An Alternative Commutation Relation Between Position and Momentum Operators of Massless Particles

Generalized proof of uncertainty relations in terms of commutation relation and interpretation based on action function

The uncertainty principle is the most important for the foundations of quantum mechanics but it still remains failed to reach a consensus of its interpretation, which gives rise to debates upon its physical nature. In this work, we address the problem of its foundation from a different aspect to present an alternative formulation for proving the uncertainty relations in a general way in terms of commutation relations and action function. The relationship between the de Broglie relation and the uncertainty principle is studied from a new angle. As a result, it is demonstrated that the de Brogli…

Relativistic dispersion relation and putative metric structure in noncommutative phase-space

The deformation of the relativistic dispersion relation caused by noncommutative (NC) Quantum Mechanics (QM) is studied using the extended phase-space formalism. The introduction of the additional commutation relations induces Lorentz invariance violation. It is shown that this deformation does not affect the propagation speed of free massless particles. From the deformation of the dispersion relation for massless particles, gamma ray burst data is used to establish an upper bound on the noncommutative parameter, $η$, namely $\sqrtη \lesssim 10^{-12} \,\mathrm{eV/c}$. Additionally, a putative …

Phonon-induced Floquet second-order topological phases protected by space-time symmetries

The co-existence of spatial and non-spatial symmetries together with appropriate commutation/anticommutation relations between them can give rise to static higher-order topological phases, which host gapless boundary modes of co-dimension higher than one. Alternatively, space-time symmetries in a Floquet system can also lead to anomalous Floquet boundary modes of higher co-dimensions, presumably with alterations in the commutation/anticommutation relations with respect to non-spatial symmetries. We show how a coherently excited phonon mode can be used to promote a spatial symmetry with which t…

Position and spin in relativistic quantum mechanics

The problem of the position and spin in relativistic quantum mechanics is analyzed in detail. It is definitively shown that the position and spin operators in the Foldy-Wouthuysen representation (but not in the Dirac one) are quantum-mechanical counterparts of the classical position and spin variables. The probabilistic interpretation is valid only for Foldy-Wouthuysen wave functions. The relativistic spin operators are discussed. The spin-orbit interaction does not exist for a free particle if the conventional operators of the orbital angular momentum and the rest-frame spin are used. Alterna…

Photons in the Quantum World

Einstein's photo-electric effect allows us to regard electromagnetic waves as massless particles. Then, how is the photon helicity translated into the electric and magnetic fields perpendicular to the direction of propagation? This is an issue of the internal space-time symmetries defined by Wigner's little group for massless particles. It is noted that there are three generators for the rotation group defining the spin of a particle at rest. The closed set of commutation relations is a direct consequence of Heisenberg's uncertainty relations. The rotation group can be generated by three two-b…

PDM creation and annihilation operators of the harmonic oscillators and the emergence of an alternative PDM-Hamiltonian

The exact solvability and impressive pedagogical implementation of the harmonic oscillator creation and annihilation operators make it a problem of great physical relevance and the most fundamental one in quantum mechanics. So would be the position dependent mass oscillator for the position dependent mass quantum mechanics. We, hereby, construct the position dependent mass creation and annihilation operators for the position dependent mass oscillator via two different approaches. First, via von Roos position dependent mass Hamiltonian and show that the commutation relation between the position…

光锥弦的粗糙与光滑

The Rough with the Smooth of the Light Cone String

本文通过光锥弦中粗糙算子R的定义域与旋转群表示的冲突，证明无质量态上R与SO(D-1)酉表示不相容，从而使D=26临界维数的代数推导失效。

动量与位置的同时测量及仪器外尔-海森堡群

Simultaneous Momentum and Position Measurement and the Instrumental Weyl-Heisenberg Group

该研究从同时测量概念出发求解微分几何问题，提出7维的仪器外尔-海森堡群IWH作为通用测量仪器，为基于正变换的量子理论提供基础，其POVM可替代能量量子化。