Band structure in the polymer quantization of the harmonic oscillator

被引：15

作者：

Fernando Barbero G, J. ^{[1
,2
]}

Prieto, Jorge ^{[3
]}

Villasenor, Eduardo J. S. ^{[2
,3
]}

机构：

[1] CSIC, Inst Estruct Mat, E-28006 Madrid, Spain

[2] Univ Carlos III Madrid, Unidad Asociada IEM CSIC, Inst Univ Gregorio Millan Barbany, Grp Teorias Campos & Fis Estadist, Madrid, Spain

[3] Univ Carlos III Madrid, Inst Gregorio Millan, Grp Modelizac & Simulac Numer, E-28911 Leganes, Spain

来源：

CLASSICAL AND QUANTUM GRAVITY | 2013年 / 30卷 / 16期

关键词：

BACKGROUND INDEPENDENT QUANTIZATIONS; PERIODIC SCHRODINGER-OPERATORS; SCALAR FIELD; QUANTUM; REPRESENTATIONS; L2(BR);

D O I：

10.1088/0264-9381/30/16/165011

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

We discuss the detailed structure of the spectrum of the Hamiltonian for the polymerized harmonic oscillator and compare it with the spectrum in the standard quantization. As we will see the non-separability of the Hilbert space implies that the point spectrum consists of bands similar to the ones appearing in the treatment of periodic potentials. This feature of the spectrum of the polymeric harmonic oscillator may be relevant for the discussion of the polymer quantization of the scalar field and may have interesting consequences for the statistical mechanics of these models.

引用

页数：15

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