• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Gravity and Spin Forces in Gravitational Quantum Field Theory?

    2018-08-02 07:35:40YueLiangWu吳岳良andRuiZhang張睿
    Communications in Theoretical Physics 2018年8期
    關(guān)鍵詞:張睿

    Yue-Liang Wu(吳岳良)and Rui Zhang(張睿)

    1Key Laboratory of Theoretical Physics,Institute of Theoretical Physics,Chinese Academy of Sciences,Beijing 100190,China

    2School of Physical Sciences,University of Chinese Academy of Sciences,No.19A Yuquan Road,Beijing 100049,China

    3International Center for Theoretical Physics Asia-Pacific(ICTP-AP),University of Chinese Academy of Sciences,Beijing 100049,China

    AbstractIn the new framework of gravitational quantum field theory(GQFT)with spin and scaling gauge invariance developed in Phys.Rev.D 93(2016)024012-1,we make a perturbative expansion for the full action in a background field which accounts for the early inflationary universe.We decompose the bicovariant vector fields of gravifield and spin gauge field with Lorentz and spin symmetries SO(1,3)and SP(1,3)in biframe spacetime into SO(3)representations for deriving the propagators of the basic quantum fields and extract their interaction terms.The leading order Feynman rules are presented.A tree-level 2 to 2 scattering amplitude of the Dirac fermions,through a gravifield and a spin gauge if eld,is calculated and compared to the Born approximation of the potential.It is shown that the Newton’s gravitational law in the early universe is modified due to the background field.The spin dependence of the gravitational potential is demonstrated.

    Key words:gravifield,spin gauge field,background field,quantum gravity,tensor projection operators,scattering amplitudes,modified Newton’s law

    1 Introduction

    The gravitational quantum field theory(GQFT)with spin and scaling gauge invariance was developed in Refs.[1–2]to overcome the long term obstacle between the general theory of relativity(GR)and quantum mechanics.In fact,there has been enormous efforts on the theory beyond Einstein’s theory since the GR was established by Einstein in 1915.[3]The metric describing the geometry of the spacetime are commonly factorized linearly to explore the quantum structure of gravity and its interaction with matter fields,[4?5]and the Ricci scalar has been shown to be the key of the dynamics of gravity.The property of GR with spin and torsion was investigated in Refs.[6–8]where the totally antisymmetric coupling of the torsion to spin was presented.The general quadratic terms of the 2-rank tensor fields that satisfy the ghost-free and locality conditions were discussed in Ref.[9].With the tool named tensor projection operators developed in Ref.[10],which projects the SO(1,3)tensor representation to the components of different SO(3)representations,the general propagators and gauge freedoms were investigated and extrapolated to a more general case including propagating torsion.[11]The totally antisymmetric part and its renormalizability was anayzed in Ref.[12].

    Recently,a new framework of gravitational quantum field theory(GQFT)was proposed to treat the gravitational interaction on the same footing as electroweak and strong interactions,[1?2]where a biframe spacetime is initiated,namely,the locally flat non-coordinate spacetime and the globally flat Minkowski spacetime,a basic gravifield is defined on the biframe spacetime as a bicovariant vector field which is in general a 16-component field.The spin gauge field and scaling gauge field are introduced to keep the action invariant under a local SP(1,3)×SG(1)gauge transformation.A non-constant background solution has been obtained,which may account for the inflationary behaviour of the early universe.In a proceeding work,a more general action for a hyperunified field theory(HUFT)under the hyper-spin gauge and scaling gauge symmetries was proposed[13]to merge all elementary particles into a single hyper-spinor field and unify all basic forces into a fundamental interaction governed by a hyperspin gauge symmetry.A background solution remains to exist.In such an HUFT,it enables us to demonstrate the gravitational origin of gauge symmetry as the hypergravifield plays an essential role as a Goldstone-like field.The gauge-gravity and gravity-geometry correspondences lead to the gravitational gauge-geometry duality.It has been shown that a general conformal scaling gauge symmetry in HUFT results in a general condition of coupling constants,which eliminates the higher derivative terms due to the quadratic Riemann and Ricci tensors,so that the HUFT will get rid of the so-called unitarity problem caused by the higher order gravitational interactions.To demonstrate explicitly,in the present paper,we consider the gravitational interactions of gravifield and spin gauge field only in four dimensional case with a background field solution.Expanding the full action under such a background field,it is natural to extract the dynamics and interactions of the quantum fields.The interactions among these fields will reflect the gravitational behavior in the early universe.

    2 Action Expansion in a Non-Constant Background Field

    Let us start from a basic action by simply taking four dimentional spacetime,i.e.,D=4,from the hyperunified field theory(HUFT)[13]in hyper-spacetime,

    The tensors are taken the general forms presented in Ref.[13]

    The quantized field are expressed as:

    We can expand the action(1)and collect the leading order interactions and quadratic terms.As the quadratic term of the quantum gravifield includes a non-constant coefficientit is useful to absorb it into the field via a field-rede finition

    The final quadratic terms are given by:

    There are other terms,which involves two quantum fields,but with higher orders of the background field,we present them in the Appendix A.In the early universe,the background field ?(x)is sufficiently small,so that we can ignore the effect of those terms and only consider the quadratic terms in Eq.(2).

