To what extent are canonical and coherent state quantizations physically equivalent?

Quantizing Braids and Other Mathematical Objects: The General Quantization Procedure

Extending the methods from our previous work on quantum knots and quantum graphs, we describe a general procedure for quantizing a large class of mathematical structures which includes, for example, knots, graphs, groups, algebraic varieties, categories, topological spaces, geometric spaces, and more. This procedure is different from that normally found in quantum topology. We then demonstrate the power of this method by using it to quantize braids. This general method produces a blueprint of a quantum system which is physically implementable in the same sense that Shor's quantum factoring alg…

Entropy and entanglement in polymer quantization

Polymer quantization is as a useful toy model for the mathematical aspects of loop quantum gravity and is interesting in its own right. Analyzing entropies of physically equivalent states in the standard Hilbert space and the polymer Hilbert space we show that they converge in the limit of vanishing polymer scale. We derive a general bound that relates entropies of physically equivalent states in unitarily inequivalent representations.

Canonical Group Quantization, Rotation Generators and Quantum Indistinguishability

Using the method of canonical group quantization, we construct the angular momentum operators associated to configuration spaces with the topology of (i) a sphere and (ii) a projective plane. In the first case, the obtained angular momentum operators are the quantum version of Poincare's vector, i.e., the physically correct angular momentum operators for an electron coupled to the field of a magnetic monopole. In the second case, the obtained operators represent the angular momentum operators of a system of two indistinguishable spin zero quantum particles in three spatial dimensions. We expli…

非标准Hamilton系统的量子化

Quantization of Nonstandard Hamiltonian Systems

量子化的经典理论，承认一个以上的哈密顿描述被认为是。这是从几何的观点，在量子化水平（几何量子化）和在量子理论的动力学水平。以自旋为1/2的系统为例，说明了所有步骤都能完成。结果表明，量子理论的几何形状对物理上允许的非标准量子理论施加了限制。

Can the canonical quantization be accomplished within the intrinsic geometry?

For particles constrained on a curved surface, how to perform quantization within Dirac's canonical quantization scheme is a long-standing problem. On one hand, Dirac stressed that the Cartesian coordinate system has fundamental importance in passing from the classical Hamiltonian to its quantum mechanical form while preserving the classical algebraic structure between positions, momenta and Hamiltonian to the extent possible. On the other, on the curved surface, we have no exact Cartesian coordinate system within intrinsic geometry. These two facts imply that the three-dimensional Euclidean s…

一维双δ函数势标量场中的有限温度卡西米尔效应

Finite temperature Casimir effect in one-dimensional scalar field with double delta-function potentials

本文研究一维双δ函数势标量场的有限温度卡西米尔效应，采用正则量子化方法计算力与熵，并与Lifshitz理论对比，发现正则量子化给出热力学自洽的正熵。