V.N. Popov

Bio: V.N. Popov is an academic researcher from Steklov Mathematical Institute. The author has contributed to research in topics: Quantization (physics) & Quasiparticle. The author has an hindex of 6, co-authored 6 publications receiving 2778 citations.

Functional integrals and collective excitations

Abstract: Part I. Functional Integrals and Diagram Techniques in Statistical Physics: Part II. Superfluid Bose Systems: Part III. Plasma and Superfluid Fermi Systems: Part IV. Crystals, Heavy Atoms, Model Hamiltonians.

Covariant quantization of the gravitational field

Abstract: A review dedicated to the contemporary methods of quantization of the gravitational field. In view of possible applications to elementary particle theory, the authors consider only asymptotically flat gravitational fields. The basis of the exposed method of quantization is the method of quantization of gauge fields in the functional integration formalism. The main result is the formulation of covariant rules for a diagrammatic perturbation theory. Its elements are the lines representing gravitons and the vertices of graviton-graviton interaction, as well as the lines and interaction vertices of fictitious vector particles ("Faddeev-Popov ghosts") characteristic for the theory of gauge fields. The expressions for the propagators and vertex functions are given explicitly. It is shown that the presence of fictitious particles in the covariant diagram technique guarantees the unitarity of the theory and the agreement between the covariant quantization with the canonical quantization. The bibliography contains 44 entries (54 names).

Perturbation theory for gauge invariant fields

Abstract: A method is developed for the manifestly covariant quantization of gaugeinvariant fields by means of a functional integration. It is shown that for the fields with non-Abelian gauge groups (the Yang–Mills and gravitational fields) fictitious particles appear naturally in the diagram technique, which are not present in the initial Lagrangian. An appearance of these particles restores the transversality of scattering amplitudes and the unitarity of the S-matrix.

Many-Body Physics with Ultracold Gases

Abstract: This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.

Theory of Bose-Einstein condensation in trapped gases

Abstract: The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Various properties of these systems are discussed, including the density profiles and the energy of the ground-state configurations, the collective oscillations and the dynamics of the expansion, the condensate fraction and the thermodynamic functions. The thermodynamic limit exhibits a scaling behavior in the relevant length and energy scales. Despite the dilute nature of the gases, interactions profoundly modify the static as well as the dynamic properties of the system; the predictions of mean-field theory are in excellent agreement with available experimental results. Effects of superfluidity including the existence of quantized vortices and the reduction of the moment of inertia are discussed, as well as the consequences of coherence such as the Josephson effect and interference phenomena. The review also assesses the accuracy and limitations of the mean-field approach.