    Though the propagators can hardly be read from the action,we can utilize the tensor projection operators to decompose the spin components of the tensor fields,and then derive their propagators.The scaling gauge field decouples from the Dirac spinors,so we would not include it in our present considerations.We shall discuss the details in Sec.3.We can also get the leading-order interaction terms,which are given in the appendix B.Notice that we have absorbed the gauge coupling constant gh,which depends on the normalization of coefficients g1,g2and g4.We shall do a field rede finition after some normalization of the propagator in Sec.5 and turn the interactions to a usual form of gauge interactions.

    3 Tensor Projection Operators and Propagators of Gravifield and Spin Gauge Field as Well as Scalar Field

    The SO(1,3)tensor-like fields hμaand ?μabcan be decomposed into different SO(3)spin-parity components:Following Ref.[9],we shall de fine the tensor projection operatorswhere the subscripts f1and f2denoting the field type,the superscripts J and P label the spin and parity.The tensor projection operators satisfy the following relations:

    with the de finition

    To be specific,we write down the explicit forms for the tensor projection operator of the 2+component of the gravifield

    with the de finition

    and the tensor projection operator of the totally antisymmetric part of the spin gauge field ?μab,

    The explicit forms of other tensor projection operators are presented in the appendix C.

    In general,the tensor projection operators have the following properties,

    Thus we can write the quadratic terms of the action in terms of the tensor projection operators as follows,

    The field equations of the field typecan be expressed by tensor projection operators as:

    The explicit forms of the coefficient matrices are given by

    It is obvious that most of the matrices are degenerate,and these degeneracies indicate certain symmetries of the quadratic terms[11]relevant to unphysical degrees of freedom.When considering only the tree-level calculations,we do not need to know the exact gauge- fixing terms and gauge transformations by introducing the Faddeev-Popov ghosts.Instead,we can just apply the specific gauge- fixing conditions by setting the constraints

    without breaking the field equations,and neglect the corresponding lines in the coefficient matrices.Thus we only need to invert the“reduced” matrices and get the propagators.

    The resulting propagators are given as follows in the specific gauge:

    In general,when treating the fields χμaand ?μabas Yang-Mills gauge fields in GQFT,we can simply add the usual gauge- fixing terms for the gauge-type gravifield χμaand the spin gauge field ?μab.For simplicity,we take the following explicit forms for their gauge fixing conditions

    In such a case,the coefficient matrices of the field equations are given by

    Except for the 1+component of the gravifield,all other coefficient matrices are non-degenerate.Thus we are able to inverse the matrices by requiring

    and get the propagators:

    It is seen that in this case the propagator of the gravifield recovers the same one as the case without adding gauge fixing condition,while the propagator of the spin gauge field is modified for the spin 1 component with even parity,which is relevant to the total antisymmetric part of spin gauge field.

    It is noticed that there is an intersection term ??h,which is caused as the choice of h and ? is not orthogonal.To avoid such a complication,it is useful to rede fine the quantum field

    so that the propagator of the field Hμabecomes

    which is compatible with the propagator in the usual linear gravity approach[5]up to a gauge term pμpν/p2.If we take the gauge coefficients λ,to be 3/2,the explicit form of the H-H propagator is

    When taking the gauge fixing parameters as follows

    the explicit form of the ?-? propagator is

    so that the highest order pole in the propagator isterm,which behaves like a Yang-Mills gauge field propagator.In the following section,we will use the rede fined symmetric quantum gravifield to calculate the physical observable.

    4 Gravitational Scattering Amplitude of Dirac Spinor and Modified Newton’s Law with Background Field

    Let us now focus on the gravitational interaction between the Dirac spinor field Ψ in the early universe.The leading order vertex of the fermion involves the background field.

    In the momentum space,the background scaling factor is given by

    where ?kμ≡ ?/?kμ.Corresponding to Feynman rules shown in Figs.1 and 2.

    Fig.1 3-vertex for f-f-h.The dashed line connected to the cross is the background.

    Fig.2 3-vertex for ?-?-h.The dashed line connected to the cross is the background.

    Note that in calculating the fermion-fermion scatter-ing,the gamma matrix in the vertex is contracted with the two external spinors,which satisfies the equationSo that the couplings to ? do not contribute to the tree-level diagrams.For the same reason,the third term from the H propagator does not contribute to the result,either.

    The tree level amplitude of the two-fermion scattering,with in-state momenta p1and p2,and out-state momenta p3and p4,is shown in Fig.3

    Fig.3 Tree diagram for 2-fermion scattering via gravifield.

