Some remarks on Nelson's stochastic field

An attempt to extend Nelson's stochastic quantization procedure to tensor fields indicates that the results of Guerra et al. on the connection between a euclidean Markov scalar field and a stochastic scalar field fails to hold for tensor fields.     

Renormalization of a quadratic interaction in the Hamiltonian formalism

The method of the dressing transformation is used to perform a mass renormalization of a neutral scalar free field in the Hamiltonian formalism, for arbitrary space dimension. The resulting situation is analyzed by means of a Bogoliubov transformation, and seen to yield the expected results.Laboratoire associé au C.N.R.S.     

Renormalization effects in a field theory of finite nuclei

In case of thep-α system, the Coulomb exchange potential of the resonating group model and of the fish bone optical model are compared with each other. It is seen that the difference between the two approximations arises mainly from the unrealistic shortdistance behaviour of the proton-protone ²/r potential, which has been assumed in both models. In case of the α-¹⁶O system, it is demonstrated that the importance of the Coulomb exchange potential can be very much reduced by an off-shell transformation.     

Renormalization and asymptotic behavior in a finite quantum field theory with shadow states

In this paper we present a study of the renormalization problem in a finite quantum field theory with shadow states for a system of a physical scalar field interacting with a physical fermion field. In order to make the theory finite, two fermion shadow fields are introduced. We observe that the stability criterion of renormalization can not be satisfied simultaneously by both physical fields and shadow fields, if the finiteness of the theory is to be maintained. A physical interpretation of this result is given. Furthermore, we find that the effective complete propagators for large space-like momenta behave like free field propagators without the logarithmic factors observed in the non-abelian gauge theory.     

Renormalization of a quantum field theory model in a curved space-time with torsion

A quantum field theory model that contains interacting non-Abelian gauge fields, scalar fields, and spinor fields is considered in a curved space-time with torsion. The cone-loop counterterms are found. It is shown that the multiplicative renormalization condition requires a nonminimal coupling of the matter with the gravitational field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 94–100, August, 1985.     

Renormalization group equation in a theory with spontaneously broken symmetry and decoupling of heavy scalar particles

Renormalization group equations for light-particle processes are examined in a simple spontaneously broken symmetry theory (SBT) for energy-momentum far below a heavy scalar particle threshold. The results confirm the generalized decoupling theorem for SBT with the introduction of a new effective coupling constant.     

Dirac's equation and a new group of external symmetry

It is shown how the handedness of the massless leptons, and the Poincaré invariance of leptonic interactions, can be based on a new group of external symmetry.     

Renormalization in the theory of a quantized scalar field interacting with a robertson-walker spacetime

We demonstrate the possibility of removing the divergences in the energy-momentum tensor by identifying divergent terms with renormalizations of the coupling constants in the gravitational field equation, modified to include a cosmological term and terms quadratic in the curvature. The model studied is that of a classical Robertson-Walker metric and a quantized minimally coupled neutral scalar field. The theory is constructed first with an ultraviolet cutoff as a phenomenological ansatz. The cutoff is then removed in an attempt to obtain a more fundamental theory, whereupon the question arises of the covariance and uniqueness of the resulting renormalized energy-momentum tensor. In the case of a massless field in a spatially flat universe, an apparent infrared divergence is discussed from the point of view of operational determination of the renormalized coupling constants. In the other cases, although the divergences are successfully accounted for by renormalization, we are left with finite leading terms which do not appear to be identifiable with geometrical tensors; the significance of this result is under investigation. If these anomalous terms are dropped, the renormalized energy-momentum tensor agrees with that defined by adiabatic regularization, provided that the limit of slow time variation taken in that method is generalized to a limit of “spacetime flatness.”     

A grand unified model with Bogolubov's symmetry breaking mechanism

It is shown that E₆ is the minimal group in the E-chain of the Dynkin diagrams which allows the construction of a unified model of elementary particles in the framework of the Bogolubov method for dynamic symmetry breaking. The idea is based on the introduction of a fundamental self-coupled spinor field, the collective modes of which have the properties of gauge and Higgs particles. The hierarchy of fermion masses is discussed.     

Spontaneous symmetry breaking and Higgs' mechanism in the nonsymmetric Kaluza-Klein theory

The nonsymmetric Kaluza-Klein theory unifying Moffat's theory of gravitation, the Yang-Mills' field and the Higgs' fields are constructed in a geometric manner. Spontaneous symmetry breaking, the Higgs' mechanism and mass generation in the theory are discussed. The connection between R₊ invariance (dilatation on the space-time) from Moffat's theory of gravitation and U(1)_F from GUTs, is proposed within the framework of fermion number conservation.     

Green's function approach in the theory of interaction of exciton-polaritons in semiconductors with direct band gaps

The renormalization procedure of perturbation theory is applied to study polariton effects in the optical processes involving photons with energies near that of an exciton: resonant Raman scattering, resonant electronic Raman scattering, and resonant high — order optical harmonic generation. To demonstrate the general method and the computation technique we consider in this work a simple model with the following properties: (a) The semiconductor has a direct band gap with allowed electrical dipole transition and with nondegenerate valence and conduction bands. (b) We consider only the photons in a definite polarization state; they are in resonance with one bound state of an electron-hole pair, and we take into account only the transition between this exciton state and the photon in the given polarization state. We work in the framework of the Green's function approach and we shall see that this approach provides for the inclusion of damping effects in a relatively rigorous manner.     

Deviations from Ohm's law for a metal at high current densities

High current pulses were generated in thin copper wires and the specific resistance for different current densities as the same temperature was determined. The measured values show an increase of resistance with current density reaching nearly a factor 3 at 1.6 × 10⁸A/cm²     

Multipole sum rules and giant resonances with skyrme's interaction

Energy-weighted and inverse energy-weighted (polarizability) sum rules are calculated with Skyrme's effective interaction. The electric dipole, and the isoscalar and isoveetor monopole and quadrupole excitations are considered. A simple analytic treatment of stiffness parameters and giant resonances is given using the Thomas-Fermi approximation. Results are compared with experiment and with other calculations based on RPA.     

Scalar quantum field theory with a complex cubic interaction

In this Letter it is shown that an i phi(3) quantum field theory is a physically acceptable model because the spectrum is positive and the theory is unitary. The demonstration rests on the perturbative construction of a linear operator C, which is needed to define the Hilbert space inner product. The C operator is a new, time-independent observable in PT-symmetric quantum field theory.     

Deviations from Ohm's law for a metal at high current densities?

The current-voltage characteristics of copper was measured up to current densities of 2 × 10⁹ A/cm² at 300 K. Joule heating was avoided by using pulses with a duration of less than 500 ps. Within the experimental accuracy of 1.5% no deviation from Ohm's law was found. Our results are in contrast to a recent publication of Jäger et al.     

Features of electron-phonon interaction in nanotubes with chiral symmetry placed in a magnetic field

The interaction of electrons with acoustic phonons is considered in a nanotube with chiral symmetry placed in a magnetic field parallel to the nanotube axis. It is shown that in such a system, the electronic energy spectrum is not invariant under electron wavevector reversal and, therefore, the electron-phonon interaction is different for identical phonons with oppositely directed wavevectors. This phenomenon leads to the occurrence of an electromotive force during spatially homogeneous heating of an electron gas and to the presence of a term quadratic in current in the current-voltage characteristic of a nanotube.