Extrinsic geometry sensitive bosonic string theory

A modified rigid string theory with infrared behavior governed by a nontrivial fixed point is presented.Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 2, pp. 276–279, May, 1993.     

Quantization of a bosonic relativistic string in four-dimensional space

Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 84, No. 3, pp. 441–418, September, 1990.     

Quantization of bosonic string field and infinite-dimensional pseudodifferential operators. Fixed gauge

Institute of Electronic Technology, Moscow. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 80, No. 2, pp. 226–238, August, 1989.     

Open string in background non-Abelian field

Joint Institute for Nuclear Research, Dubna. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 85, No. 2, pp. 176–182, November, 1990.     

Regularized adelic formulas for string and superstring amplitudes in one-class quadratic fields

We obtain regularized adelic formulas for gamma and beta functions for fields of rational numbers and the one-class quadratic fields and arbitrary quasicharacters (ramified or not). We consider applications to four-tachyon tree string amplitudes, generalized Veneziano amplitudes (open string), perturbed Virasoro amplitudes (closed string), massless four-particle tree open and closed superstring amplitudes, Ramond-Neveu-Schwarz superstring amplitudes, and charged heterotic superstring amplitudes. We establish certain relations between different string and superstring amplitudes.     

Extreme bosonic linear channels

The set of all channels with a fixed input and output is convex. We first give a convenient formulation of the necessary and sufficient condition for a channel to be an extreme point of this set in terms of the complementary channel, a notion of great importance in quantum information theory. This formulation is based on the general approach to extremality of completely positive maps in an operator algebra in the spirit of Arveson. We then use this formulation to prove our main result: under certain nondegeneracy conditions, environmental purity is necessary and sufficient for the extremality of a bosonic linear (quasifree) channel. It hence follows that a Gaussian channel between finite-mode bosonic systems is extreme if and only if it has minimum noise.     

Average-optimal string matching

The exact string matching problem is to find the occurrences of a pattern of length m from a text of length n symbols. We develop a novel and unorthodox filtering technique for this problem. Our method is based on transforming the problem into multiple matching of carefully chosen pattern subsequences. While this is seemingly more difficult than the original problem, we show that the idea leads to very simple algorithms that are optimal on average. We then show how our basic method can be used to solve multiple string matching as well as several approximate matching problems in average optimal time. The general method can be applied to many existing string matching algorithms. Our experimental results show that the algorithms perform very well in practice.     

Algebraic string operations

We first discuss how open/closed chord diagrams, both with and without marked points, act on appropriate Hochschild complexes possibly coupled with the two-sided cobar complex. Then, in the main part of the paper, we introduce the notion of a V _k -algebra and obtain suitable homotopy versions.     

Practical analyticity of scattering amplitudes

Institute of Nuclear Research, USSR Academy of Sciences; All-Union Scientific-Research Institute of Physicotechnical and Radio Engineering. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 79, No. 3, pp. 416–422, June, 1989.     

Bogolyubov canonical transformation and collective states of bosonic fields

Joint Institute for Nuclear Research, Dubna. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 89, No. 3, pp. 438–445, December, 1991.     

The homotopy invariance of the string topology loop product and string bracket

Let Mⁿ be a closed, oriented, n-manifold, and LM its free loopspace. In [Chas and Sullivan, ‘String topology’,Ann. of Math., to appear] a commutative algebra structure inhomology, H_*(LM), and a Lie algebra structure in equivarianthomology , were defined.In this paper, we prove that these structures are homotopy invariantsin the following sense. Let f:M₁ M₂ be a homotopy equivalenceof closed, oriented n-manifolds. Then the induced equivalence,Lf:LM₁ LM₂ induces a ring isomorphism in homology, and an isomorphismof Lie algebras in equivariant homology. The analogous statementalso holds true for any generalized homology theory h_* thatsupports an orientation of the M_i. Received February 5, 2007.