    The main purpose is to check the newtonian potential in the early universe with the existence of background field.For the case that all fields are massless,we cannot take a non-relativistic limit to simplify the amplitude.Let us first check the cross section of this scattering process to contract all the spinors.After integrating the momenta of the propagator,the amplitude in Eq.(34)becomes:

    The derivatives of δ(p)can be expressed as some functions multiplied by δ(p),thus we can write the second line in Eq.(35)to the following general form

    Then our result of the scattering amplitude,except for the overall coefficient and F(p1?p3)term that are related to the background field,is consistent with the leading order result shown in Ref.[14].If we were working in another gauge if xing condition,the difference would be terms proportional to qμqν/q2,contracted with the vertex will gives the termboth of which are vanishing because of the on-shell condition of the external fermions.So our result is indeed gauge independent.

    The squared matrix element,after throwing all the spin information,is:

    we can simplify Eq.(36)into the follow form

    As long as the two massless fermions are not in the same direction,we can always make a Lorentz boost to a centerof-energy frame,so thatWhen taking the weak interaction limit that θ→ 0,we have

    In comparison with the Born approximation of the cross section[16]

    To compare our result with those from the usual Newtonian potential,we identify the factorwith the coefficient of the Einstein equation 8πG.So the relation between αEand Newtonian gravitational constant GNis

    Then we obtain the potential in the momentum space as:

    The leading term will contribute to a 1/r potential in the coordinate space.Such a term coincides with the Newton’s law,but it is modified by a factorwhich depends on the size of the inverse of scaling factorIn the early universe,the scaling factor is much smaller,thus the gravitational potential can become much stronger.The modified termcontains the structure of the derivatives of delta functions,we shall investigate its effect elsewhere.

    Note that the coefficient 16πGNis four times than the gravitational potential for the massive Dirac fermions.This is because we are working on the massless Dirac fermions.When considering the Dirac fermion getting a mass from spontaneous symmetry breaking,a mass term will be generated.In a unitary scaling gauge condition detχ=1,we need to consider the change of the spinor structure,and an additional

    from the third term(30)of the graviton propagator.The massive Dirac fermion allows us to take a non-relativistic approximation

    The leading order and next-to-leading-order contributions fromis found to be

    The leading term for μ =0 requires r=r′,which together with Eq.(42)enables us to get a factor 1/4 for the potential(50).The next-to-leading-order term forμ=0 comes from the expansion of E

    The next-to-leading order fromμ=i can be simplified to

    the spinor formalism can be re-expressed as a four-vector

    Substituting it into the expression of the amplitude Eq.(34)

    we can obtain the total contribution up to next-to-leading order,

    So the potential for massive fermions is

    Ignoring the kinematic energies,the next-to-leading order effect is proportional to the inner product of two particles,

    If we consider the anti-fermion,its spinor structure is

    and the vertex would have a minus sign from ?(p2+p4)μ.The vertex spinor contraction is

    So the there was only an overall minus sign from the momentum,and will be compensated by the commutation of the fermion operator in the Wick contraction,thus the amplitude does not flip sign.The only possible difference lies in spin of the anti-fermion η?σiη.Thus we may use a separate spin notation to distinguish particle and antiparticle

    So the next-to-leading order effect between fermion and anti-fermion is

    Let us now consider the special case that the two massless ingoing particles are in the same direction.Suppose that their momenta are chosen as follows

    As the overall δ4(p1?p3+p2?p4)guarantees the momentum conservation,the outgoing momenta must be in the same direction.In this case,all the momenta are in the same direction,they are null vectors.So that their product gives zero,namely s=t=u=0.As a consequence,the cross-section becomes vanishing.

    5 Scattering Amplitude of the Dirac Spinor via the Spin Gauge Field

    It is interesting to consider the scattering amplitude of Dirac spinor via the spin gauge field.The leading order spin gauge interaction of Dirac spinor is given by the totally antisymmetric coupling of the spin gauge field.The vertex Feynman rule in Fig.4 can be derived from the last term in Eq.(33).

    Fig.4 3-vertex for f-f-?.

    The propagator of the totally antisymmetric part of the spin gauge field is taken the following form

    We may rede fine the coupling constants[13]

    and rede fine the spin gauge field and replace the vertex

    The Dirac spinor scattering amplitude via the spin gauge field is shown in Fig.5.

    Fig.5 Tree diagram for 2-fermion scattering via spin gauge field.

    If the Dirac spinor acquires a mass from some symmetry breaking,we may take the non-relativistic limit of this amplitude.Different from the Coulomb potential where the leading contribution comes fromthe γ5in Eq.(57)will lead to

    It is shown that the potential for 2-fermion scattering without spin change can be attractive(repulsive)for aligned spins and repulsive(attractive)for opposed spins,which relies on the sign of the coefficient(1?αW+βW)whether it is positive 1 ? αW+ βW> 0(negative 1?αW+βW<0).The potential of the totally antisymmetric field was studied in a different way in Ref.[6],which arrived at the case of negative coefficient 1?αW+βW<0.Such an interaction is independent of the background field.In the early universe,the scaling factor is so small that the gravitational effect becomes dominant to the cross sections.The spin gauge coupling is no longer significant,its cross section is found to be:

    When taking the weak interaction limit that θ → 0,we have

    which leads to a 1/r potential in the coordinate space.

