Quantization of gauge-fields in the fock-schwinger gauge

The gauge conditionx _μ A ^μ =0 produces a theory which is free from Faddeev-Popov ghosts, but whose Green's functions obviously lack translational invariance. We present for the first time a consistent perturbation theory in this gauge. Besdes discussing example howlocal counter-terms in the action suffice for the one-loop renormalization ofS-matrix elements.     

Inelastic 2-prong events in 147 GeV/cπ−p collisions

An SU(3) gauge-field non-topological soliton in three space-dimensions is discussed. Let N be the largest among the magnitudes of eigenvalues of the matrix Σ₁⁸λ_aQ_a, where the Q_a's are the eight conserved charges in the classical SU(3) gauge theory, and the λ_a's the usual 3 × 3 Gell-Mann matrices. We show that stable solitons exist if N > a critical value N_S, and if the ratio between the mass of the SU(3) gauge field and that of a relevant spin-0 field is >√6. Our trial function analysis suggests that, for large N, states with dets (Σ₁⁸λ_aQ_a) ≠ 0 are unstable against fission.     

Ghost-free non-Abelian gauge theory: renormalization and gauge-invariance

Although it has been known for a long time that the special case n^μA_μ = 0 for an axial gauge of a vector field A_μ, characterized by a direction n_μ, is free from the peculiar loop complications inherent in all other known gauges of non-Abelian gauge theories, practical use of this ghost-free gauge has often met with some reserve. The reasons were always difficulties in the development of the theoretical formalism, all of which can be traced back to a singularity at n^μp_μ = 0 where p is some four-momentum. This paper, which is a sequel to an earlier one by one of the authors, is intended to show that within the functional integration formalism a consistent field theory can be developed. Here we first prove the gauge invariance of the renormalized theory, allowing for the presence of an arbitrary number of scalar and fermion fields with spontaneous symmetry breaking. Then it is shown that all on-shell elements for the physical S-matrix between properly selected physical sources are independent of n_μ (gauge invariant) and so are the renormalized masses.     

Fields nonlocal in clifford space

A previously proposed field theory is quantized. The theory contains a parameter having the character of an elementary length. We fix the value of this parameter by scaling it to the weak interaction strength. It is shown that this way negative metric states are confined to a region of the order 10^?15 cm. The resulting quantum theory of interacting fields is Lorentz and gauge invariant, has a unitaryS-matrix, and is convergent.     

Asymptotic states and infrared divergences in non-abelian theories

We give a general definition of a class of asymptotic states in non-abelian gauge theories. We argue, using unitarity, that they give infrared-finite S-matrix elements. We discuss the energy of the soft gluons in these states.     

Representation of osp (2, 2) q (2) andS-matrix of super sine-Gordon theory

We investigate the representations of the osp (2, 2) _q ⁽²⁾ algebra, which leads to theS-matrix of super sine-Gordon theory. TheS-matrix has been derived from supersymmetric conformal field theory with some assumptions. We show that the conjecturedS-matrix can be derived from the representation theory using a correspondence between the representations of osp (1, 2) _q and those of sl(2) _q .     

J/ψ+η′ Production ine + e −-annihilation: A perturbative QCD calculation

The cross section for the reactione ⁺ e ^?→³S₁+¹S₀ is calculated in the framework of perturbative QCD, using the nonrelativistic approximation for the³S₁ and¹S₀ bound states. The model is applied toJ/Ψ plus η,η,η′, andl production. We find extremely small rates in contrast to previous estimates based on vector meson dominance and discuss possible reasons for this difference.     

A minimal gauge inflation model

In this paper, we present a gauge inflation model based on the orbifold M_4×S~1/Z_2 with non-Abelian SU(2) gauge symmetry, which is probably the simplest model in this category. As the inflaton potential is fully radiatively generated exclusively by gauge self-interactions, the model is predictive; thus, it is protected by gauge symmetry itself, without the introduction of any additional matter fields or arbitrary interactions. We show that the model fully agrees with the recent cosmological observations within the controlled perturbative regime of gauge interactions, g4≤1/(2πRMP), with the compactification radius(10 ≤ RMP ≤ 100): the expected magnitude of the curvature perturbation power spectrum and the value of the corresponding spectral index are in perfect agreement with the recent observations. The model also predicts a large fraction of the gravitational waves, negligible nonGaussianity, and a sufficiently high reheating temperature.     

