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We prove that the essential dimension of the spinor group Spinn grows exponentially with n and use this result to show that quadratic forms with trivial discriminant and Hasse-Witt invariant are more...
The article consists of the Russian and English variants of Ph.D. Thesis in which the answers is given on the following questions.
Abstract: We investigate the long-term dynamics of spin textures prepared by cooling unmagnetized spinor gases of F=1 $^{87}$Rb to quantum degeneracy, observing domain coarsening and a strong dependen...
Abstract: Using a new proposal for the "picture lowering" operators, we compute the tree level scattering amplitude in the minimal pure spinor formalism by performing the integration over the pure spi...
Abstract: We present a new framework for defining fuzzy approximations to geometry in terms of a cutoff on the spectrum of the Dirac operator, and a generalization of it that we call the Dirac-Flux op...
The compact exceptional Lie groups F4,E6,E7 and E8 have spinor groups as a subgroup as follows.
The analytical algorithm previously proposed by the author for matching the Volkov-Akulov (VA) and Komargodski-Seiberg (KS) actions describing the Nambu-Goldstone (NG) fermion, is discussed.
Vacuum expectation value of the stress-energy-momentum tensor for scalar and spinor fields is obtainted on the homogeneous space with G-invariant metrics using the orbits of coadjoint representation o...
The tree-level amplitude of six massless open strings is computed using the pure spinor formalism. The OPE poles among integrated and unintegrated vertices can be efficiently organized according to th...
We investigate the St¨uckelberg oscillations of a spin-1 Bose-Einstein condensate subject to a spatially inhomogeneous transverse magnetic field and a periodic longitudinal field. We show that the ti...
In this work, we theoretically construct exact mappings of many-particle bosonic systems onto quantum rotor models. In particular, we analyze the rotor representation of spinor Bose-Einstein condensa...
We study the ground state phases for a mixture of two atomic spin-1 Bose-Einstein condensates (BECs) in the presence of a weak magnetic (B-) field. The ground state is found to contain a broken-axis...
Higher secants of spinor varieties     spinor varieties  math       2010/11/15
Let $S_h$ be the even pure spinors variety of a complex vector space $V$ of even dimension $2h$ endowed with a non degenerate quadratic form $Q$ and let $\sigma_k(S_h) $ be the $k$-secant variety of ...
The concept of phase space amplitudes for systems with continuous degrees of freedom is generalized to finite-dimensional spin systems. Complex amplitudes are obtained on both a sphere and a finite la...
We propose a scheme for the realization of a quantum walker and a quantum simulator for the Dirac equation with ultracold spinor atoms in driven optical lattices. A precise control of the dynamics of ...

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