    6 Conclusion

    We have investigated the gravitational interactions with the background field in the framework of GQFT.The full action of the GQFT with spin gauge and scaling gauge transformations has been expanded in a nonconstant background field.To the leading order gravitational interactions in GQFT,we have derived the Feynman rules for the propagators and interacting vertices of the quantum fields by using the tensor projection operators.The quantum gravifield has been rede fined to be normalized and diagonal,which leads to an interaction between the Dirac spinor and scalar fields.In the leading order,the scalar interaction with the Dirac spinor vanishes when the massless Dirac spinor are on-mass shell as the external fields.We have calculated the tree-level two Dirac spinors scattering through the gravitational interaction and analyzed its amplitude and cross section.Besides the modified term from the derivative of delta function,the overall amplitude is proportional to the inverse of the scaling factors,which implies that the gravitational potential is much stronger in the early universe.The spin dependence of the gravitational potential in the nonrelativistic case has been analyzed.We have also calculated the interaction between the Dirac spinor and the totally antisymmetric part of the spin gauge field at the leading order,which is similar to the result of the scattering through a vector field,but with a flip sign in the amplitude due to the property of axial vector,resulting in a spin gauge force,which depends on the sign of the coefficient in its quadratic terms.

    Appendix A Next-to-Leading Order Quadratic Terms

    We have presented the leading order quadratic terms in the context,the following are the higher order terms of the background field.We de fine

    The next-to-leading order quadratic terms for hμa-? are:

    The terms for hμa-wνare:

    The terms for ?-wμare:

    The terms for wμ-wνare:

    The terms for ?-? are:

    The terms for hμa-hνbare:

    Appendix B Leading Order Vertices

    We have presented the leading order vertices of the fermions in the context,the following are the 3-vertices for the spin gauge field ?μabwith the rede fined field ? by a coupling constant:

    For the gravifield hμainteractions,we have

    For the scalar field ?,except the pure scalar interaction term 4λs?3?,and the scalar and gravifield interactions are found to be,

    for h-?-h,and

    for h-?-?,as well as

    or h-w-?,and

    for h-h-w.With coupling to the spin gauge field,we obtain

    for h-?-?.More interactions include

    Appendix C Tensor Projection Operators

    Here we show the exact expression of projection operatorsfor the spin gauge field,gravifield and scalar,in which we have used the de finitionsfor short.

