Methods of quantization

Heimo G. Latal, W. Schweiger

Mikhail S. Plyushchay, A. V. Razumov

The relationship between the Dirac and reduced phase space quantizations is investigated for spin models belonging to the class of Hamiltonian systems having no gauge conditions. It is traced out that the two quantization methods may give similar, or essentially different physical results, and, moreover, it is shown that there is a class of constrained systems, which can be quantized only by the Dirac method. A possible interpretation of the gauge degrees of freedom is given. Introduction There are two main methods to quantize the Hamiltonian systems with first class constraints: the Dirac quantization [1] and the reduced phase space quantization [2], whereas two other methods, the path integral method [3, 2] and the BRST quantization [4] being the most popular method for the covariant quantization of gauge-invariant systems, are based on and proceed from them [2, 5]. The basic idea of the Dirac method consists in imposing quantum mechanically the first class constraints as operator conditions on the states for singling out the physical ones [1]. The reduced phase space quantization first identifies the physical degrees of freedom at the classical level by the factorization of the constraint surface with respect to the action of the gauge group, generated by the constraints. Then the resulting Hamiltonian system is quantized as a usual unconstrained system [2]. Naturally, the problem of the relationship of these two methods arises. It was discussed in different contexts in literature [6], and there is an opinion that the differences between the two quantization methods can be traced out to a choice of factor ordering in the construction of various physical operators.

Qiliang Zhang, You Ping Wu, Songping Wang +2 more

With the development of wireless communication technology, the application of the physical layer key generation method based on channel characteristics is becoming more and more widespread. In this method, the selection of quantization algorithm in the quantization stage is particularly important. The poor performance of the initial key will affect the efficiency of key reconciliation, and even cause the failure of the whole key generation method. In the existing quantization algorithms, the quantization level and guard interval are fixed, so the performance of the initial key cannot always be optimized in the face of complex and changeable communication environment. Aiming at the above problems, this paper combines the adaptive adjustment of quantization level and guard interval effectively on the basis of existing multi-bit quantization algorithm. This method continues the method of deleting eigenvalues by index value in multi-bit quantization algorithm, which improves the consistency of initial key. Based on information theory, this method selects optimal quantization level on the premise that the initial key is theoretically error-free under different SNR. This method sets the guard interval based on the average error probability of the eigenvalue and the quantization level, which solves the problem of deleting too many eigenvalues when the SNR is high in the method of setting fixed guard interval. Simulation results show that this method is feasible.

Laure Gouba

The similarity between classical and quantum physics is large enough to make an investigation of quantization methods a worthwhile endeavour. As history has shown, Dirac's canonical quantization method works reasonably well in the case of conventional quantum mechanics over Rn but it may fail in non-trivial phase spaces and also suffer from ordering problems. Affine quantization is an alternative method, similar to the canonical quantization, that may offer a positive result in situations for which canonical quantization fails. In this paper we revisit the affine quantization method on the half-line. We formulate and solve some simple models, the free particle and the harmonic oscillator.