16,767 research outputs found
Soliton representations and Sobolev diffeomorphism symmetry in CFT
No full textWe show that any positive energy representation of the group of (orientation preserving) smooth diffeomorphisms of the circle Diff(S^1) can be extended to a strongly continuous unitary projective representation of the group of (orientation preserving) fractional Sobolev diffeomorphisms D^s(S^1) with real Sobolev exponent s>3. For some positive energy representations, i.e for the positive energy vacuum representations of Diff(S^1) with positive integer central charge, we can improve the implementation to the group D^s(S^1) with s>2. We show that a conformal net of von Neumann algebras on the circle is always D^s(S^1)-covariant, s>3.
Furthermore, we show that a given positive energy representation U of Diff(S^1) cannot be extended to some less-smooth diffeomorphisms, and from this fact we obtain an uncountable family of proper soliton representations. From these soliton representations we construct irreducible unitary projective positive energy representations of the group ΛSU(N) consisting of loops with support not containing the
point -1 (resp. B_0, the stabilizer subgroup of -1) which do not extend to LSU(N) (resp. Diff(S^1))
Minimal index and braided subfactors
No full textThe minimal index is shown to be multiplicative: if M1 ⊂ M2 ⊂ M3 are factors, then Ind(M1, M3) = Ind(M1, M2) Ind(M2, M3), extending a previous result (H. Kosaki and R. Longo, J. Funct. Anal. 107 (1992), 458-470). If M is an infinite factor, it follows that the dimension (the square root of the index) is an involutive homomorphism d: SectO(M) → R+ of the semiring of sectors with finite index. The result is applied to the study of the class of endomorphisms with a braid group symmetry that satisfies the relation between index and statistics in Quantum Field Theory (R. Longo, Commun. Math. Phys. 126 (1989), 217-247 and 130 (1990), 285-309); the analysis is generalized to this case. For these endomorphisms, the set of possible index values has several gaps besides the Jones restriction, for example, the index does not lie in the interval (4, 3 √2). As a consequence, subfactors arising in low-dimensional Quantum Field Theory cannot be arbitrary. © 1992
Signal communication and modular theory
No full textWe propose a conceptual frame to interpret the prolate differential operator,
which appears in Communication Theory, as an entropy operator; indeed, we write
its expectation values as a sum of terms, each subject to an entropy reading by
an embedding suggested by Quantum Field Theory. This adds meaning to the
classical work by Slepian et al. on the problem of simultaneously concentrating
a function and its Fourier transform, in particular to the ``lucky accident"
that the truncated Fourier transform commutes with the prolate operator. The
key is the notion of entropy of a vector of a complex Hilbert space with
respect to a real linear subspace, recently introduced by the author by means
of the Tomita-Takesaki modular theory of von Neumann algebras. We consider a
generalization of the prolate operator to the higher dimensional case and show
that it admits a natural extension commuting with the truncated Fourier
transform; this partly generalizes the one-dimensional result by Connes to the
effect that there exists a natural selfadjoint extension to the full line
commuting with the truncated Fourier transform.Comment: 22 page
Analytical solutions of the discrete Boltzmann equation for the Rayleigh flow problem for gas mixtures
No full text
Formal security proof for a scheme on a topological network
No full textKey assignment and key maintenance in encrypted networks of resource-limited devices may be a challenging task, due to the permanent need of replacing out-of-service devices with new ones and to the consequent need of updating the key information. Recently, Aragona et al. proposed a new cryptographic scheme, ECTAKS, which provides a solution to this design problem by means of a Diffie-Hellman-like key establishment protocol based on elliptic curves and on a prime field. Even if the authors proved some results related to the security of the scheme, the latter still lacks a formal security analysis. In this paper, we address this issue by providing a security proof for ECTAKS in the setting of computational security, assuming that no adversary can solve the underlying discrete logarithm problems with non-negligible success probability
Considerazioni sull'opportunità di ulteriori sperimentazioni nelle gallerie ferroviarie per l'esercizio ad alta velocità
No full textRecent experiments allow to define aerodinamic effects of high speed trains in tunnels. On this ground it is possible to define the aims of another series of experiments in order to determine the functional relationship between some variables, which are to be fixed during the project, and some relevant physical quantities. At the present time it is possible only to create some suppositions about these functions but it appears evident the necessity of a quantitative analysis to be done as soon as possible in order to plan tunnels correctly
Analytical solution of the discrete Boltzmann equation for the Rayleigh flow problem for gas mixtures
No full text- …
