亚洲免费av电影一区二区三区,日韩爱爱视频,51精品视频一区二区三区,91视频爱爱,日韩欧美在线播放视频,中文字幕少妇AV,亚洲电影中文字幕,久久久久亚洲av成人网址,久久综合视频网站,国产在线不卡免费播放

        ?

        Dirac Oscillator Under the New Generalized Uncertainty Principle From the Concept Doubly Special Relativity

        2019-11-07 02:58:28SargolzaeiporHassanabadiandChung
        Communications in Theoretical Physics 2019年11期

        S.Sargolzaeipor,H.Hassanabadi, and W.S.Chung

        1Faculty of Physics, Shahrood University of Technology, Shahrood, Iran

        2Department of Physics and Research Institute of Natural Science, College of Natural Science, Gyeongsang National University, Jinju 660-701, Korea

        Abstract We discuss one-dimensional Dirac oscillator, by using the concept doubly special relativity.We calculate the energy spectrum by using the concept doubly special relativity.Then, we derive another representation that the coordinate operator remains unchanged at the high energy while the momentum operator is deformed at the high energy so that it may be bounded from the above.Actually,we study the Dirac oscillator by using of the generalized uncertainty principle version and the concept doubly special relativity.

        Key words:Dirac equation, generalized uncertainty principle, doubly special relativity

        1 Introduction

        Very interesting subjects in physics are quantum gravity and quantum groups.The structure and representation theory of the generalized uncertainty principle[1?19]were initially accomplished by Kempf, Mangano, and mann.[20]The generalized uncertainty principle is written by the modified commutation relation between position and momentum operators

        whereMplis the Planck mass andβ0is of the order of the unity.

        The modified commutation relation can be written as[21?23]

        In Eq.(3), K[P]is the generalized uncertainty principle deformation function which reduces to one when the generalized uncertainty principle effect is removed.The standard representation for Eq.(3) is the momentum representation appears as

        where (X, P) implies the position and momentum operators at the high energy while (x, p) the position and momentum operators at the low energy.The momentum operator at the high energy should be bounded from the above if we consider the doubly special relativity.[24?29]Indeed the doubly special relativity says that the momentum has the maximum called a Planck momentum, which is another invariant in the doubly special relativity.

        In this paper, we investigate another representation where the coordinate remains unchanged at the high energy while the momentum is deformed at the high energy so that it may be bounded from the above.Our generalized uncertainty principle model becomes from the concept doubly special relativity.[30?34]This paper is organized as follows:In Sec.2, we study the new generalized uncertainty principle from the concept of doubly special relativity.In Sec.3, we discuss the Dirac equation in one-dimensional.Finally, we present the results in our conclusion.

        2 New Generalized Uncertainty Principle from the Concept of Doubly Special Relativity

        Instead of the representation (4) one can consider the following representation[35]

        wherePis the generalized uncertainty principle momentum.The inverse relation of Eq.(5) becomes

        and by inserting in Eq.(5), one can easily find

        From Eq.(5), we obtain

        Differentiating Eqs.(5), (7) with respect topwe obtain

        Combination of above equations gives

        By substitution of Eq.(7) and Eq.(10) in Eq.(8), we obtain

        Based on the doubly special relativity, we consider the following relation

        whereκis the Planck momentum.Equation (5) gives

        The inverse transformation is

        Equation (6) gives

        In limitp →∞corresponds toP=κ, that there exists the maximum momentum in our model.Then, inserting Eq.(15) into Eq.(11) we have

        which gives the generalized uncertainty principle

        3 The Dirac Oscillator

        The coordinate representation of the algebra (16) is

        The one-dimensional Dirac oscillator for a free fermion is written as (=c=1)

        which

        with Ψ=(ψ, φ)Tin the presence of the coordinate representation Eq.(18), Eq.(19) becomes

        Eq.(21) can be rewritten in terms of following coupled equations

        From these equations we obtain

        Then, the operatorsaanda?act as ladder operators:

        the momentumpand positionxoperators are directly written in terms of the boson operatorsaanda?introduced above with

        Finally, considering an expansion ofφin terms of|n〉Eq.(23) takes the following form

        When 1/κ →0 the well-know relation

        is recovered.[36]The energy(+,?)in Eq.(27)are for particle and antiparticle, respectively.Figure 1 shows plots ofEversusn.We know that the energy decreases due to the generalized uncertainty principle effect.We observe that the behavior of the absolute value of the energy increases with the increasing 1/κ, also, the absolute value of the energy increases with the increasingn.

        Fig.1 Spectrum of energy versus quantum number for different values of the parameter κ.

        4 Conclusion

        In this paper,we studied another representation where the coordinate remains unchanged at the high energy while the momentum is deformed at the high energy so that it may be bounded from the above.We investigated one-dimensional Dirac oscillator then we obtained the energy spectrum by using of generalized uncertainty principle version of the concept doubly special relativity and also especially we tested the energy spectrum in(1/κ →0)case in ordinary results were recovered.

        Acknowledgment

        It is a great pleasure for the authors to thank the referees for helpful comments.

        久久99热国产精品综合| 国产激情视频在线| 亚洲国产人成自精在线尤物| 久久一二区女厕偷拍图| 国产精品v片在线观看不卡| 夜夜高潮夜夜爽国产伦精品| 久久精品国产亚洲av蜜臀| 中文人妻无码一区二区三区| 国产三级c片在线观看| 日韩午夜理论免费tv影院| 免费观看性欧美大片无片| 少妇无码av无码去区钱| 人妻中文字幕一区二区三区| 中国免费看的片| 99精品热这里只有精品| 91精品啪在线看国产网站| 亚洲av无一区二区三区综合| 又色又爽又黄的视频软件app| 久久99精品国产99久久6男男| AⅤ无码精品视频| 视频女同久久久一区二区| 娜娜麻豆国产电影| 正在播放一区| 日韩精品极品视频在线观看蜜桃| 国产三级视频不卡在线观看 | 精彩视频在线观看一区二区三区| 人禽交 欧美 网站| 波多野结衣视频网址| 免费在线av一区二区| 日本在线视频www色| 无码国产色欲xxxxx视频| 国产女同一区二区在线| 一区二区三区蜜桃av| 少妇仑乱a毛片| 日韩欧美国产丝袜视频| 亚洲精品国产熟女久久| 一区二区三区亚洲免费| 亚洲av永久无码精品漫画| 精品午夜福利1000在线观看| 韩国免费一级a一片在线| 水蜜桃在线观看一区二区 |