Quantization of Length in Spaces with Position-Dependent Noncommutativity

We present a novel approach to quantizing the length in noncommutative spaces with positional-dependent noncommutativity. The method involves constructing ladder operators that change the length not only along a plane but also along the third direction due to a noncommutative parameter that is a combination of canonical/Weyl-Moyal type and Lie algebraic type. The primary quantization of length in canonical-type noncommutative space takes place only on a plane, while in the present case, it happens in all three directions. We establish an operator algebra that allows for the raising or lowering of eigenvalues of the operator corresponding to the square of the length. We also attempt to determine how the obtained ladder operators act on different states and work out the eigenvalues of the square of the length operator in terms of eigenvalues corresponding to the ladder operators. We conclude by discussing the results obtained.Comment: 14 pages, 1 figur

Remarks on the Formulation of Quantum Mechanics on Noncommutative Phase Spaces

We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and also with canonically conjugate momenta. With a postulated normalized distribution function in the quantum domain, the square of the Dirac delta density distribution in the classical case is properly realised in noncommutative phase space and it serves as the quantum condition. With only these inputs, we pull out the entire formalisms of noncommutative quantum mechanics in phase space and in Hilbert space, and elegantly establish the link between classical and quantum formalisms and between Hilbert space and phase space formalisms of noncommutative quantum mechanics. Also, we show that the distribution function in this case possesses 'twisted' Galilean symmetry.Comment: 25 pages, JHEP3 style; minor changes; Published in JHE

On the Quantization of Length in Noncommutative Spaces

We consider canonical/Weyl-Moyal type noncommutative (NC) spaces with rectilinear coordinates. Motivated by the analogy of the formalism of the quantum mechanical harmonic oscillator problem in quantum phase-space with that of the canonical-type NC 2-D space, and noting that the square of length in the latter case is analogous to the Hamiltonian in the former case, we arrive at the conclusion that the length and area are quantized in such an NC space, if the area is expressed entirely in terms of length. We extend our analysis to the 3-D case and formulate a ladder operator approach to the quantization of length in 3-D space. However, our method does not lend itself to the quantization of spacetime length in 1+1 and 2+1 Minkowski spacetimes if the noncommutativity between time and space is considered. If time is taken to commute with spatial coordinates and the noncommutativity is maintained only among the spatial coordinates in 2+1 and 3+1 dimensional spacetime, then the quantization of spatial length is possible in our approach

Using Quantum hybrid join prediction model to predict future trajectory motion during transit train movement

Predicting future train motion from the yard to the main track via an autonomous driving train is an essential task in a terminal railway station. Existing models fail to address the multiple agents that cross the track as the train transits. Still, there is available research in this area, such as how to predict scene-compliant trajectories across multiple agents jointly. The number of agents significantly increases prediction space as the number of challenges grows exponentially. This study focuses on joint motion prediction between an interacting agent and a transit train. The complex joint prediction problem is divided into marginal sub-prediction issues. In the joint prediction space where the marginal prediction model and conditional prediction model are processed, our Quantum Hybrid Joint Prediction (QHJP) model effectively classifies both influencers and reactors. The proposed model combined the interacting agent features to improve prediction likelihood at the joint relative motion. We test and analyse our model's effectiveness as subjected to the acquired database from publicly real-world surveillance camera records from terminal railway junctions. We recreate a simulation view of an authentic, interactive agent scenario and compare the evaluation result with the well-known prediction benchmark Waymo Open Motion (WOM) dataset for experimental purposes