Results 1 - 10 of 990
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[en] In a low energy approximation of the massless Yukawa theory (Nelson model) we derive a Faddeev–Kulish type formula for the scattering matrix of N electrons and reformulate it in LSZ terms. To this end, we perform a decomposition of the infrared finite Dollard modifier into clouds of real and virtual photons, whose infrared divergencies mutually cancel. We point out that in the original work of Faddeev and Kulish the clouds of real photons are omitted, and consequently their wave-operators are ill-defined on the Fock space of free electrons. To support our observations, we compare our final LSZ expression for with a rigorous non-perturbative construction due to Pizzo. While our discussion contains some heuristic steps, they can be formulated as clear-cut mathematical conjectures.
[en] We calculate the unpolarized twist-2 three-loop splitting functions and and the associated anomalous dimensions using massive three-loop operator matrix elements. While we calculate directly, is computed from 1200 even moments, without any structural prejudice, using a hierarchy of recurrences obtained for the corresponding operator matrix element. The largest recurrence to be solved is of order 12 and degree 191. We confirm results in the foregoing literature.
[en] We study integrable models solvable by the nested algebraic Bethe ansatz and described by or superalgebras. We obtain explicit determinant representations for form factors of the monodromy matrix entries. We show that all form factors are related to each other at special limits of the Bethe parameters. Our results allow one to obtain determinant formulas for form factors of local operators in the supersymmetric model.
[en] One-loop corrections to the neutrino mass matrix within the MSSM with bilinear R-parity violation are calculated, paying attention to the approach in which an effective 3×3 neutrino mass matrix is used. The full mass matrix is block-diagonalized, it is found that second and third order terms can be numerically important, and this is analytically understood. Top–stop loops do not contribute to the effective 3×3 approach at the first order, nevertheless they contribute at the third. An improved 3×3 approach that includes these effects is proposed. A scan over parameter space is made supporting the conclusions
[en] A general method for the construction of smooth flat connections on 3-manifolds is introduced. The procedure is strictly connected with the deduction of the fundamental group of a manifold M by means of a Heegaard splitting presentation of M. For any given matrix representation of the fundamental group of M, a corresponding flat connection A on M is specified. It is shown that the associated classical Chern–Simons invariant assumes then a canonical form which is given by the sum of two contributions: the first term is determined by the intersections of the curves in the Heegaard diagram, and the second term is the volume of a region in the representation group which is determined by the representation of and by the Heegaard gluing homeomorphism. Examples of flat connections in topologically nontrivial manifolds are presented and the computations of the associated classical Chern–Simons invariants are illustrated.
[en] Inspired by Okounkov's work (2001)  which relates KP hierarchy to determinant point process, we establish a relationship between BKP hierarchy and Pfaffian point process. We prove that the correlation function of the shifted Schur measures on strict partitions can be expressed as a Pfaffian of skew symmetric matrix kernel, whose elements are certain vacuum expectations of neutral fermions. We further show that the matrix integrals solution of BKP hierarchy can also induce a certain Pfaffian point process.
[en] We generalize a recently proposed on-shell approach to renormalize the Cabibbo-Kobayashi-Maskawa quark-mixing matrix to the case of an extended leptonic sector that includes Dirac and Majorana neutrinos in the framework of the seesaw mechanism. An important property of this formulation is the gauge independence of both the renormalized and bare lepton mixing matrices. Also, the texture zero in the neutrino mass matrix is preserved.
[en] We continue to develop the tensor-algebra approach to knot polynomials with the goal to present the story in elementary and comprehensible form. The previously reviewed description of Khovanov cohomologies for the gauge group of rank N−1=1 was based on the cut-and-join calculus of the planar cycles, which are involved rather artificially. We substitute them by alternative and natural set of cycles, not obligatory planar. Then the whole construction is straightforwardly lifted from SL(2) to SL(N) and reproduces Khovanov–Rozansky (KR) polynomials, simultaneously for all values of N. No matrix factorization and related tedious calculations are needed in such approach, which can therefore become not only conceptually, but also practically useful
[en] We present arguments that the structure of the spectrum of the supersymmetric matrix model with 16 real supercharges in the large N limit is rather nontrivial, involving besides the natural energy scale ∼λ1/3=(g2N)1/3 also a lower scale ∼λ1/3N-5/9. This allows one to understand a nontrivial behaviour of the mean internal energy of the system E∝T14/5 predicted by gauge-string duality arguments.
[en] We study invariant operators in general tensor models. We show that representation theory provides an efficient framework to count and classify invariants in tensor models of (gauge) symmetry . As a continuation and completion of our earlier work, we present two natural ways of counting invariants, one for arbitrary and another valid for large rank of . We construct bases of invariant operators based on the counting, and compute correlators of their elements. The basis associated with finite rank of diagonalizes the two-point function of the free theory. It is analogous to the restricted Schur basis used in matrix models. We show that the constructions get almost identical as we swap the Littlewood–Richardson numbers in multi-matrix models with Kronecker coefficients in general tensor models. We explore the parallelism between matrix model and tensor model in depth from the perspective of representation theory and comment on several ideas for future investigation.