On the energy-momentum tensor in gauge field theories

The energy-momentum tensor in spontaneously broken non-Abelian gauge field theories is studied. The motivation is to show that recent results on the finiteness and gauge independence of S-matrix elements in gauge theories extends to observable amplitudes for transitions in a gravitational field. Path integral methods and dimensional regularization are used throughout. Green's functions Γ_μν^(j)(q; p₁,…,p_j) involving the energy-momentum tensor and j particle fields are proved finite to all orders in perturbation theory to zero and first order in q, and finite to one loop order for general q. Amputated Green's functions of the energy momentum tensor are proved to be gauge independent on mass shell.     

On the renormalization of the charm quartet model

Some aspects of the renormalization program for the charm quartet model are discussed, with special emphasis on the role played by the Cabibbo angle. The cancellation of divergences in the W-quarks and Higgs-quarks sector is examined by explicit calculations at the one-loop level, both in the unitary and 't Hooft-Feyman gauges. The main analysis is based on a renormalization scheme which allows for the most general counter-terms generated by the Yukawa couplings. A second approach, equivalent at the S-matrix level, is briefly discussed. As a byproduct of our work we verify that the standard perturbative analysis leads to the same expressions for the coefficients of the divergent parts in the renormalization of the gauge coupling g₀ as a recent current algebra formulation of the radiative corrections.     

Two-loop free energy for finite temperatureSU(3) gauge theory in a constant external field

A two-loop calculation of the free energy for finite temperatureSU(3) gauge theory in an external fieldA ₀=const is carried out using background Feynman gauge. Nontrivial minima of the free energy are obtained atA ₀{gT forg→0 corresponding to the gauge symmetry breakingSU(3)→U(1)×U(1). Higher order perturbative effects are briefly discussed.     

The 90,92Zrd(p,p′) reactions at Ep = 800 MeV+

Angular distributions of analyzing powers and differential cross sections have been measured for elastic and inelastic scattering of 800 MeV protons from ⁹⁰Zr and ⁹²Zr. The data have been interpreted using both the collective-model distorted-wave Born approximation and the semimicroscopic distorted-wave impulse approximation with the Love and Franey t-matrix. Clear differences in the data for transitions to both the 2⁺₁ and the 4⁺ states in the two nuclei, attributable to differences in the microscopic structures of the states, have been observed. These differences are only partially explained by the semimicroscopic analyses. Interpreting the A_y data with the help of recent data-to-data relations suggests that the free L · S interaction used at 800 MeV is incorrect.     

Statistical reactions with memory and thermalized-nonequilibrated nuclear states

Starting from the Feshbach S-matrix pole expansion we modify the standard statistical model for compound reactions by introducing correlations between fluctuating S-matrix elements with different J (total spin) and π (parity) values. The S-matrix (J, π)-correlations are obtained at the expense of introducing infinitesimally small entrance-exit channel off-diagonal (J, π)-correlations between the random variables of the statistical model. Although later on these correlations are switched off by means of a properly applied limiting procedure, the S-matrix (J, π)-correlations do not vanish and can be strong. The physical origin of the S-matrix (J, π)-correlations resembles the effect of spontaneous symmetry breaking while S-matrix (J, π)-decoherence is due to quantum chaos. Novel reaction mechanism results in the excitation of peculiar nuclear states: The intermediate system is thermalized so that the shape of the spectrum is angle-independent and Maxwellian with angle-independent slope, yet the intermediate nucleus is not equilibrated since the angular distribution is forward-peaked, i.e., memory of the direction of the initial beam is not lost. The existence of thermalized-nonequilibrated nuclear states is supported by data on the 50–100% forward peaking of neutrons in the typically evaporation (1–3.5 MeV) part of the spectrum observed in the ⁹³ N b(n, n′) scattering with E _n = 7 MeV.     

Three-nucleon calculations without the explicit use of two-body potentials

Using as two-nucleon interaction input the ³S₁-³D₁ and ¹S₀ partial waves, the Faddeev equations are solved for the three-nucleon bound state. The ³S₁³D₁T-matrix is calculated from the Reid potential. Avoiding the usual potential fit, the ¹S₀T-matrix is directly continued off-shell and is constructed consistent with the ¹S₀ phase shift of elastic two-nucleon scattering. The off-shell part of the ¹S₀T-matrix is parametrized and with this parametrization the dependence of the three-nucleon bound-state properties is studied. As a result it is found that the binding energy varies only between 6.2 MeV and 6.8 MeV, while the minimum in the charge form factor for electron scattering from ³He lies between 12.9 fm^?2 and 18.7 fm^?2. The larger (smaller) ³He binding energy is accompanied by a ³He charge form factor whose minimum is at larger (smaller) momentum transfers.     