    猜你喜歡
    張睿
    A Lost Ball
    I ’m a Dog Lover
    廣播操比賽
    小主人報(2022年7期)2022-08-16 06:59:28
    小主人報(2022年5期)2022-04-01 01:12:02
    The dilemma and development of industrial design in contemporary life
    秋天到了
    Wechat, life in our Palm
    張睿 主宰人生, 睿不可當(dāng)
    我的新發(fā)現(xiàn)
    我的開心事
    国产一区二区三区视频了| 亚洲中文字幕一区二区三区有码在线看| 欧美日韩精品网址| 亚洲电影在线观看av| 三级国产精品欧美在线观看| 两个人的视频大全免费| 老司机在亚洲福利影院| 成人国产综合亚洲| 日本黄色视频三级网站网址| 91久久精品电影网| 日本免费一区二区三区高清不卡| 久久精品人妻少妇| 国产精品影院久久| 午夜a级毛片| 久久久久久九九精品二区国产| 别揉我奶头~嗯~啊~动态视频| 十八禁人妻一区二区| 亚洲欧美激情综合另类| 国产成人啪精品午夜网站| 一级毛片女人18水好多| 国产探花在线观看一区二区| netflix在线观看网站| 亚洲中文日韩欧美视频| 日韩欧美在线乱码| 久久精品国产亚洲av涩爱 | 欧美在线一区亚洲| 成年人黄色毛片网站| 黄色片一级片一级黄色片| 国产亚洲欧美98| 丰满人妻熟妇乱又伦精品不卡| 99精品在免费线老司机午夜| 国产精品乱码一区二三区的特点| 亚洲国产高清在线一区二区三| 国产av在哪里看| 婷婷六月久久综合丁香| 亚洲av成人av| 色吧在线观看| 亚洲av成人av| 午夜福利免费观看在线| 99国产精品一区二区蜜桃av| av视频在线观看入口| 麻豆成人午夜福利视频| 在线观看免费视频日本深夜| 亚洲最大成人中文| 三级男女做爰猛烈吃奶摸视频| 久久香蕉精品热| 99视频精品全部免费 在线| 国产精品1区2区在线观看.| 夜夜看夜夜爽夜夜摸| 午夜免费成人在线视频| 国产蜜桃级精品一区二区三区| 九色成人免费人妻av| 精品久久久久久久毛片微露脸| 欧美黑人巨大hd| 在线看三级毛片| 国产高清videossex| 国产亚洲精品综合一区在线观看| 老司机在亚洲福利影院| 日韩人妻高清精品专区| 国产主播在线观看一区二区| 久久精品综合一区二区三区| 一个人观看的视频www高清免费观看| 麻豆成人午夜福利视频| 欧美乱码精品一区二区三区| 午夜福利欧美成人| 91久久精品国产一区二区成人 | 国产伦在线观看视频一区| 无遮挡黄片免费观看| 叶爱在线成人免费视频播放| 99热这里只有精品一区| 全区人妻精品视频| 国产一区二区亚洲精品在线观看| 国产麻豆成人av免费视频| 中文字幕高清在线视频| 搡老岳熟女国产| 狠狠狠狠99中文字幕| 精品午夜福利视频在线观看一区| 久久久久国产精品人妻aⅴ院| 国产真实伦视频高清在线观看 | 身体一侧抽搐| 婷婷六月久久综合丁香| а√天堂www在线а√下载| 别揉我奶头~嗯~啊~动态视频| 国产精品久久久久久久久免 | 国产成人a区在线观看| 亚洲avbb在线观看| 午夜久久久久精精品| 成人精品一区二区免费| 天天一区二区日本电影三级| 亚洲中文字幕一区二区三区有码在线看| 香蕉av资源在线| 午夜福利视频1000在线观看| 亚洲中文日韩欧美视频| 国产成人系列免费观看| 日韩欧美精品免费久久 | 亚洲人成网站在线播放欧美日韩| 成人特级av手机在线观看| 精品无人区乱码1区二区| 午夜日韩欧美国产| 午夜福利欧美成人| 久9热在线精品视频| 亚洲av中文字字幕乱码综合| 国产精品香港三级国产av潘金莲| 99在线视频只有这里精品首页| 国产精品野战在线观看| 欧美av亚洲av综合av国产av| 久久精品91无色码中文字幕| 午夜免费男女啪啪视频观看 | 丰满人妻熟妇乱又伦精品不卡| 中文亚洲av片在线观看爽| 亚洲精品色激情综合| 别揉我奶头~嗯~啊~动态视频| 一区二区三区国产精品乱码| 51国产日韩欧美| 国产成人av激情在线播放| 国产精品综合久久久久久久免费| 亚洲av第一区精品v没综合| 欧美中文综合在线视频| 午夜福利高清视频| а√天堂www在线а√下载| 成人18禁在线播放| 国产爱豆传媒在线观看| 最近最新中文字幕大全免费视频| 亚洲精品乱码久久久v下载方式 | 在线免费观看不下载黄p国产 | 中文字幕高清在线视频| 无遮挡黄片免费观看| 99久久无色码亚洲精品果冻| 国产aⅴ精品一区二区三区波| 国产一区二区三区视频了| 欧美性猛交黑人性爽| 