Speaker
Description
Inspired by the resemblance of the Hamiltonian of harmonic oscillator with that of the square of length operator in 2-D space, we propose a method to quantize length and area in 2-D canonical noncommutative space in analogy to the quantization of energy of harmonic oscillator problem. We attempt to extend our method to the case of other canonical noncommutative spaces. In 3-D, we explicitly construct a set of raising and lowering operators along with other operators in such a way that the square of length operator is expressed in terms of the normal ordering of operators. Taking noncommutativity among spatial coordinates in 3D, we solve the eigenvalue equation involving the square of length operator to get the quantization of length from which the quantizations of area and volume are inferred. In Minkowski spacetimes where time and space noncommutes, quantization is not possible in 1+1 and 2+1 dimensions. We also analyze the possibility of quantization of length in 3+1 dimensions when time noncommutes with spatial coordinates.
| Session | Formal Theory |
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