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this manuscript is dedicated to the memory of gerald e. brown who was my ph . d. thesis advisor , a mentor in my professional career and a lifelong friend . i first met gerry in the fall of 1972 when i was a graduate student in stony brook . he just returned from nordita . he summoned me to his office one day and asked me if i could do some calculation for him . the problem is calculating the spectrum of two nucleons in the orbital @xmath0 with a delta function interaction.the next day , i went to show him my results . he had a look and said `` the gap between the @xmath1 and @xmath2 states is a factor of 2 of that between @xmath2 and @xmath3 . ok , you can work for me now . '' i did not know it was a test to help him decide whether he wanted to take me on as his research assistant . gerry is well known for many insightful quotations about physics . let me relate one which is attributed to him and it may not have been recorded in a written form before . during the opening talk at one few body conference , gerry was quoted to have said `` in classical physics , you can not solve three - body problem . with quantum mechanics , you can not solve two - body problem and with relativistic quantum mechanics , you can not solve one - body problem . in quantum field theory , you do nt know how to solve the vacuum . '' following gerry s logic , we can now append his quote by `` with the advent of string theory , you no longer know where the vacuum is . '' i have learned many - body theory and laudau s fermi - liguid theory under gerry and my ph . d. thesis was on a self - consistent rpa calculation of nuclear giant resonances on hatree - fock ground states . in the later years , i have followed gerry to work on chiral soliton model of the nucleon , particularly the skyrmion . the many intriguing properties of the nucleon both theoretically and experimentally have led me to work on lattice quantum chromodynamics ( qcd ) calculation since the late eighties .    from 1995 to 2009 , we have been meeting in caltech every january as part of a contingent of theory guests , courtesy of bob kckeown and of the kellogg lab . during these visits , gerry would explain to me his work in black holes and heavy ion collisions and i would update him on the progress in lattice qcd . over the years , i would like to think that i have inherited part of his extraordinary enthusiasm and love for physics through osmosis and i have been influenced greatly by his way of dissecting and tackling a complex problem through intuition , backed by estimation . it is natural to extend the study from nuclear structure to nucleon structure , especially when there is an excellent tool in lattice qcd . i am indebted to gerry for introducing me to the fascinating world of nuclear and nucleon structures . i would like take this opportunity to thank him for his encouragement and support over the years . historically , the study of nuclear structure started out from models like the liquid - drop model , the collective models and the shell model . the modern approaches include many - body theory , green s function monte carlo and lattice effective theory calculation . similarly , the study of nucleon structure progressed from quark model , mit bag model , chiral soliton model , qcd sum rules , instanton liquid model to the more recent lattice qcd calculation . the latter is an _ ab initio _ euclidean path - integral calculation of qcd with controllable statistical and systematic errors . i will make a comparison between the many - body theory approach to nuclear structure and the lattice qcd approach to nucleon structure . i will draw some parallels of the two approaches and point out some differences . many - body theory is a non - relativistic quantum field theory , while qcd is a relativistic quantum field theory . as such , concepts like valence and sea degrees of freedom , collective phenomenon , and vacuum polarization are common , albeit in different contexts . in the case of nucleus , the first order of approximation is the mean - field description of the ground state of fermi sea , such as the shell model or the hartree - fock approximation as depicted in fig . [ hf ] and the nucleon quasi- particle and -hole states around the fermi sea interact via an effective interaction . this is analogous to the quenched approximation of lattice qcd where the partition function is approximated by the gauge action only without the fermion determinant as depicted in fig . nucleon properties are calculated with the multi - point correlation functions with the 3-quark interpolation field for the source and sink of the nucleon at distant time slices in the pure gauge background . more refined approaches to nuclear structure to take into account the particle - hole excitation include single