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 ∗

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...

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 09 03 5 v 1 7 S ep 1 99 3 Graphical Representation of Invariants and Covariants in General Relativity

We present a grapical way to describe invariants and covariants in the (4 dim) general relativity. This makes us free from the complexity of suffixes . Two new off-shell relations between (mass)∗∗6 invariants are obtained. These are important for 2-loop off-shell calculation in the perturbative quantum gravity. We list up all independent invarians with dimensions of (mass)∗ ∗ 4 and (mass)∗∗6. F...

ar X iv : h ep - t h / 96 07 09 3 v 1 1 2 Ju l 1 99 6 Quantum dynamics of N = 1 , D = 4 supergravity compensator

ar X iv : h ep - t h / 96 05 09 3 v 1 1 4 M ay 1 99 6 The phase free , longitudinal , magnetic component of vacuum electromagnetism

A charge q moving in a reference laboratory system with constant velocity V in the X-axis produces in the Z-axis a longitudinal, phase free, vacuum magnetic field which is identified as the radiated B (3) field of Evans, Vigier and others.