Eigenvalues of the volume operator in loop quantum gravity
نویسنده
چکیده
We present a simple method to calculate certain sums of the eigenvalues of the volume operator in loop quantum gravity. We derive the asymptotic distribution of the eigenvalues in the classical limit of very large spins which turns out to be of a very simple form. The results can be useful for example in the statistical approach to quantum gravity.
منابع مشابه
Discreteness of Area and Volume in Quantum Gravity
We study the operator that corresponds to the measurement of volume, in non-perturbative quantum gravity, and we compute its spectrum. The operator is constructed in the loop representation, via a regularization procedure; it is finite, background independent, and diffeomorphism-invariant, and therefore well defined on the space of diffeomorphism invariant states (knot states). We find that the...
متن کاملar X iv : 0 70 6 . 03 82 v 1 [ gr - q c ] 4 J un 2 00 7 Properties of the Volume Operator in Loop Quantum Gravity II : Detailed Presentation
The properties of the Volume operator in Loop Quantum Gravity, as constructed by Ashtekar and Lewandowski, are analyzed for the first time at generic vertices of valence greater than four. The present analysis benefits from the general simplified formula for matrix elements of the Volume operator derived in [24], making it feasible to implement it on a computer as a matrix which is then diagona...
متن کاملThe Area Operator in the Spherically Symmetric Sector of Loop Quantum Gravity
Utilizing the previously established general formalism for quantum symmetry reduction in the framework of loop quantum gravity the spectrum of the area operator acting on spherically symmetric states in 4 dimensional pure gravity is investigated. The analysis requires a careful treatment of partial gauge fixing in the classical symmetry reduction and of the reinforcement of SU(2)gauge invarianc...
متن کاملThe length operator in Loop Quantum Gravity
The dual picture of quantum geometry provided by a spin network state is discussed. From this perspective, we introduce a new operator in Loop Quantum Gravity – the length operator. We describe its quantum geometrical meaning and derive some of its properties. In particular we show that the operator has a discrete spectrum and is diagonalized by appropriate superpositions of spin network states...
متن کاملAngle and Volume Studies in Quantized Space
The search for a quantum theory of gravity is one of the major challenges facing theoretical physics today. While no complete theory exists, a promising avenue of research is the loop quantum gravity approach. In this approach, quantum states are represented by spin networks, essentially graphs with weighted edges. Since general relativity predicts the structure of space, any quantum theory of ...
متن کامل