particle renormalization with particle - phonon coupling  @xcite and kuo - brown interaction of the valence nucleons via core excitation of phonons  @xcite . these are illustrated in fig . [ kb_core ] . on the nucleon structure side , the analogy would be the incorporation of the dynamical fermions in the gauge background field with quark loops in the vacuum which represent the fermion determinant in the partition function . this is drawn schematically in fig . [ lattice_df ] . we shall show that there are parallel developments of the same concepts in dynamics as well as classification of degrees of freedom in many - body theory and qcd , since both are quantum field theories . in section  [ collectivity ] , we shall discuss collectivity in these two theories . the z - graph in nuclear structure and the corresponding connected sea partons will be compared in section  [ z - cs ] . the core polarization will be contrasted with disconnected sea contribution in section  [ core - polarization ] . finally , we will present the latest lattice calculation to reveal the quark and glue components of the proton spin in section  [ spin ] . giant resonances in nuclei with large electric and magnetic transition rates can be qualitatively understood as a collective excitation of many particle - hole states in gerry s schematic model  @xcite . they have been successfully described in the random phase approximation ( rpa ) on hatree - fock ground states  @xcite . the rpa diagrams are illustrated in fig . [ rpa ] .        in qcd , the fact that the experimental mass of @xmath4 is much larger than all the other nambu - goldstone bosons is known as the @xmath5 problem and is believed to be related to the @xmath5 anomaly of the divergence of the flavor - singlet axial current . the resolution in the context of large @xmath6 has been given by witten  @xcite and veneziano  @xcite . in fact , the veneziano s diagrammatic formulation as illustrated in fig . [ veneziano ] is the same as gerry s schematic model for the degenerate particle - hole states . in the @xmath5 case , the collective upward lift from the @xmath7 and @xmath8 ` would - be ' nambu - goldstone bosons is due to the constant coupling related to the topological susceptibility of the pure gauge theory . we see that even though the physics contents of the giant resonance and the @xmath5 problem are different , both are the results of collectivity as is the case of bcs superconductivity . therefore , it is natural to employ similar formulations to tackle them . problem in veneziano s diagramatic approach . ] in many - body theory with time - ordered bethe - goldstone diagrams , one inevitably encounters z - graphs as demonstrated in fig . this refers to the part of the diagram where the a hole line is still connected to the valence particle lines when the interaction lines are cut . this is in contrast to the particle - hole bubble in the left diagram where the hole line is disconnected from the valence particle lines when the interaction lines are cut . this distinction of the ` connected hole ' and ` disconnected hole ' diagrams had not been introduced in the classification of the parton degrees of freedom until the surprisingly large gottfired sum rule violation was discovered in the deep inelastic scattering ( dis ) experiment by the nmc collaboration  @xcite . the gottfried sum rule  @xcite , @xmath9/x   = 1/3 $ ] , was obtained under the assumption of a symmetric @xmath10 and @xmath11 sea  @xcite . the nmc measurement of @xmath12 implies that the assumption of a symmetric @xmath10 and @xmath11 sea was invalid and the @xmath13-integrated difference of the @xmath10 and @xmath11 sea is @xmath14 dx = 0.148 \pm 0.039 $ ] . this striking result from the nmc was subsequently checked using an independent experimental technique . from measurements of the drell - yan cross section ratios of @xmath15 , the na51  @xcite and the fermilab e866 @xcite experiments clearly observed the @xmath10 and @xmath11 difference in the proton sea over the kinematic range of @xmath16 . [ hadonic_tensor ]    in order to understand the origin of this large difference between @xmath17 and @xmath18 , an euclidean path - integral description of the hadronic tensor @xmath19 for deep inelastic scattering was formulated  @xcite . in the bjorken limit , there are three gauge invariant and topologically distinct diagrams , as shown in fig . 1 . the various lines in fig . 1 represent the quark propagators from the source of the nucleon interpolation field at time @xmath20 to the sink time at @xmath21 and the currents are inserted at @xmath22 and @xmath23 . we first note that fig . [ cs ] , where the quarks propagate backward in time between @xmath22 and @xmath23 , corresponds to contributions from the anti - partons which we refer as ` connected - sea ' ( cs ) @xmath24 and @xmath25 . in contrast , the time - forward propagating quarks in fig .  [ val+cs ] correspond to valence and cs partons @xmath26 and @xmath27 , where the valence is defined as @xmath28 and @xmath29 . finally , fig . [ ds ] gives the the disconnected sea ( ds ) @xmath30 and @xmath31 for since it contains both forward and backward propagating quarks . the nomenclature of connected and disconnected seas follows from those in the time - ordered perturbation theory cs is the higher fock - state component in the z - graphs where the quark lines associated with the current insertions are connected to the valence quark lines ; whereas , the ds corresponds to vacuum polarization .    we should point out a fine difference between the cs from fig . [ cs ] and the connected hole in the z - graphs as illustrated in fig . [ z ] . in the path - integral diagram in fig . [ cs ] , the anti - quarks between the currents at @xmath22 and @xmath23 are pre - existing , i.e. they are in the nucleon wavefunction and exist before @xmath22 and after @xmath23 just as the case in fig . [ ds ] so that dis is measuring the parton density . they are not pair - produced by the hard photon from the lepton - nucleon scattering . the existence of the cs is easily revealed in the path - integral approach owing to the fact that it is a time - ordered formulation as are the bethe - goldstone diagrams . in this sense , [ cs ] can be considered a generalized z - graph . similarly , fig . [ ds ] can be considered a ` direct diagram ' in the bethe - goldstone sense ; while fig . [ cs ] , by the same token , can be considered the ` exchange diagram ' to reflect the fact that quarks are fermions .    in the isospin limit where @xmath32 , it is proved  @xcite that the ds do not contribute to the gottfried sum rule violation . the isospin symmetry breaking is small and can not explain the large observed violation . rather , the majority of the violation could only come from the cs . we see from figs . [ val+cs ] and  [ cs ] that the cs and the valence are tangled together in one flavor trace . hence , there is no isospin symmetry between @xmath24 and @xmath25 since the state of the proton , being made up of two valence @xmath33 and one valence @xmath34 , is not an isospin singlet state . furthermore , we see that while @xmath33 and @xmath34 have both cs and ds , strange and charm have only the ds . as far as the small-@xmath13 behavior is concerned , there is only reggeon exchange for the flavor non - singlet valence and cs , so the small-@xmath13 behavior for the valence and cs partons is @xmath35 on the other hand , there is flavor - singlet pomeron exchange in addition to the reggeon exchange for the ds partons , thus their small @xmath13 behaviors are @xmath36 since the cs is in the same connected insertions as the valence , it evolves like the valence ; whereas , the ds evolves differently in that it has an additional pair - creation kernel from the gluon  @xcite . while the difference of @xmath37 and @xmath38 can be obtained from @xmath39 , there is not yet a well - established way to directly obtain @xmath40 and , for that matter , separately @xmath37 and @xmath38 from experiments . we have shown a way to achieve this separation with a combination of experiments , the global fit of pdf , and a lattice calculation of the momentum fraction @xmath41 in the di in fig . the recent hermes semi - inclusive dis experiment of kaon production on deuteron  @xcite has produced the strangeness parton distribution function @xmath42 at @xmath43 . we have used this data , combined with the ratio of the lattice calculation of the strange and @xmath44 momentum fractions in the disconnected insertion , and @xmath45 from the globally fitted parton distribution function ( pdf ) , to extract @xmath40 in the following formula @xmath46 at @xmath47 , where @xmath48 is from the ct10 pdf  @xcite which contains both the cs and ds . the strange parton distribution @xmath42 is from the hermes data and @xmath49 is the ratio of the strange momentum fraction to that of the @xmath44 in the disconnected insertion in a lattice calculation with dynamical fermions  @xcite @xmath50 in extracting the cs in eq . ( [ udcs ] ) , we have assumed that the strange parton distribution is proportion to that of @xmath51 so that the proportional constant is @xmath49 . in this way , the cs @xmath52 is obtained in eq . ( [ udcs ] ) by subtracting the ds from the total @xmath48 from ct10 pdf . obtained from is plotted together with @xmath53 from e866 drell - yan experiment   and from sidis hermes experiment  .,title="fig : " ]     we plot the distribution function evaluated with eq . ( [ udcs ] ) , multiplied by the momentum fraction , i.e. @xmath54 in fig . [ csupmd ] together with @xmath55 from e866 drell - yan measurement  @xcite at @xmath56 and from semi - inclusive