Matrix Elements of Thiemann’s Hamiltonian Constraint in Loop Quantum Gravity
نویسندگان
چکیده
We present an explicit computation of matrix elements of the hamiltonian constraint operator in non-perturbative quantum gravity. In particular, we consider the euclidean term of Thiemann’s version of the constraint and compute its action on trivalent states, for all its natural orderings. The calculation is performed using graphical techniques from the recoupling theory of colored knots and links. We exhibit the matrix elements of the hamiltonian constraint operator in the spin network basis in compact algebraic form. PACS numbers: 04.60.-m, 02.70.-c, 04.60.Ds, 03.70+k Short title: Matrix elements of Thiemann’s Hamiltonian
منابع مشابه
Loop quantum gravity corrections to gravitational wave dispersion
Cosmological tensor perturbations equations are derived for Hamiltonian cosmology based on Ashtekar’s formulation of general relativity, including typical quantum gravity effects in the Hamiltonian constraint as they are expected from loop quantum gravity. This translates to corrections of the dispersion relation for gravitational waves. The main application here is the preservation of causalit...
متن کاملOn the constraint algebra of quantum gravity in the loop representation
Although an important issue in canonical quantization, the problem of representing the constraint algebra in the loop representation of quantum gravity has received little attention. The only explicit computation was performed by Gambini, Garat and Pullin for a formal point-splitting regularization of the diffeomorphism and Hamiltonian constraints. It is shown that the calculation of the algebr...
متن کاملSpherically Symmetric Quantum Geometry: Hamiltonian Constraint
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and Lorentzian Hamiltonian constraints. The construction fits completely into the general scheme available in loop quantum gravity for the quantization of the full theo...
متن کاملString theory in a vertex operator representation: a simple model for testing loop quantum gravity
The loop quantum gravity technique is applied to the free bosonic string. A Hilbert space similar to loop space in loop quantum gravity as well as representations of diffeomorphism and hamiltonian constraints on it are constructed. The string in this representation can be viewed as a set of interacting relativistic particles each carrying a certain momentum. Two different regularizations of the...
متن کاملLattice knot theory and quantum gravity in the loop representation
We present an implementation of the loop representation of quantum gravity on a square lattice. Instead of starting from a classical lattice theory, quantizing and introducing loops, we proceed backwards, setting up constraints in the lattice loop representation and showing that they have appropriate (singular) continuum limits and algebras. The diffeomorphism constraint reproduces the classica...
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 1997