A nonperturbative variational approach to the vacuum structure in quantum chromodynamics

We study the vacuum structure in QCD in a nonperturbative manner using a variational approach with gluon condensates. We show that in Coulomb gauge as the coupling becomes moderately strong, the perturbative vacuum of QCD becomes unstable leading to gluon condensates and a gauge dependent effective mass for the gluons related to the gauge independent value of 〈vac‖G _μν ^a G ^aμν‖vac〉 of Shifmanet al.     

Critical properties of high-spin Ising models on anisotropic lattices

The coordinates of the critical points of spin-S Ising models with coupling constants J and J′ are calculated for 1/2 ≤ S ≤ 13/2. The calculations are performed for several values of S and Δ ≡ J′/J independently by using the phenomenological renormalization-group method or (approximate) self-duality. Numerical results combined with a mean-field analysis show that the critical coupling strength for Δ ～ 1 (weakly anisotropic lattice) is K _c ^(S) (Δ) = K _c ^(S) (1)[1 + a(1 ? Δ)], where a = (d ? 1)/d is independent of S (d is the space dimension). Both free energy and internal energy are determined at the critical points. An extremum of the critical internal energy is found at Δ* ∈ (0, 1). The parameter Δ* can be used as a criterion that separates quasi-isotropic and quasi-one-dimensional regimes (Δ* < Δ ≤ 1 and Δ < Δ*, respectively). The finite-size scaling amplitudes A _s and A _e of the inverse spin-spin and energy-energy correlation lengths are estimated. Calculations show that the amplitudes A _s and A _e are independent of S within the accuracy of the adopted approximations. Moreover, their ratio A _e/A _s is independent of the anisotropy parameter Δ. These results support the Ising universality hypothesis.     

Dual-resonance models

Dual-resonance models are treated both as S-matrix theories and as systems of interacting strings. We show how Veneziano was able to construct a dual four-point amplitude with narrow resonances and rising Regge trajectories. The construction is generalized to the N-point amplitude in the manifestly dual manner suggested by Koba and Nielsen. We develop the operator formalism which exhibits the factorization property of the above amplitude. The related questions of ghost elimination and null states are discussed. Models with extra degrees of freedom and, in particular, the Neveu-Schwarz-Ramond model with spin, are treated. The latter model has a quark-line spectrum of mesons, but it possesses massless vector mesons and fermions. It is shown how the operator formalism is related to a quantized string. The theory of such a string is developed, with particular emphasis on the ghost-free “Coulomb-gauge” quantization. By constructing theories of interacting strings, we reproduce the dual-model S-matrix. A brief account is given of the theory of loops, in which one attempts to improve on the narrow-resonance model in a perturbative manner.     

Structure of 0+ states of 28Si and particle-hole conjugation

Full sd-shell calculations for the 0⁺ states of ²⁸Si have been performed in the SU(3) basis so that the intrinsic deformation of the shell model states can be deduced by inspection. The shell model Hamiltonian is decomposed in a symmetric part H_S and an antisymmetric part H_A with respect to particle-hole conjugation. It is shown that the splitting of prolate and oblate states is due to the spin-orbit part of H_A. The different prediction for ²⁸Si obtained with Kuo and with Preedom-Wildenthal matrix elements can be attributed to the difference in a single parameter: the strength of the spin-orbit part of H_A.     

Absorption and resonance Raman spectroscopy of the 1Bu state of trans‐1,3,5‐hexatriene including vibronic coupling

The vibronic coupling between the first excited S₁ (2¹A_g) and the second excited S₂ (1¹B_u) singlet electronic states in spectroscopy of trans‐1,3,5‐hexatriene molecule is investigated on the basis of a model consisting of two electronic states coupled by two vibrational modes. Employing a perturbation theory that treats the intramolecular couplings in a perturbative manner, the absorption and resonance Raman cross sections and excitation profiles of this molecule are calculated using the time‐correlation function formalism. The non‐Condon corrections are included in evaluation of cross sections. The multidimensional time‐domain integrals that arise in these calculations have been evaluated for the case in which S₀ (1¹A_g) S₂ (1¹B_u) electronic transition takes place between displaced and distorted harmonic potential energy surfaces. The calculated spectra are in good agreement with the experimental ones. Copyright © 2011 John Wiley & Sons, Ltd.