BRST-anti-BRST Symmetric Conversion of Second-Class Constraints

A general method of the BRST--anti-BRST symmetric conversion of second-class constraints is presented. It yields a pair of commuting and nilpotent BRST-type charges that can be naturally regarded as BRST and anti-BRST ones. Interchanging the BRST and anti-BRST generators corresponds to a symmetry between the original second-class constraints and the conversion variables, which enter the formalism on equal footing.Comment: 12 pages, misprints correcte

New bounds on neutrino magnetic moment and re-examination of plasma effect in neutrino spin light

Recent discussion on the possibility to obtain more stringent bounds on neutrino magnetic moment has stimulated new interest to possible effects induced by neutrino magnetic moment. In particular, in this note after a short review on neutrino magnetic moment we re-examine the effect of plasmon mass on neutrino spin light radiation in dense matter. We track the entry of the plasmon mass quantity in process characteristics and found out that the most substantial role it plays is the formation of the process threshold. It is shown that far from this point the plasmon mass can be omitted in all the corresponding physical quantities and one can rely on the results of massless photon spin light radiation theory in matter.Comment: to appear in Nuovo Cimento 35 C, No. 1, 2012 (based on the talk presented at the 25th Rencontres de Physique de la Vallee d'Aoste on "Results and Perspectives in Particle Physics", La Thuile, February 27 - March 5, 201

BRST Formalism and Zero Locus Reduction

In the BRST quantization of gauge theories, the zero locus $Z_Q$ of the BRST differential $Q$ carries an (anti)bracket whose parity is opposite to that of the fundamental bracket. We show that the on-shell BFV/BV gauge symmetries are in a 1:1 correspondence with Hamiltonian vector fields on $Z_Q$, and observables of the BRST theory are in a 1:1 correspondence with characteristic functions of the bracket on $Z_Q$. By reduction to the zero locus, we obtain relations between bracket operations and differentials arising in different complexes (the Gerstenhaber, Schouten, Berezin-Kirillov, and Sklyanin brackets); the equation ensuring the existence of a nilpotent vector field on the reduced manifold can be the classical Yang-Baxter equation. We also generalize our constructions to the bi-QP-manifolds which from the BRST theory viewpoint corresponds to the BRST-anti-BRST-symmetric quantization.Comment: 21 pages, latex2e, several modifications have been made, main content remains unchange

Математичне моделювання руху вільної поверхні рідини при транспортуванні сільськогосподарських напівпричіпних цистерн

Mathematical modeling of the oscillatory process ofthe longitudinal motion of a machine-tractor unit with a semitrailer tank equipped with a hydraulic liquid mixer is developed. The redistribution of liquid in the tank by the characteristics of Rayleighsurface waves is taken into consideration. The influence of the mixer operation on the total vibrational motion of the liquid in the tank is given. Thespectrum of frequencies of free mechanical oscillations is determined, and the corresponding forms ofinterconnected movements of the elements of a tractor and a tank are analyzed.Виконано математичне моделювання коливального процесу поздовжнього руху машинно-тракторного агрегату з напівпричіп-цистерною, яка має гідравлічний змішувач рідини. Для перерозподілу рідини у цистерні, що викликаний коливаннями оболонки, використано характеристики поверхневих хвиль Релея. Наведено вплив роботи змішувача на загальний коливальний рух рідини в цистерні. Знайдено спектр частот вільних механічних коливань, а також проаналізовано відповідні форми взаємопов’язаних рухів елементів трактора та цистерни

Non-Abelian Conversion and Quantization of Non-scalar Second-Class Constraints

We propose a general method for deformation quantization of any second-class constrained system on a symplectic manifold. The constraints determining an arbitrary constraint surface are in general defined only locally and can be components of a section of a non-trivial vector bundle over the phase-space manifold. The covariance of the construction with respect to the change of the constraint basis is provided by introducing a connection in the ``constraint bundle'', which becomes a key ingredient of the conversion procedure for the non-scalar constraints. Unlike in the case of scalar second-class constraints, no Abelian conversion is possible in general. Within the BRST framework, a systematic procedure is worked out for converting non-scalar second-class constraints into non-Abelian first-class ones. The BRST-extended system is quantized, yielding an explicitly covariant quantization of the original system. An important feature of second-class systems with non-scalar constraints is that the appropriately generalized Dirac bracket satisfies the Jacobi identity only on the constraint surface. At the quantum level, this results in a weakly associative star-product on the phase space.Comment: LaTeX, 21 page

Quantum treatment of neutrino in background matter

Motivated by the need of elaboration of the quantum theory of the spin light of neutrino in matter ($SL\nu$), we have studied in more detail the exact solutions of the Dirac equation for neutrinos moving in the background matter. These exact neutrino wavefunctions form a basis for a rather powerful method of investigation of different neutrino processes in matter, which is similar to the Furry representation of quantum electrodynamics in external fields. Within this method we also derive the corresponding Dirac equation for an electron moving in matter and consider the electromagnetic radiation ("spin light of electron in matter", $SLe$) that can be emitted by the electron in this case.Comment: 10 pages, in: Proceedings of QFEXT'05 (The Seventh Workshop on Quantum Field Theory under the Influence of External Conditions, IEEC, CSIC and University of Barcelona, Barcelona, Catalonia, Spain, 5-9 September 2005.), ed. by Emilio Elizalde and Sergei Odintsov; published in Journal of Physics

Spin light of electron in dense matter

We derive the modified Dirac equation for an electron undergos an influence of the standard model interaction with the nuclear matter. The exact solutions for this equation and the electron energy spectrum in matter are obtained. This establishes a rather powerful method for investigation of different processes that can appear when electrons propagate in background matter. On this basis we study in detail the spin light of electron in nuclear matter, a new type of electromagnetic radiation which can be emitted by an electron moving in dense matter.Comment: 11 pages in LaTex, 4 figures, typos correcte