32391471
Gluon propagator and transverse vertices.
It is shown explicitly that in the axial gauge the Slavnov-Taylor identity contains no useful information for determining the gluon propagator through the Dyson-Schwinger equation; rather, it is the transverse vertex which plays the crucial role.
122929166
Affine superalgebras, unitary representations and the sugawara construction
Abstract Unitary highest weight representations of the untwisted, affine, basic classical Lie superalgebras are considered. Unitary constraints (for both even and odd generators) relate the value of the central extension to the vacuum quantum numbers. The only consistent possibilities are for certain compact type I superalgebras, or for those type I and II superalgebras yielding spinor gradings of rigid two-dimensional conformal transformations. The Sugawara construction for these is presented and the value of the Virasoro central charge listed.
123137669
Generalized Gel’fand invariants and characteristic identities for quantum groups
The generalized Gel’fand invariants for an arbitrary quantum group are explicitly constructed, and their eigenvalues in any irreducible representation are computed. These invariants enable one to develop characteristic identities for the quantum group, and as a natural application, these identities are used to construct projection operators for tensor products of representations. To illustrate the general theory, the quantum group Uq(gl(m)) is studied in detail.
119709711
Serre presentations of Lie superalgebras
We prove an analogue of Serre’s theorem, which describes presentations in terms of Chevalley generators and Serre type relations for the finite dimensional simple contragredient Lie superalgebras relative to all possible choices of Borel sub-algebras.
120111183
Grand unification and Grassmannian Kaluza-Klein theory
It is possible to construct a grand unified model, including gravity, by adjoining further anticommuting coordinates to space-time. We carry out this program for SU(5) and SO(10) unified models; curiously, the former is much more economical than the latter and simply requires five complex Grassmann variables ξm in addition to the four xμ.
6725107
Super duality and Kazhdan-Lusztig polynomials
We establish a direct connection between the representation theories of Lie algebras and Lie superalgebras (of type A) via Fock space reformulations of their Kazhdan-Lusztig theories. As a consequence, the characters of finite-dimensional irreducible modules of the general linear Lie superalgebra are computed by the usual parabolic Kazhdan-Lusztig polynomials of type A. In addition, we establish closed formulas for canonical and dual canonical bases for the tensor product of any two fundamental representations of type A.
35314072
Geometrical structure and critical phenomena in the fermion dynamical symmetry model: Sp(6).
858386
Chiral symmetry, quark mass, and scaling of the overlap fermions
The chiral symmetry relation and scaling of the overlap fermions are studied numerically on the quenched lattices at 3 couplings with about the same physical volume. We find that the generalized Gell-Mann-Oakes-Renner relation is satisfied to better than 1% down to the smallest quark mass at m(0)a = 0.006. We also obtain the quark mass from the PCAC relation and the pseudoscalar masses. The renormalization group invariant quark mass is shown to be fairly independent of scale. The pi and rho masses at a fixed m(pi)/m(rho) ratio indicate small O(a(2)) corrections. It is found that the critical slowing down sets in abruptly at a very small quark mass close to those of the physical u and d quarks.
6589068
Top quark as a topological color soliton.
In this paper I propose a scenario for the top quark as a topological color soliton. I illustrate some features of the top quark as a soliton in a toy model based on a nonlinear realization of SU{sub {ital L}}(3){times}SU{sub {ital R}}(3)/SU{sub {ital L}+{ital R}}(3) with SU{sub {ital L}+{ital R}}(3) being the color gauge group.
45750229
Geometrical structure and critical phenomena in the fermion dynamical symmetry model: SO(8).
Geometrical properties of the recently proposed fermion dynamical symmetry model via the coherent state methodology is presented. Critical phenomena of this model are discussed in detail.
41901069
Geometrical interpretation of SO(7): A critical dynamical symmetry.
Potential-energy surfaces are obtained for the three dynamical-symmetry chains of SO(8) within the fermion-dynamical-symmetry model. A remarkable feature is that the SO(7) dynamical symmetry is transitional and ..beta.. soft. The transitional or ''critical'' behavior of SO(7) is vividly demonstrated.