122614311
Algebraic aspects of the descent equations
The algebraic meanings of the descent equations, delta omega 41=d omega 32 and delta omega 32=d omega 23 identical to omega 3 are examined in the Hamiltonian framework.
17047722
Infinite Families of Gauge-Equivalent R-Matrices and Gradations of Quantized Affine Algebras
Associated with the fundamental representation of a quantum algebra such as Uq(A1) or Uq(A2), there exist infinitely many gauge-equivalent R-matrices with different spectralparameter dependences. It is shown how these can be obtained by examining the infinitely many possible gradations of the corresponding quantum affine algebras, such as and , and explicit formulae are obtained for those two cases. Spectral-dependent similarity (gauge) transformations relate the R-matrices in different gradations, Nevertheless, the choice of gradation can be physically significant, as is illustrated in the case of quantum affine Toda field theories.
119694191
Construction of basis vectors for symmetric irreducible representations of O(5) $ \supset$ O(3)
Abstract.A recursive method for the construction of symmetric irreducible representations of $ O(2l+1)$ in the $ O(2l+1)\supset O(3)$ basis for identical boson systems is proposed. The formalism is realized based on the group chain $ U(2l+1)\supset U(2l-1)\otimes U(2)$ , of which the symmetric irreducible representations are simply reducible. The basis vectors for symmetric irreducible representations of the $ O(2l+1)\supset O(2l-1)\otimes U(1)$ can easily be constructed from those of U(2l + 1) $ \supset$U(2l - 1) ⊗ U(2) $ \supset$O(2l - 1) ⊗ U(1) with no l -boson pairs, namely with the total boson number exactly equal to the seniority number in the system, from which one can construct symmetric irreducible representations of $ O(2l+1)$ in the $ O(2l-1)\otimes U(1)$ basis when all symmetric irreducible representations of O(2l - 1) are known. As a starting point, basis vectors of symmetric irreducible representations of O(5) are constructed in the $ O_{1}(3)\otimes U(1)$ basis, where $ O_{1}(3)\equiv O(2l-1)$ , when l = 2 , which is generated not by the angular momentum operators of the d -boson system, but by the operators constructed from d -boson creation (annihilation) operators $ d^{\dagger}_{\mu}$ ( $ d_{\mu}$ with $ \mu=1$ , 0, -1 . Matrix representations of $ O(5)\supset O_{1}(3)\otimes U(1)$ , together with the elementary Wigner coefficients, are presented. After the angular momentum projection, a three-term relation in determining the expansion coefficients of the $ O(5)\supset O(3)$ basis vectors, where the O(3) group is generated by the angular momentum operators of the d -boson system, in terms of those of $ O_{1}(3)\otimes U(1)$ is derived. The eigenvectors of the projection matrix with zero eigenvalues constructed according to the three-term relation completely determine the basis vectors of $ O(5)\supset O(3)$ . Formulae for evaluating the elementary Wigner coefficients of $ O(5)\supset O(3)$ are derived explicitly. Analytical expressions of some elementary Wigner coefficients of $ O(5)\supset O(3)$ for the coupling $ (\tau 0)\otimes(1 0)$ with resultant angular momentum quantum number L = 2$ \tau$ + 2 - k for $ k=0,2,3,\ldots,6$ with a multiplicity 2 case for k = 6 are presented.
2107479
Local Quasitriangular Hopf Algebras
We find a new class of Hopf algebras, local quasitriangular Hopf algebras, which generalize quasitriangular Hopf algebras. Using these Hopf algebras, we obtain solutions of the Yang-Baxter equation in a systematic way. The category of modules with finite cycles over a local quasitriangular Hopf algebra is a braided tensor category.
121731174
Some algebraic identities in anomalous gauge theories
Some useful algebraic relations between the anomaly of Dmu Jmu and anomalous commutators are derived using only the canonical commutators and the equation of motion. Their applications are discussed.
1264030
Elliptic Gaudin models and elliptic KZ equations
The Gaudin models based on the face-type elliptic quantum groups and the XYZ Gaudin models are studied. The Gaudin model Hamiltonians are constructed and are diagonalized by using the algebraic Bethe ansatz method. The corresponding face-type Knizhnik–Zamolodchikov equations and their solutions are given.