首页视频小说图片口味搜索| 国产精品98久久久久久宅男小说| 久久久久久久午夜电影| 99热这里只有精品一区| 九九在线视频观看精品| 美女大奶头视频| eeuss影院久久| 丁香欧美五月| 麻豆国产97在线/欧美| 男人的好看免费观看在线视频| 国模一区二区三区四区视频| 欧美又色又爽又黄视频| 日韩欧美精品v在线| 亚洲精品粉嫩美女一区| a在线观看视频网站| 国产淫片久久久久久久久 | 亚洲国产精品合色在线| 免费av不卡在线播放| 美女大奶头视频| 日日干狠狠操夜夜爽| 色视频www国产| 99热这里只有是精品50| 亚洲va日本ⅴa欧美va伊人久久| 欧美一区二区精品小视频在线| 国产精品影院久久| 亚洲激情在线av| 乱人视频在线观看| av女优亚洲男人天堂| 中文在线观看免费www的网站| 欧美日韩瑟瑟在线播放| 2021天堂中文幕一二区在线观| 国产一区二区在线av高清观看| 十八禁人妻一区二区| 久久伊人香网站| 岛国在线观看网站| 国产男靠女视频免费网站| 99在线人妻在线中文字幕| 国产精华一区二区三区| 高清在线国产一区| 成人国产综合亚洲| 热99在线观看视频| 久久久久久久精品吃奶| 色av中文字幕| 婷婷精品国产亚洲av| 午夜a级毛片| 亚洲精华国产精华精| 国产激情欧美一区二区| 国产精品久久久人人做人人爽| 熟女人妻精品中文字幕| 在线a可以看的网站| 19禁男女啪啪无遮挡网站| 国产亚洲欧美98| 女同久久另类99精品国产91| 在线观看美女被高潮喷水网站 | 99热精品在线国产| 草草在线视频免费看| 最近在线观看免费完整版| 国产伦一二天堂av在线观看| АⅤ资源中文在线天堂| 内地一区二区视频在线| 久久精品人妻少妇| 国产亚洲精品久久久com| 欧美乱码精品一区二区三区| 18禁国产床啪视频网站| 少妇的丰满在线观看| 午夜福利在线观看免费完整高清在 | 亚洲欧美日韩无卡精品| a在线观看视频网站| 91九色精品人成在线观看| 国产91精品成人一区二区三区| 狂野欧美白嫩少妇大欣赏| 少妇高潮的动态图| 偷拍熟女少妇极品色| 亚洲国产精品久久男人天堂| 亚洲精品一区av在线观看| 亚洲国产精品成人综合色| 成人欧美大片| 国产主播在线观看一区二区| 国产精品亚洲av一区麻豆| 午夜福利在线观看免费完整高清在 | 一区二区三区免费毛片| 国产又黄又爽又无遮挡在线| 亚洲欧美日韩东京热| 一个人看的www免费观看视频| ponron亚洲| 亚洲国产精品999在线| 丰满乱子伦码专区| 午夜免费激情av| av片东京热男人的天堂| 日韩欧美国产在线观看| 老司机深夜福利视频在线观看| 日本与韩国留学比较| 99国产综合亚洲精品| 97超级碰碰碰精品色视频在线观看| 国产伦在线观看视频一区| 国产成人系列免费观看| 岛国在线免费视频观看| 色av中文字幕| 亚洲色图av天堂| 亚洲美女视频黄频| 最近最新免费中文字幕在线| 久久伊人香网站| 中文亚洲av片在线观看爽| 五月玫瑰六月丁香| 久99久视频精品免费| 午夜日韩欧美国产| 午夜影院日韩av| 嫁个100分男人电影在线观看| 欧美丝袜亚洲另类 | 精品国内亚洲2022精品成人| 香蕉av资源在线| 成人鲁丝片一二三区免费| 精品国产超薄肉色丝袜足j| 日本免费a在线| 高潮久久久久久久久久久不卡| 国产av在哪里看| 俺也久久电影网| 国产探花极品一区二区| or卡值多少钱| 亚洲av中文字字幕乱码综合| 亚洲av成人av| 男女那种视频在线观看| 免费av毛片视频| 桃色一区二区三区在线观看| 国产乱人视频| 俺也久久电影网| 757午夜福利合集在线观看| 国产黄a三级三级三级人| 亚洲国产中文字幕在线视频| 91av网一区二区| 狂野欧美白嫩少妇大欣赏| 亚洲 欧美 日韩 在线 免费| 午夜老司机福利剧场| 亚洲va日本ⅴa欧美va伊人久久| 有码 亚洲区| 国产精品永久免费网站| 国产午夜精品久久久久久一区二区三区 | 欧美日韩乱码在线| 少妇的逼好多水| 国产爱豆传媒在线观看| 国产成年人精品一区二区| 性色av乱码一区二区三区2| 嫩草影视91久久| 在线免费观看的www视频| 午夜免费观看网址| 国产高清有码在线观看视频| 欧美乱妇无乱码| 亚洲av不卡在线观看| 欧美精品啪啪一区二区三区| 国产一区在线观看成人免费| 香蕉丝袜av| 久久精品国产99精品国产亚洲性色| 国产色婷婷99| 精品电影一区二区在线| 天堂√8在线中文| 无人区码免费观看不卡| 成人高潮视频无遮挡免费网站| 草草在线视频免费看| 1024手机看黄色片| 国产亚洲精品综合一区在线观看| 美女免费视频网站| 最后的刺客免费高清国语| 99久久精品一区二区三区| 