the and final states is also presented. Received: 9 July 1999 / Published online: 17 February 2000     

Four-fermion interaction from torsion as dark energy

The observed small, positive cosmological constant may originate from a four-fermion interaction generated by the spin-torsion coupling in the Einstein–Cartan–Sciama–Kibble gravity if the fermions are condensing. In particular, such a condensation occurs for quark fields during the quark-gluon/hadron phase transition in the early Universe. We study how the torsion-induced four-fermion interaction is affected by adding two terms to the Dirac Lagrangian density: the parity-violating pseudoscalar density dual to the curvature tensor and a spinor-bilinear scalar density which measures the nonminimal coupling of fermions to torsion.     

Some special features in the filling of the Fermi sphere with quark quasiparticles

The filling of the Fermi sphere with quarks treated as quasiparticles of the model Hamiltonian for four-fermion interaction is studied.     

Induced current and transmission through the barrier in the four-fermion model in 2 + 1 dimensions

A three-dimensional theoretical model with compactification of the third dimension in the presence of a four-fermion interaction under the A ₃ external gauge field, where the mass was generated in a two-dimensional brane, has been considered. In the framework of this model the appearance of an induced current was predicted. The induced current was obtained as the function of the flux of Aharonov-Bohm field. The resulting expression oscillates with frequency, depending on the value of the flux. In the absence of compactification, the transmission coefficient through the delta-shaped barrier that was formed by the four-fermion interaction was obtained.     

On the spectrum of excitations in some strong coupling gauge models

The spectrum of spinless excitations in (3+1)-dimensional ladder QED with additional four-fermion interaction and in (2+1)-dimensional QED is considered.     

Fermion Self-Energy and Chiral Symmetry Breaking from Four-Fermion and Gauge Interactions

The exact analytic solutions of the linearized Schwinger-Dyson equation of fermion self-energy are used to obtain the effective four-fermion and gauge coupling criticality curves for dynamical chiral symmetry breaking. The results show that when the zero-momentum gauge coupling a(0) < a₀(0), the critical gauge coupling in the pure gauge interaction case, the minimal critical four-fermion coupling β_min is always nonzero and positive and will go up as the a(0) decreases. The use of the exact solutions also allows us to make quite definite estimations of the momentum scales where chiral symmetry breaking would happen if the values of an infrared parameter ξ are given separately.     

The ground state and the thermodynamics of an extended BCS model of superconductivity

The thermodynamics of an extended BCS model of superconductivity is investigated. A physical system is described by a Hamiltonian containing the BCS interaction and an attractive four-fermion interaction. The four-fermion potential is caused by attractions between Cooper pairs mediated by the phonon field. The weakness of this potential allows the use of perturbation theory. The perturbation expansion was restricted to the first order because in the ground state the second order terms are not larger than 0.5 percent of first order correction for parameters used for calculations. The BCS Hamiltonian is an unperturbed one. The ground state and the thermal properties are examined. As a result the jump in the specific heat is higher than that in the BCS case. Moreover, the squared critical field is larger than the corresponding one in the BCS theory. Additionally, we show connections with the Bogolyubov's mean field approach used earlier in order to investigate general physical consequences of the model.     

Fine splitting in the charmonium spectrum with a channel coupling effect

We study the fine splitting in the charmomium spectrum in the quark model with the channel coupling effect, including DD, DD^*, D^*D^* and D_sD_s, D_sD_s^*, D_s^*D_s^* channels. The interaction for channel coupling is constructed from the current-current Lagrangian related to the color confinement and the one-gluon exchange potentials. By adopting the massive gluon propagator from the lattice calculation in the nonperturbative region, the coupling interaction is further simplified to four-fermion interaction. The numerical calculation still prefers the assignment 1⁺⁺ of X(3872).     

The three-flavor LOFF phase of QCD

We explore the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase of QCD with three flavors, using the Ginzburg-Landau expansion of the free energy, and the NJL pointlike four-fermion interaction, with the quantum numbers of single-gluon exchange. The text was submitted by the author in English.     

Solution of the SU(N) massless thirring model

In the present work a method is proposed of constructing the eigenvectors and finding the quantum numbers of SU(N) symmetric massless theories with four-fermion interaction for an arbitrary value of N.     

A Dynamical Mapping Method in Nonrelativistic Models of Quantum Field Theory

Abstract

Exact solutions of Heisenberg equations and two-particle eigenvalue problems for the nonrelativistic four-fermion interaction and N, Θ model are obtained in the framework of a dynamical mapping method. Equivalence of different dynamical mappings is shown.     

A fixed point for quantum gravity

Using the 1/N expansion a fixed point of the renormalization group is found for quantized gravitational theories which is non-trivial in all dimensions, d, including four. Using the fixed point it is shown how Einstein's theory can be renormalized for 3<d<4. In four dimensions the pure Einstein theory does not exist, but the R + C_μναβ² theory does. It is shown how gravitational theories whose quantum lagrangians are scale invariant may be renormalized such that the scale invariance is broken only by the choice of the critical renormalization group trajectory. A comparison is made with the renormalization of four-fermion and Yukawa theories in 4?? dimensions which suggests that quantum gravity might exist in four dimensions even if those theories do not.     

Quantization of relativistic systems with constraints

The general dynamical system with constraints is quantized, and the S-matrix is constructed in the most general class of gauges including relativistic ones. In the case when constraints do not form a group a new type of additional diagrams arises securing unitarity of the theory: the four-fermion interaction of ghost fields.     

“Fine-tuning” renormalization and associated constants in a nonrelativistic four-fermion model

Exact solutions of a two-particle eigenvalue problem are obtained for a four-fermion contact interaction. Composite Goldstone modes are found. A relationship, is found between the renormalization procedure and the construction of self-adjoint solutions. Irkutsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 62–66, July, 1997.     

Weak interactions of a light gravitino: A lower limit on the gravitino mass from the decay ψ→gravitino + antiphotino

The massive gravitino of spontaneously-broken locally supersymmetric theories may well be very light, leading to a mixing between weak and gravitational interactions. Particularly interesting is the photon coupling to a gravitino-antiphotino pair, with a vertex factor ($\text{κ/m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext><mtext>\surd 6</mtext>}}\text{) γ}{}^{\mathrm{\mu }}\text{q}{}^2$: a one-photon exchange with ordinary fermions is equivalent to a local four-fermion interaction. From the upper limit on the decay ψ → gravitino + antiphotino we get a lower limit ～ 10^?8 eV/c² on the gravitino mass.