54593568
On genera of curves from high-loop generalized unitarity cuts
A bstractGeneralized unitarity cut of a Feynman diagram generates an algebraic system of polynomial equations. At high-loop levels, these equations may define a complex curve or a (hyper-)surface with complicated topology. We study the curve cases, i.e., a 4-dimensional L-loop diagram with (4L−1) cuts. The topology of a complex curve is classified by its genus. Hence in this paper, we use computational algebraic geometry to calculate the genera of curves from two and three-loop unitarity cuts. The global structure of degenerate on-shell equations under some specific kinematic configurations is also sketched. The genus information can also be used to judge if a unitary cut solution could be rationally parameterized.
119221055
An integrand reconstruction method for three-loop amplitudes
A bstractWe consider the maximal cut of a three-loop four point function with massless kinematics. By applying Gröbner bases and primary decomposition we develop a method which extracts all ten propagator master integral coefficients for an arbitrary triple-box configuration via generalized unitarity cuts. As an example we present analytic results for the three loop triple-box contribution to gluon-gluon scattering in Yang-Mills with adjoint fermions and scalars in terms of three master integrals.
119263398
Multi-loop Integrand Reduction with Computational Algebraic Geometry
We discuss recent progress in multi-loop integrand reduction methods. Motivated by the possibility of an automated construction of multi-loop amplitudes via generalized unitarity cuts we describe a procedure to obtain a general parameterisation of any multi-loop integrand in a renormalizable gauge theory. The method relies on computational algebraic geometry techniques such as Grobner bases and primary decomposition of ideals. We present some results for two and three loop amplitudes obtained with the help of the MACAULAY2 computer algebra system and the Mathematica package BASISDET.
118866595
Atmospheric Neutrino Mixing and b → s Transitions: Testing Lopsided SO(10) Flavor Structure in B physics
We point out that the correlation between the large atmospheric neutrino mixing and the b! s transition, if exists, comes from the lopsided flavor structure in SO(10) grand unification theory. We suggest testing the correlation by studying the deviation of SKS and S�'KS from the standard model predictions along with the constraints fromMBS and b! s in a realistic SO(10) model with lopsided flavor structure. We find a specific correlation between SKS and S�'KS that is intrinsic to the lopsided structure and discuss how to confirm or rule out this flavor pattern by the more accurate measurements of these CP violation quantities in B decay. The standard model (SM), although has passed many precision experimental tests, still has a number of out- standing problems which beg for a more fundamental the- ory. In terms of phenomenology, there are many places to test the more fundamental theory and, quite often, it is not one piece of phenomenology but a specific pattern of many pieces of phenomenology that fulfils this job. Neutrino oscillation clearly indicates the beyond SM physics in that it violates the accidental symmetry Le,µ,� of SM lepton flavor. Moreover, the tiny neutrino masses can be most naturally explained by the seesaw mech- anism (1), indicating the Majorana nature of neutrinos that leads to violation of another accidental symmetry B − L of SM at a very high scale close to the grand unification theory (GUT) scale. For this reason, study- ing neutrino oscillation in the GUT framework becomes particularly interesting. In SO(10) GUT, quarks and leptons are unified into a single 16 multiplet, yet experimental data shows that the 2-3 (generation) mixing is dramatically different in the quark and lepton sectors. While the quark mixing an- gle θ CKM is around 0.04, the lepton mixing angle θ PMNS (atmospheric mixing angle) is quite large and could be a maximum of π/4. This difference can be rather naturally explained by the lopsidedness in the 2-3 sector of mass matrices of down-type quarks and charged leptons:
122762455
TeV Gamma Ray Survey on the Direction of Fermi-LAT Pulsars with the Tibet Air Shower Array
We search for steady TeV γ-rays from 18 pulsars in the Fermi-LAT pulsar catalog using the Tibet air shower array. We observe 8 sources including the Crab against expected 0.41 sources at a significance of 2σ or more among the 18 pulsars. The chance probability from Poisson statistics is estimated to be 1.4×10-8.With the Crab excluded, it is estimated to be 1.8×10-7. These low chance probabilities clearly show that the Fermi pulsars have a statistically significant correlation with TeV γ-ray excesses observed by the Tibet air shower array.