ar X iv : h ep - t h / 93 09 03 5 v 1 7 S ep 1 99 3 Graphical Representation of Invariants and Covariants in General Relativity

ar X iv : h ep - t h / 96 09 01 3 v 1 3 1 A ug 1 99 6 Weak Field Expansion of Gravity and Graphical Representation ∗

We introduce a graphical representation for a global SO(n) tensor ∂μ∂νhαβ , which generally appears in the perturbative approach of gravity around the flat space: gμν = δμν + hμν . We systematically construct global SO(n) invariants. Independence and completeness of those invariants are shown by taking examples of ∂∂h-, and (∂∂h)invariants. They are classified graphically. Indices which charact...

ar X iv : h ep - t h / 93 09 02 9 v 1 6 S ep 1 99 3 Multivariable Invariants of Colored Links Generalizing the Alexander Polynomial ∗

We discuss multivariable invariants of colored links associated with the N dimensional root of unity representation of the quantum group. The invariants for N > 2 are generalizations of the multi-variable Alexander polynomial. The invariants vanish for disconnected links. We review the definition of the invariants through (1,1)-tangles. When (N, 3) = 1 and N is odd, the invariant does not vanis...

ar X iv : h ep - t h / 97 09 01 6 v 1 2 S ep 1 99 7 Free boson representation of DY h̄ ( gl N ) k

ar X iv : h ep - t h / 93 03 13 5 v 1 2 4 M ar 1 99 3 214 / COSMO −

We clarify the relation between 2-form Einstein gravity and its topological version. The physical space of the topological version is contained in that of the Einstein gravity. Moreover a new vector field is introduced into 2-form Einstein gravity to restore the large symmetry of its topological version. The wave function of the universe is obtained for each model. † Talk given at the Workshop ...

X iv : h ep - t h / 98 03 23 8 v 1 2 8 M ar 1 99 8 Weak Field Expansion of Gravity : Graphs , Matrices and Topology ∗

We present some approaches to the perturbative analysis of the classical and quantum gravity. First we introduce a graphical representation for a global SO(n) tensor (∂)hαβ , which generally appears in the weak field expansion around the flat space: gμν = δμν+hμν . Making use of this representation, we explain 1) Generating function of graphs (Feynman diagram approach), 2) Adjacency matrix (Mat...