QG1 - Loop Quantum Gravity |
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Speaker |
Lewandowski, Jerzy |
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Coauthors |
Zhang, Cong; Lewandowski, Jerzy; Ma, Yongge |
| Talk Title |
On the Hamiltonian operator in loop quantum gravity |
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Abstract |
Although the physical Hamiltonian operator can be constructed in the deparametrized model of loop quantum gravity coupled to a scalar field, its property is still unknown. This open issue is attacked in this paper by considering an operator Hˆv representing the square of the physical Hamiltonian op- erator acting nontrivially on a two-valent vertex of spin networks. The Hilbert space Hv preserved by the graphing changing operator Hˆv is consist of spin networks with a single two-valent non-degenerate vertex. The matrix element of Hˆv are explicitly worked out in a suitable basis. It turns out that the operator Hˆv is essentially self-adjoint, which implies a well-defined physical Hamiltonian operator in Hv for the deparametrized model. |
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