Generalized Uncertainty Principle, Modified Dispersion Relation and Barrier Penetration by a Dirac Particle
详细信息 查看全文
- 作者：Sumit Ghosh
- 关键词：Generalised uncertainty principle ; Modified dispersion relation ; Klein’s paradox
- 刊名：International Journal of Theoretical Physics
- 出版年：2015
- 出版时间：March 2015
- 年：2015
- 卷：54
- 期：3
- 页码：736-748
- 全文大小：456 KB
- 参考文献：1. Amelino-Camelia, G.: Int. J. Mod. Phys. D 11, 35-0 (2002). arXiv:gr-qc/0012051: Phys. Lett. B 510, 255-263 (2001) arXiv:hep-th/0012238v1 CrossRef
2. Amati, D., Ciafaloni, M., Veneziano, G.: Phys. Lett. B 216, 41-7 (1989) CrossRef
3. Maggiore, M.: Phys. Lett. B 319, 83-6 (1993). arXiv:hep-th/9309034 CrossRef
4. Kempf, A., Mangano, G., Mann, R.B.: Phys. Rev. D 52, 1108-118 (1995). arXiv:hep-th/9412167 CrossRef
5. Girelli, F., Livine, E.R., Oriti, D.: Nuc. Phys. B 708, 411-33 (2005). arXiv:gr-qc/0406100 CrossRef
6. Hossenfelder, S.: Phys. Rev. D 73, 105013 (2006). arXiv:hep-th/0603032 CrossRef
7. Hossenfelder, S.: Class. Quant. Grav. 23, 1815-821 (2006). arXiv:hep-th/0510245 CrossRef
8. Hossenfelder, S.: Class. Quant. Grav. 25, 038003 (2008). arXiv:0712.2811 CrossRef
9. Chang, L.N., Lewis, Z., Minic, D., Takeuchi, T.: Adv. High Energy Phys. 2011, 493514 (2011). arXiv:hep-th/1106.0068
10. Hossenfelder, S.: Living Rev. Relativ. 16, 2 (2013). arXiv:gr-qc/1203.6191
11. Panes, B.: Eur. Phys. J.C 72, 1930 (2012). arXiv:hep-ph/1112.3753v3 CrossRef
12. Amelino-Camelia, G., Arzano, M., Ling, Y., Mandanici, G.: Class. Quant. Grav. 23, 2585-606 (2006). arXiv:gr-qc/0506110 CrossRef
13. Maggiore, M.: Phys. Lett. B 304, 65 (1993). arXiv:hep-th/9301067 CrossRef
14. Scardigli, F.: Phys. Lett. B 452, 39 (1999). arXiv:hep-th/9904025 CrossRef
15. Banerjee, R., Ghosh, S.: Phys. Lett. B 688, 224-29 (2010). arXiv:gr-qc/1002.2302 CrossRef
16. Hossenfelder, S., Bleicher, M., Hofmann, S., Ruppert, J., Scherer, S., St?cker, H.: Phys. Lett. B 575, 85-9 (2003). arXiv:hep-th/
文摘
We have studied the energy band structure of a Dirac particle in presence of a generalised uncertainty principle (GUP). We start from defining a modified momentum operator and derive corresponding modified dispersion relation (MDR) and GUP. Apart from the forbidden band within the range ±m, m being the mass of the particle, we find the existence of additional forbidden bands at the both ends of the spectrum. Such band structure forbids a Dirac particle to penetrate a potential step of sufficient height (?em class="a-plus-plus">E P , E P being Planck energy). This is also true for massless particle. Unlike the relativistic case, a massless particle also can reflect from a barrier of sufficient height. Finally we discuss about the Klein’s paradox in presence of the GUP.