arXiv subjects
Publications and source records attributed to A. P. Zubarev.
The classical problem of the fluid mechanics is the problem of a supersonic motion around a thin body was generalized to the case of non-equilibrium gas. The drag and lift force coefficients were founded. It is shown that the drag and lift force coefficients in the acoustically active supersonic flow are both decreased
We found the energetic stability criteria of non-equilibrium gase plain flows.
We consider an interaction representation in the Boltzmann field theory. It describes the master field for a subclass of planar diagrams in matrix models, so called half-planar diagrams. This interaction representation was found in the previous paper by Accardi, Volovich and one of us (I.A.) and it has an unusual property that one deals with a rational function of the interaction Lagrangian instead of the ordinary exponential function. Here we study the interaction representation in more details and show that under natural assumptions this representation is in fact unique. We demonstrate that corresponding Schwinger-Dyson equations lead to a closed set of integral equations for two- and four-point correlation functions. Renormalization of the model is performed and renormalization group equations are obtained. Some model examples with discrete number of degrees of freedom are solved numerically. The solution for one degree of freedom is compared with the planar approximation for one matrix model. For large variety of coupling constant it reproduces the planar approximation with good accuracy.
A parquet approximation (generalized ladder diagrams) in matrix models is considered. By means of numerical calculations we demonstrate that in the large $N$ limit the parquet approximation gives an excellent agreement with exact results.
In this talk results of study in various dimensions of the Boltzmann master field for a subclass of planar diagrams, so called half-planar diagrams, found in the recent work by Accardi, Volovich and one of us (I.A.) are presented.
Starting from string field theory for 2d gravity coupled to c=1 matter we analyze N-point off-shell tree amplitudes of discrete states. The amplitudes exhibit the pole structure and we use the oscillator representation to extract the residues. The residues are generated by a simple effective action. We show that the effective action can be directly deduced from a string field action in a special transversal-like gauge.
$D=2$ free string in linear dilaton background is considered in so called target space/world-sheet light cone gauge $ X^{+}=0,~g_{++}=0,~g_{+-}=1$. After gauge fixing the theory has the residual Virasoro and $U(1)$ current symmetries. The physical spectrum related to $SL_2$ invariant vacuum is found to be trivial. We find that the theory has a nontrivial spectrum if the states in different non-equivalent representations ("pictures") of CFT algebra of matter fields are considered.
Scattering amplitudes for discrete states in 2D string theory are considered. Pole divergences of tree-level amplitudes are extracted and residues are interpreted as renormalized amplitudes for discrete states. An effective Lagrangian generating renormalized amplitudes for open string is written and corresponding Ward identities are presented. A relation of this Lagrangian with homotopy Lie algebra is discussed.
String field theory for the non-critical NSR string is described. In particular it gives string field theory for the 2D super-gravity coupled to a $\hat{c}=1$ matter field. For this purpose double-step pictures changing operators for the non-critical NSR string are constructed. Analogues of the critical supersymmetry transformations are written for $D<10$, they form a closed on-shell algebra, however their action on vertices is defined only for discrete value of the Liouville momentum. For D=2 this means that spinor massless field has its superpartner in the NS sector only if its momentum is fixed. Starting from string field theory we calculate string amplitudes. These amplitudes for D=2 have poles which are related with discrete set of primary fields, namely 2R$\to$2R amplitude has poles corresponding to the n-level NS excitations with discrete momenta $p_1=n,~~p_2=-1\pm (n+1)$.
Starting from string field theory for 2d gravity coupled to c=1 matter we analyze the off-shell tree amplitudes of discrete states. The amplitudes exhibit the pole structure and we use the off-shell calculus to extract the residues and prove that just the residues are constrained by the Ward Identities. The residues generate a simple effective action.