日本与韩国留学比较| 欧美黑人巨大hd| 国产成人av激情在线播放| 久久久久亚洲av毛片大全| 亚洲av熟女| 天堂网av新在线| 午夜福利18| 国产精品久久视频播放| 国产激情偷乱视频一区二区| 欧美av亚洲av综合av国产av| 午夜福利在线观看吧| 天天一区二区日本电影三级| 精品免费久久久久久久清纯| 国产亚洲精品av在线| 国产三级黄色录像| 亚洲av中文字字幕乱码综合| 成年女人永久免费观看视频| 啦啦啦韩国在线观看视频| 黄片小视频在线播放| 日本在线视频免费播放| 久久久成人免费电影| 国产精品久久久久久久久免 | 好男人电影高清在线观看| 国产精品嫩草影院av在线观看 | 精品久久久久久久久久免费视频| 97超视频在线观看视频| 九色国产91popny在线| 国内揄拍国产精品人妻在线| 国产久久久一区二区三区| www日本黄色视频网| 首页视频小说图片口味搜索| 成人三级黄色视频| 狂野欧美激情性xxxx| 精品人妻1区二区| 精品熟女少妇八av免费久了| 午夜福利在线观看免费完整高清在 | 亚洲成av人片免费观看| 动漫黄色视频在线观看| 久久性视频一级片| 色哟哟哟哟哟哟| 嫁个100分男人电影在线观看| 亚洲专区国产一区二区| 18禁裸乳无遮挡免费网站照片| 亚洲av五月六月丁香网| 一个人观看的视频www高清免费观看| 日本熟妇午夜| av视频在线观看入口| 99国产精品一区二区三区| 听说在线观看完整版免费高清| 免费一级毛片在线播放高清视频| 午夜福利免费观看在线| 亚洲无线观看免费| 中文字幕熟女人妻在线| 香蕉久久夜色| 在线观看美女被高潮喷水网站 | 99久久成人亚洲精品观看| 色在线成人网| 国产真实乱freesex| 国产精品亚洲一级av第二区| 俺也久久电影网| 国产视频一区二区在线看| 日本 欧美在线| 婷婷精品国产亚洲av| 欧美黑人巨大hd| 国产黄片美女视频| 在线观看午夜福利视频| 国产极品精品免费视频能看的| 男插女下体视频免费在线播放| 九九在线视频观看精品| 日韩亚洲欧美综合| 91字幕亚洲| 国产成人av教育| 97碰自拍视频| 性欧美人与动物交配| 久久国产乱子伦精品免费另类| 国产69精品久久久久777片| 国产午夜精品久久久久久一区二区三区 | 在线观看舔阴道视频| 听说在线观看完整版免费高清| 亚洲国产日韩欧美精品在线观看 | 国产黄片美女视频| 午夜免费激情av| 夜夜看夜夜爽夜夜摸| 给我免费播放毛片高清在线观看| 成人av一区二区三区在线看| 精品无人区乱码1区二区| 人人妻,人人澡人人爽秒播| x7x7x7水蜜桃| 亚洲自拍偷在线| 国产精品久久久久久久久免 | 一二三四社区在线视频社区8| 日韩大尺度精品在线看网址| 丰满乱子伦码专区| 国产精品99久久久久久久久| 亚洲黑人精品在线| 日韩中文字幕欧美一区二区| 一级作爱视频免费观看| 99国产极品粉嫩在线观看| 日本黄色片子视频| 亚洲av成人不卡在线观看播放网| 中文字幕精品亚洲无线码一区| 国产三级中文精品| 成人鲁丝片一二三区免费| 18禁黄网站禁片免费观看直播| 色视频www国产| av中文乱码字幕在线| 美女高潮的动态| 亚洲成人中文字幕在线播放| 日韩欧美在线二视频| 婷婷六月久久综合丁香| 国产高清videossex| 97超视频在线观看视频| 看片在线看免费视频| 国产精品自产拍在线观看55亚洲| www日本在线高清视频| 母亲3免费完整高清在线观看| 网址你懂的国产日韩在线| 欧美xxxx黑人xx丫x性爽| 女同久久另类99精品国产91| 午夜精品久久久久久毛片777| 97碰自拍视频| 国产精品久久久久久久久免 | 国产精品免费一区二区三区在线| 免费人成在线观看视频色| 淫秽高清视频在线观看| 欧美精品啪啪一区二区三区| 性色avwww在线观看| 三级国产精品欧美在线观看| 久久久久性生活片| 少妇丰满av| 天堂影院成人在线观看| 国产一区二区在线av高清观看| 9191精品国产免费久久| 99国产精品一区二区蜜桃av| 一区二区三区激情视频| 无人区码免费观看不卡| 亚洲精品成人久久久久久| 性欧美人与动物交配| 免费在线观看亚洲国产| 日本黄色视频三级网站网址| 啪啪无遮挡十八禁网站| 91在线观看av| 国产av不卡久久| 国产又黄又爽又无遮挡在线| 久久亚洲精品不卡| 欧美中文日本在线观看视频| 日韩欧美国产一区二区入口| 国产淫片久久久久久久久 | 制服人妻中文乱码| avwww免费| 亚洲av电影不卡..