Topic
Quantum geometry
About: Quantum geometry is a research topic. Over the lifetime, 3739 publications have been published within this topic receiving 140706 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, it was shown that the non-commutativity in quantum Hall system may get modified by the self-adjoint extension of the corresponding Hamiltonian leading to a family of noncommutative geometries.
Abstract: It is shown that the non-commutativity in quantum Hall system may get modified. The self-adjoint extension of the corresponding Hamiltonian leads to a family of non-commutative geometries labeled by the self-adjoint extension parameters. We explicitly perform an exact calculation using a singular interaction and show that, when projected to a certain Landau level, the emergent non-commutative geometries of the projected coordinates belong to a one parameter family. There is a possibility of obtaining the filling fraction of fractional quantum Hall effect by suitably choosing the value of the self-adjoint extension parameter.
Posted Content•
TL;DR: In the light of a recent novel definition of a relativistic quantum theory as discussed by the authors, we ask ourselves the question what it would mean to make the gravitational field itself dynamical.
Abstract: In the light of a recent novel definition of a relativistic quantum theory [1, 3, 4], we ask ourselves the question what it would mean to make the gravitational field itself dynamical. This could lead to a couple of different viewpoints upon quantum gravity which we shall explain carefully; this paper expands upon some ideas in [2] and again confirms ones thought that we are still far removed from a (type one) theory of quantum gravity.
Posted Content•
TL;DR: In this article, a non-commutative generalisation of the Hamilton-Jacobi equation for relativistic particles is proposed, and it can be argued that such a formulation is equivalent to standard quantum mechanics.
Abstract: It has earlier been argued that there should exist a formulation of quantum mechanics which does not refer to a background spacetime. In this paper we propose that, for a relativistic particle, such a formulation is provided by a noncommutative generalisation of the Hamilton-Jacobi equation. If a certain form for the metric in the noncommuting coordinate system is assumed, along with a correspondence rule for the commutation relations, it can be argued that this noncommutative Hamilton-Jacobi equation is equivalent to standard quantum mechanics.