From BRST to light-cone description of higher spin gauge fields

In this short note we show, at the level of action principles, how the light-cone action of higher spin gauge fields can easily be obtained from the BRST formulation through the elimination of quartets. We analyze how the algebra of cohomology classes is affected by such a reduction. By applying the reduction to the Poincare generators, we give an alternative way of analyzing the physical spectrum of the Fronsdal type actions, with or without trace condition.Comment: 13 pages Latex file, Proceedings of the Workshop "Quantum Field Theory and Hamiltonian Systems'', Caciulata, Romania, 16 - 21 Oct, 2004; more references added, acknowledgments correcte

Pinning control of spatiotemporal chaos

Linear control theory is used to develop an improved localized control scheme for spatially extended chaotic systems, which is applied to a coupled map lattice as an example. The optimal arrangement of the control sites is shown to depend on the symmetry properties of the system, while their minimal density depends on the strength of noise in the system. The method is shown to work in any region of parameter space and requires a significantly smaller number of controllers compared to the method proposed earlier by Hu and Qu [Phys. Rev. Lett. 72, 68 (1994)]. A nonlinear generalization of the method for a 1D lattice is also presented

Slow oscillations of magnetoresistance in quasi-two-dimensional metals

Slow oscillations of the interlayer magnetoresistance observed in the layered organic metal $\beta$-(BEDT-TTF)$_2$IBr$_2$ are shown to originate from the slight warping of its Fermi surface rather than from independent small cyclotron orbits. Unlike the usual Shubnikov-de Haas effect, these oscillations are not affected by the temperature smearing of the Fermi distribution and can therefore become dominant at high enough temperatures. We suggest that the slow oscillations are a general feature of clean quasi-two-dimensional metals and discuss possible applications of the phenomenon.Comment: 11 pages, 3 figure

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

Parent field theory and unfolding in BRST first-quantized terms

For free-field theories associated with BRST first-quantized gauge systems, we identify generalized auxiliary fields and pure gauge variables already at the first-quantized level as the fields associated with algebraically contractible pairs for the BRST operator. Locality of the field theory is taken into account by separating the space--time degrees of freedom from the internal ones. A standard extension of the first-quantized system, originally developed to study quantization on curved manifolds, is used here for the construction of a first-order parent field theory that has a remarkable property: by elimination of generalized auxiliary fields, it can be reduced both to the field theory corresponding to the original system and to its unfolded formulation. As an application, we consider the free higher-spin gauge theories of Fronsdal.Comment: LaTeX, amsart++, 40 pages, references added, final version to appear in Commun. Math. Phy

Parent form for higher spin fields on anti-de Sitter space

We construct a first order parent field theory for free higher spin gauge fields on constant curvature spaces. As in the previously considered flat case, both Fronsdal's and Vasiliev's unfolded formulations can be reached by two different straightforward reductions. The parent theory itself is formulated using a higher dimensional embedding space and turns out to be geometrically extremely transparent and free of the intricacies of both of its reductions.Comment: 39 pages, LaTeX; misprints corrected, references adde

On the expressive power of read-once determinants

We introduce and study the notion of read-$k$ projections of the determinant: a polynomial $f \in \mathbb{F}[x_1, \ldots, x_n]$ is called a {\it read-$k$ projection of determinant} if $f=det(M)$, where entries of matrix $M$ are either field elements or variables such that each variable appears at most $k$ times in $M$. A monomial set $S$ is said to be expressible as read-$k$ projection of determinant if there is a read-$k$ projection of determinant $f$ such that the monomial set of $f$ is equal to $S$. We obtain basic results relating read-$k$ determinantal projections to the well-studied notion of determinantal complexity. We show that for sufficiently large $n$, the $n \times n$ permanent polynomial $Perm_n$ and the elementary symmetric polynomials of degree $d$ on $n$ variables $S_n^d$ for $2 \leq d \leq n-2$ are not expressible as read-once projection of determinant, whereas $mon(Perm_n)$ and $mon(S_n^d)$ are expressible as read-once projections of determinant. We also give examples of monomial sets which are not expressible as read-once projections of determinant

Resonant Amplification of Electroweak Baryogenesis at Preheating

We explore viable scenarios for parametric resonant amplification of electroweak (EW) gauge fields and Chern-Simons number during preheating, leading to baryogenesis at the electroweak (EW) scale. In this class of scenarios time-dependent classical EW gauge fields, essentially spatially-homogeneous on the horizon scales, carry Chern-Simons number which can be amplified by parametric resonance up to magnitudes at which unsuppressed topological transitions in the Higgs sector become possible. Baryon number non-conservation associated with the gauge sector and the highly non-equilibrium nature of preheating allow for efficient baryogenesis. The requisite large CP violation can arise either from the time dependence of a slowly varying Higgs field (spontaneous baryogenesis), or from a resonant amplification of CP violation induced in the gauge sector through loops. We identify several CP violating operators in the Standard Model and its minimal extensions that can facilitate efficient baryogenesis at preheating, and show how to overcome would-be exponential suppression of baryogenesis associated with tunneling barriers.Comment: 51 pages, 8 figues; minor corrections; references adde