在线观看| 国产真实伦视频高清在线观看 | 99热只有精品国产| 高清在线国产一区| 少妇丰满av| 丰满人妻熟妇乱又伦精品不卡| 男女床上黄色一级片免费看| 在线观看舔阴道视频| 亚洲aⅴ乱码一区二区在线播放| 国产老妇女一区| 1024手机看黄色片| 亚洲成人精品中文字幕电影| 级片在线观看| 久久久国产精品麻豆| 免费看光身美女| www.www免费av| 日韩免费av在线播放| 亚洲成a人片在线一区二区| 在线观看一区二区三区| 高潮久久久久久久久久久不卡| 一个人免费在线观看的高清视频| 亚洲av五月六月丁香网| 欧美色视频一区免费| 男女午夜视频在线观看| 久久伊人香网站| 免费高清视频大片| 国产免费男女视频| 亚洲五月婷婷丁香| 女人高潮潮喷娇喘18禁视频| 丰满人妻熟妇乱又伦精品不卡| 国产国拍精品亚洲av在线观看 | 九色成人免费人妻av| 亚洲无线观看免费| 一边摸一边抽搐一进一小说| 好男人电影高清在线观看| 欧美一级毛片孕妇| 国产精品一区二区三区四区久久| 搡老熟女国产l中国老女人| 嫩草影院入口| 99久久久亚洲精品蜜臀av| 国产69精品久久久久777片| 国产精品久久久人人做人人爽| 成人欧美大片| 亚洲av熟女| 欧美日韩黄片免| xxxwww97欧美| 高清日韩中文字幕在线| 亚洲午夜理论影院| 欧美成人一区二区免费高清观看| 老熟妇仑乱视频hdxx| 国产精品亚洲av一区麻豆| 午夜免费观看网址| 亚洲午夜理论影院| 久久久久国内视频| 亚洲精品亚洲一区二区| 亚洲精品乱码久久久v下载方式 | 国产精品一区二区三区四区免费观看 | 熟妇人妻久久中文字幕3abv| 黄片大片在线免费观看| 男女午夜视频在线观看| 精品人妻一区二区三区麻豆 | 成人一区二区视频在线观看| а√天堂www在线а√下载| 亚洲色图av天堂| 嫩草影院入口| 女同久久另类99精品国产91| 在线免费观看不下载黄p国产 | 免费看光身美女| 亚洲最大成人手机在线| 亚洲国产精品sss在线观看| av黄色大香蕉| 中文字幕熟女人妻在线| 欧美区成人在线视频| 免费在线观看成人毛片| 久久久成人免费电影| 人人妻人人看人人澡| 亚洲精华国产精华精| 嫩草影视91久久| 欧美国产日韩亚洲一区| or卡值多少钱| 久久香蕉精品热| 夜夜夜夜夜久久久久| 丰满人妻一区二区三区视频av | 国产一区二区亚洲精品在线观看| 99久久九九国产精品国产免费| av女优亚洲男人天堂| 午夜福利欧美成人| 国产激情偷乱视频一区二区| 日本 欧美在线| 此物有八面人人有两片| 中文字幕人妻熟人妻熟丝袜美 | 又紧又爽又黄一区二区| 日本撒尿小便嘘嘘汇集6| 午夜免费观看网址| 一本综合久久免费| 国产亚洲av嫩草精品影院| 男女午夜视频在线观看| 久久久久久久亚洲中文字幕 | 成熟少妇高潮喷水视频| 麻豆国产97在线/欧美| 精品福利观看| 免费在线观看亚洲国产| 国产91精品成人一区二区三区| 国产熟女xx| 青草久久国产| 亚洲精品成人久久久久久| 成人一区二区视频在线观看| 母亲3免费完整高清在线观看| 男人舔奶头视频| 中文在线观看免费www的网站| 国产精品女同一区二区软件 | h日本视频在线播放| 国产中年淑女户外野战色| 香蕉av资源在线| 国产精品亚洲美女久久久| 午夜精品在线福利| 欧美bdsm另类| 在线国产一区二区在线| 日本一二三区视频观看| 国产真人三级小视频在线观看| av专区在线播放| 一区二区三区免费毛片| 色在线成人网| 欧美最黄视频在线播放免费| 99久久无色码亚洲精品果冻| 国产精品影院久久| 亚洲av成人精品一区久久| 成人午夜高清在线视频| 好男人电影高清在线观看| 亚洲天堂国产精品一区在线| 一个人免费在线观看电影| 999久久久精品免费观看国产| 色av中文字幕| 国产精品爽爽va在线观看网站| 国产亚洲精品久久久久久毛片| 成年免费大片在线观看| 国产国拍精品亚洲av在线观看 | 日本a在线网址| 精品国产超薄肉色丝袜足j| 欧美极品一区二区三区四区| 露出奶头的视频| 成年女人看的毛片在线观看| 欧美一级毛片孕妇| 亚洲无线在线观看| 亚洲中文字幕日韩| 成熟少妇高潮喷水视频| 国产一区二区三区在线臀色熟女| 亚洲精品在线美女| 精品久久久久久成人av| 亚洲成人免费电影在线观看| 精品午夜福利视频在线观看一区| 成人特级av手机在线观看| 亚洲国产高清在线一区二区三| 人妻久久中文字幕网| 国产一区二区三区在线臀色熟女| 国产一级毛片七仙女欲春2| 亚洲avbb在线观看| 听说在线观看完整版免费高清| 精品不卡国产一区二区三区| 一级黄片播放器| 波多野结衣高清作品| 国产精品98久久久久久宅男小说| 欧美丝袜亚洲另类 | 久久久久久久久大av| 两性午夜刺激爽爽歪歪视频在线观看| 国产美女午夜福利| 久久久久久久久久黄片| 成人国产综合亚洲| 亚洲成a人片在线一区二区| 变态另类丝袜制服| 国产视频一区二区在线看|