Independent Loop Invariants for 2+1 Gravity
نویسنده
چکیده
We identify an explicit set of complete and independent Wilson loop invariants for 2+1 gravity on a three-manifold M = IR × Σ, with Σ a compact oriented Riemann surface of arbitrary genus g. In the derivation we make use of a global cross section of the PSU(1, 1)principal bundle over Teichmüller space given in terms of Fenchel-Nielsen coordinates. 1 address after Aug 94: Sezione INFN di Firenze, Largo E. Fermi 2, Arcetri, I-50125 Firenze, Italy
منابع مشابه
New Improvement in Interpretation of Gravity Gradient Tensor Data Using Eigenvalues and Invariants: An Application to Blatchford Lake, Northern Canada
Recently, interpretation of causative sources using components of the gravity gradient tensor (GGT) has had a rapid progress. Assuming N as the structural index, components of the gravity vector and gravity gradient tensor have a homogeneity degree of -N and - (N+1), respectively. In this paper, it is shown that the eigenvalues, the first and the second rotational invariants of the GGT (I1 and ...
متن کاملar 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...
متن کاملar 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...
متن کاملVassiliev Invariants and the Loop States in Quantum Gravity
The purpose of this paper is to expose properties of Vassiliev invariants by using the simplest of the approaches to the functional integral definition of link invariants. These methods are strong enough to give the top row evaluations of Vassiliev invariants for the classical Lie algebras. They give an insight into the structure of these invariants without using the full perturbation expansion...
متن کاملExtended knots and the space of states of quantum gravity
In the loop representation the quantum constraints of gravity can be solved. This fact allowed significant progress in the understanding of the space of states of the theory. The analysis of the constraints over loop dependent wavefunctions has been traditionally based upon geometric (in contrast to analytic) properties of the loops. The reason for this preferred way is twofold: for one hand th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1994