The Continual Approach in the Yang-Mills Theory in the External Non-Abelian Field

The theory of Yang-Mills field in interaction with matter fields is considered in the presence of external gauge field. A closed expression for the generating functional of the Green functions is obtained, and a detailed analysis of the Green functions of the scalar, spinor, ghost and Yang-Mills fields is performed. The path-integral solution for all these Green functions is obtained, which includes the functional averaging over the classical trajectories in the space of commuting and anticommuting variables, the latter being anociated with the particle spin and isospin. For illustration an arbitrary Abelian-like external field is considered, as well as non-Abelian-like constant external field.     

Doppler three-level (V-scheme) laser without population inversion

The theory of amplification and lasing without population inversion in a three-level medium with inhomogeneous broadening via the formation of an open V configuration is elaborated. The conditions for energy transfer from the infrared into the visible spectral range, i.e., the conditions of up-conversion n _b >n _c >n _a , and the external field required for saturation of the b?a transition are established. Two-photon resonant Raman transitions in ensemble of mobile atoms of a gas-discharge plasma are analyzed. The frequency shift of the probe field spectrum as a whole is shown to be governed by the frequency shift of the pump field multiplied by the ratio of the wave numbers of the probe amplification field and the pump field. The interaction of atoms through Ne transitions with the pump field (λ=1.15 εm, 2p ₄-2s ₂ transition) and the lasing field (λ=0.6328 εm, 3s ₂-2p ₂ transition) with an increase in the lasing frequency by a factor of 1.82 with respect to the absorbed radiation is calculated.     

One-loop effective potential in gauged O(4) supergravity and the problem of the Λ term

We calculate the one-loop, off-shell, effective action in O(4) gauged supergravity assuming an (anti) de Sitter metric and constant scalar fields as a background. The problem of the large induced Λ term (present already for free matter fields) is stressed and the possibility of dynamical breakdown of local supersymmetry is pointed out. We illustrate our techniques and qualitative conclusions on a number of examples, including Ø⁴ theory and QED scalar potentials on a de Sitter background and an effective action in Einstein theory with a cosmological constant. Possible solutions of the Λ-term problem are also discussed.     

Recent developments in conformal invariant quantum field theory

A review of the recent results concerning the kinematics of conformal fields, the analysis of dynamical equations and dynamical derivation of the operator product expansion is given.The classification and transformational properties of fields which are transformed according to the representations of the universal covering group of the conformal group have been considered. A derivation of the partial wave expansion of Wightman functions is given. The analytical continuation to the Euclidean domain of coordinates is discussed. As shown, in the Euclidean space the partial wave expansion can be applied either to one-particle irreducible vertices or to the Green functions, depending on the dimensions of the fields.The structure of Green functions, which contain a conserved current and the energy-momentum tensor, has been studied. Their partial wave expansion has been obtained. A solution of the Ward identity has been found. Special cases are discussed.The program of the construction of exact solution of dynamical equations is discussed. It is shown, that integral dynamical equations for vertices (or Green's functions) can be diagonalized by means of the partial wave expansion. The general solution of these equations is obtained. The equations of motion for renormalized fields are considered. The way to define the product of renormalized fields at coinciding points (arising on the right-hand side) is discussed. A recipe for calculating this product is presented. It is shown, that this recipe necessarily follows from the renormalized equations.The role of bare term and of canonical commutation relations (for unrenormalized fields) is discussed in connection with the problem of the field product determination at coinciding points. As a result an exact relation between fundamental field dimensions is found for various three-linear interactions (section 16 and Appendix 6). The problem of closing the infinite system of dynamical equations is discussed.Al above said results are demonstrated using Thirring model as an example. A new approach to its solving is developed.The program od closing the infinite system of dynamical equations is discussed. The Thirring model is considered as an example. A new approach to the solution of this model is discussed.Methods are developed for the approximate calculation of dimensions and coupling constants in the 3-vertex and 5-vertex approximations. The dimensions are calculated in the γ_?³ theory in 6-dimensional space.The problem of calculating the critical indices in statistics (3-dimensional Euclidean space) is considered. The calculation of the dimension is carried out in the framework of the γ_?⁴ model. The value of the dimension and the critical indices thus obtained coincide with the experimental ones.     

Coherent nonlinear interference effect for devices of long-term memory with femtosecond pulses

Computer simulation of the response (polarization) of three-level systems (for example, of quantum dots) with the common upper level (the Λ-scheme) was carried out for devices of long-term memory with femtosecond driving and signal pulses. For producing an efficient response, the pulse area should be on the order of π. Under the action of the first driving pulse on the 1–2 transition and the simultaneous action of the probe pulse on the 3–2 transition, a long-lived polarization with the lifetime dependent on the lifetimes of the lower (1 and 3) levels appears owing to the nonlinear interference effect. Under the action of the second driving pulse, a signal pulse appears on the 3–2 transition, whose amplitude is proportional to the amplitude of the input probe pulse and exponentially decreases with the delay time between the first and the second driving pulses. The set of equations for the density matrix was solved numerically in the semiclassical approximation and in the rotating wave approximation. The temporal evolution of the nondiagonal matrix elements reflects the temporal evolution of the nonlinear polarization. The polarization spectrum is found by the Fourier transform of the time dependence of the nondiagonal elements. The polarization spectrum (the power spectrum) possesses an interference structure with a fringe period governed by the delay time between the first and the second driving pulses. The inverse Fourier transform reconstructs the temporal shape of the pulses.