dis hermes measurement  @xcite at @xmath57 . we see that @xmath58 from eq . ( [ udcs ] ) is peaked at medium @xmath59 , the same way as @xmath53 from e866 and . this is consistent with the expectation that the small-@xmath13 of cs , like the valence , behaves as @xmath60 as we alluded to earlier ; so that , when cs is multiplied with @xmath13 , it would be peaked at medium @xmath13 , in contrast to that of the ds , e.g. @xmath61 from the hermes experiment . furthermore , we note that @xmath58 is generally larger than @xmath53 in this @xmath13-range as it should and is larger by a factor @xmath62 4 at the peak . we also plot @xmath63 , @xmath64 and @xmath65 from ct10 in fig . [ csu+d ] to show that the cs and ds have very different @xmath13-dependence . the different shapes of cs and ds are in good agreement with the expectation discussed earlier . this agreement lends support to the approach we have adopted . it is interesting to note that should a very different value of @xmath49 be used , the @xmath13-dependence of cs and ds would no longer agree with expectation . obtained from is plotted together with @xmath66 from ct10 and @xmath67 which is taken to be @xmath68.,title="fig : " ]     besides having different small @xmath13 behavior , the cs and ds evolve differently in the evolution equation  @xcite . the cs evolves the same way as the valence , while the the ds evolution has an additional contribution from the gluon splitting . the global analyes of pdfs have not yet incorporated the separate evolutions for cs and ds . in improving the magnetic moment calculation of one particle outside the closed shell , the core - polarization has been considered which involves the particle - hole excitation as depicted in fig . this is referred to as the arima - horie effect  @xcite in the nuclear physics literature , as shown in fig . [ core ] .        in the case of lattice qcd , the nucleon form facts are calculated through the 3-point functions in fig . [ 3pt ] . the connected insertion in fig . [ ci ] contains the valence and the cs , while fig . [ di ] contains the ds . it is the latter that corresponds to the core polarization in the nuclear structure . for deep inelastic scattering , the valence and cs contributions from fig . [ val+cs ] and fig . [ cs ] have merged into the moment calculation of fig . [ ci ] under the operator product expansion ( it is the short - distance taylor expansion in euclidean path - integral formulation ) . on the other hand , the ds parton and anti - parton contributions in fig . [ ds ] has become the sum of di moments in fig .  [ di ] . we have done a complete calculation of the quark and glue momenta and angular momenta in the proton  @xcite . these include the quark contributions from both the connected and disconnected insertions . the quark disconnected insertion loops are computed with @xmath69 noise ,  and the signal - to - noise is improved with unbiased subtractions . the glue operator is comprised of gauge - field tensors constructed from the overlap operator . the calculation is carried out on a @xmath70 quenched lattice at @xmath71 for wilson fermions with @xmath72 ,  and @xmath73 which correspond to pion masses at @xmath74 ,  and @xmath75  mev ,  respectively . the chirally extrapolated @xmath33 and @xmath34 quark momentum / angular momentum fraction is found to be @xmath76 ,  the strange momentum / angular momentum fraction is @xmath77 ,  and that of the glue is @xmath78 .  the previous study of quark spin on the same lattice revealed that it carries a fraction of @xmath79 of proton spin . the orbital angular momenta of the quarks are then obtained from subtracting the spin from their corresponding angular momentum components . we find that the quark orbital angular momentum constitutes @xmath80 of the proton spin with almost all of it coming from the disconnected insertions .    in table [ tab : chiral ] ,  we list the quark momentum fractions @xmath81 for the connected insertion ( ci ) ( @xmath33 and @xmath34 ) and disconnected insertion ( di ) ( @xmath44 and @xmath82 ) as well as that of the glue . we also list the corresponding @xmath83 and total angular momenta fraction @xmath84 for each quark flavor and glue . these values are obtained at @xmath85  gev in @xmath86 scheme after perturbative renormalization and mixing between the quark and glue operators  @xcite . .renormalized values in @xmath86 scheme at @xmath87  gev . [ cols="^,^,^,^,^,^,^",options="header " , ]      and @xmath82 quarks.,title="fig : " ]    we illustrate the composition of proton spin in a pie chart in fig .  [ pie ] . the total quark spin constitutes 25(12)% and the glue also gives 28(8)% . the rest ( 47(13)% ) comes from the quark orbital angular momentum . since the @xmath33 and @xmath34 quark orbital angular momenta in the connected insertion ( i.e.  valence ) almost cancel , almost all of the quark orbital angular momentum comes from the disconnected insertion ( i.e.  vacuum polarization ) . we have used the momentum and angular momentum sum rules to obtain the renormalization constants for the lattice quark and glue energy - momentum tensor operators and used perturbative renormalization and mixing between the quark and glue operators to quote our final numbers in the @xmath86 scheme at @xmath87  gev . this is the first time that a complete calculation on the decomposition of the proton momentum and spin is carried out . now that we have gone through the complete calculation in the quenched approximation , the next step in to carry out the same calculations with valence overlap fermion on @xmath88-flavor dynamical domain - wall fermion gauge configurations on several lattices with different lattice spacings and sea quark masses so that we can obtain definitive results of the proton spin components at the physical pion mass and the continuum limit with realistic dynamical quarks in the vacuum in order to compare with experiments and make predictions . one of the quantities to calculate is the quark spin and the most challenging part is the disconnected insertion . we first calculated the quark loop for the axial - vector current and found that , contrary to the pseudoscalar and scalar cases , it is not dominated by the low modes . as a result , one needs a large number of noises to control the statistical error of the high modes . instead of increasing the number of noises , we take another approach . we shall calculate the axial - vector matrix element from the anomalous ward identity @xmath89 where @xmath90 is the local topological charge operator . for the overlap fermion , the topological charge is given by the overlap dirac operator , i.e. + we see from the r.h.s of eq . ( [ awi2 ] ) that the renormalization of the pseudoscalar density is canceled by the renormalization of the quark mass for overlap fermion and there is no renormalization for the topological term due the index theorem as obeyed by the @xmath90 defined by the overlap operator . therefore , calculating the r.h.s . ( [ awi2 ] ) gives the non - perturbatively renormalized axial - vector matrix element which is the quark spin . we show our preliminary results on the topological charge contribution whose signal is coded in the slope of the figure . .,title="fig : " ]    the slope is @xmath91 . this is done on the @xmath92 lattice with 100 configurations and both the valence and sea quarks are at pion mass of 330 mev . this is the contribution of the anomaly to the quark spin for each flavor and at @xmath93 . when the @xmath94 extrapolation to @xmath95 and chiral extrapolation to the physical pion are carried out , we expect the number to be larger . the pseudoscalar density contribution turns out to the very small . we are analyzing them with more configurations and with more nucleon sources . a statistical error of 15% is targeted . production is ongoing for the two @xmath96 lattices with lattice spacings of @xmath97 and @xmath98 fm . when the continuum and physical pion mass limits are taken , we should have a better picture on the quark spin in the proton . we see that nuclear structure in many - body theory and lattice qcd calculation of nucleon structure share many conceptual similarities in the classification of fermion degrees of freedom and collective phenomena . however , there is a significant difference in that the nucleon structure involves explicit glue contributions which are absent in the study of nuclear structure . furthermore , there are triangle anomaly and trace anomaly in qcd which have significant consequences in quark spin and nucleon mass . these are novel and challenging features in the study of nucleon structure both theoretically and experimentally . i thank my colleagues in the @xmath99 collaboration for the lattice results . the research is supported partially by the u.s . department of energy grant de - fg05 - 84er40154 and the center for computational sciences of university of kentucky .
similarities between nuclear structure study with many - body theory approach and nucleon structure calculations with lattice qcd are pointed out . 
 we will give an example of how to obtain the connected sea partons from a combination of the experimental data , a global fit of parton distribution functions and a lattice calculation . 
 we also present a complete calculation of the quark and glue decomposition of the proton momentum and angular momentum in the quenched approximation . 
 it is found that the quark orbital angular momentum constitutes about 50% of the proton spin .    nuclear structure , nucleon structure , quantum chromodynamics , quark and glue momentum and angular momentum 21.60.jz , 24.10.cn , 24.30 . 
 cz , 12.38 . 
 gc , 12.38.-t