Second quantization and gauge invariance

量子哈密顿-雅可比量子化与形状不变性

Quantum Hamilton-Jacobi Quantization and Shape Invariance

本文证明常规势的可加形状不变性与未破缺超对称性足以保证其在量子哈密顿-雅可比量子化框架中可解，从而扩展了该方法的适用范围。

On the canonical quantization of the electromagnetic field and the emergence of gauge invariance

In the framework of the canonical quantization of the electromagnetic field, we impose as primary condition on the dynamics the positive definiteness of the energy spectrum. This implies that (Glauber) coherent states have to be considered for the longitudinal and the scalar photon fields. As a result we obtain that the relation holds which in the traditional approach is called the Gupta-Bleuler condition. Gauge invariance emerges as a property of the physical states. The group structure of the theory is recognized to be the one of $SU(2) \otimes SU(1,1)$.

Fuzzy Topology, Quantization and Gauge Invariance

Dodson-Zeeman fuzzy topology considered as the possible mathematical framework of quantum geometric formalism. In such formalism the states of massive particle m correspond to elements of fuzzy manifold called fuzzy points. Due to their weak (partial) ordering, m space coordinate x acquires principal uncertainty dx. It's shown that m evolution with minimal number of additional assumptions obeys to schroedinger and dirac formalisms in norelativistic and relativistic cases correspondingly. It's argued that particle's interactions on such fuzzy manifold should be gauge invariant.

Time and energy operators in the canonical quantization of special relativity

Based on Lorentz invariance and Born reciprocity invariance, the canonical quantization of Special Relativity (SR) is shown to provide a unified origin for: i) the complex vector space formulation of Quantum Mechanics (QM); ii) the momentum and space commutation relations and the corresponding representations; iii) the Dirac Hamiltonian in the formulation of Relativistic Quantum Mechanics (RQM); iv) the existence of a self adjoint Time Operator that circumvents Pauli's objection.

电阻量子化作为对称不变性的结果

Quantization of resistivity as consequence of symmetry invariance

本文通过分析朗道规范下电磁场中电子的薛定谔方程，证明需同时考虑两个守恒广义动量算符才能完整描述系统，并构建基态，发现其在幺正变换下不变时电阻量子化为冯·克利青常数的整数倍。

Gauge invariance and the vacuum state

Quantum field theory is assumed to be gauge invariant. It is shown that for a Dirac field the assumption of gauge invariance impacts on the way the vacuum state is defined. It is shown that the conventional definition of the vacuum state must be modified to take into account the requirements of gauge invariance.