Light front quantization: Difference between revisions

Revision as of 14:01, 17 August 2020

Revision as of 17:00, 29 September 2020

Line 14:

doi= 10.1016/j.nuclphysbps.2014.05.004

|volume=251–252

|bibcode=2014NuPhS.251..165B|s2cid=117029089 |display-authors=etal}}</ref><ref name="Burkardt">{{ Cite book |

last=Burkardt |first=Matthias |title=Light Front Quantization |

titlechapter= Light front quantization |

journal=[[Advances in Nuclear Physics]] | volume= 23 | pages= 1–74 | year=1996 |

doi= 10.1007/0-306-47067-5_1|arxiv=hep-ph/9505259 |

isbn= 978-0-306-45220-8 |s2cid=19024989 }}</ref><ref name="PhysRep">{{ cite journal |author1=S.J. Brodsky |author2=H.-C. Pauli |author3=S.S. Pinsky |

title= Quantum chromodynamics and other field theories on the light cone |

journal=[[Physics Reports]] | volume= 301 |issue=4–6 | pages= 299–486 | year=1998 |

doi= 10.1016/S0370-1573(97)00089-6 | bibcode=1998PhR...301..299B|arxiv = hep-ph/9705477 |s2cid=118978680 }}</ref>

of [[Quantum field theory|quantum field theories]]

provides a useful alternative to ordinary equal-time

Line 160:

title= The Covariant structure of light front wave functions and the behavior of hadronic form-factors |

journal=[[Physical Review D]] | volume= 69 |issue=7 | page= 076001 | year=2004 |

doi= 10.1103/PhysRevD.69.076001|arxiv = hep-ph/0311218 |bibcode = 2004PhRvD..69g6001B |s2cid=855584 }}</ref>

the eigensolution of the light-front

Hamiltonian. The [[James Bjorken|Bjorken]] kinematic variable <math>x_{bj}</math> of deep

Line 168:

title= BFKL pomeron in the next-to-leading approximation |

journal=[[Physics Letters B]] | volume= 429 |issue=1–2 | pages= 127–134 | year=1998 |

doi= 10.1016/S0370-2693(98)00473-0|arxiv = hep-ph/9802290 |bibcode = 1998PhLB..429..127F |s2cid=15965017 }}</ref>

Regge behavior of structure functions can be

demonstrated from the behavior of light-front wave functions at small <math>x</math>.

Line 184:

title= Exclusive Processes in Perturbative Quantum Chromodynamics |

journal=[[Physical Review D]] | volume= 22 |issue=9 | pages= 2157–2198 | year=1980 |

doi= 10.1103/PhysRevD.22.2157 | bibcode=1980PhRvD..22.2157L|osti=1445541 }}</ref>

<ref name="Efremov:1979qk">{{ cite journal |author1=A. V. Efremov |author2=A. V. Radyushkin |

title= Factorization and Asymptotical Behavior of Pion Form-Factor in QCD |

Line 200:

journal=[[Physical Review Letters]] | volume= 24 |issue=4 | pages= 181–186 | year=1970 |

doi= 10.1103/PhysRevLett.24.181

| bibcode=1970PhRvL..24..181D|osti=1444780 |s2cid=17438828 |url=https://semanticscholar.org/paper/0e7e211f436478c766f3e3a3f957d22e518e15ed }}</ref>

<ref name="West:1970av">{{ cite journal |

author= G. B. West |

Line 210:

title= The Anomalous Magnetic Moment and Limits on Fermion Substructure |

journal=[[Physical Review D]] | volume= 22 |issue=9 | pages= 2236–2243 | year=1980 |

doi= 10.1103/PhysRevD.22.2236 | bibcode=1980PhRvD..22.2236B|osti=1445649 }}</ref>

[[File:ComptonScattering.jpg|thumbnail|right|alt=Compton scattering|

Line 233:

title= Factorization Property of the Deuteron |

journal=[[Physical Review D]] | volume= 33 |issue=9 | pages= 2653–2659 | year=1986 |

doi= 10.1103/PhysRevD.33.2653|pmid=9956950 |bibcode = 1986PhRvD..33.2653B }}</ref>

and (b) the vanishing

of the anomalous gravitomagnetic moment for any Fock state of a

Line 239:

title= Light cone representation of the spin and orbital angular momentum of relativistic composite systems |

journal=[[Nuclear Physics B]] | volume= 593 |issue=1–2 | pages= 311–335 | year=2001 |

doi= 10.1016/S0550-3213(00)00626-X|arxiv = hep-th/0003082 |bibcode = 2001NuPhB.593..311B |s2cid=7435760 }}</ref>

one also can show that a nonzero

[[Anomalous magnetic dipole moment|anomalous magnetic moment]] of a bound state requires nonzero

Line 253:

title= Recursion relations and scattering amplitudes in the light-front formalism |

journal=[[Nuclear Physics B]] | volume= 875 |issue=2 | pages= 368–387 | year=2013 |

doi= 10.1016/j.nuclphysb.2013.07.019|arxiv = 1308.1062 |bibcode = 2013NuPhB.875..368C |s2cid=119214902 }}</ref>

The counting-rule<ref name="Brodsky:1994kg">{{ cite journal |author1=S. J. Brodsky |last2=Burkardt |first2=Matthias |author3=I. Schmidt |

title= Perturbative QCD constraints on the shape of polarized quark and gluon distributions |

journal=[[Nuclear Physics B]] | volume= 441 |issue=1–2 | pages= 197–214 | year=1995 |

doi= 10.1016/0550-3213(95)00009-H|arxiv = hep-ph/9401328 |bibcode = 1995NuPhB.441..197B |s2cid=118969788 }}</ref>

behavior of structure functions

at large <math>x</math> and Bloom-Gilman

Line 275:

title= Final state interactions and single spin asymmetries in semiinclusive deep inelastic scattering |

journal=[[Physics Letters B]] | volume= 530 |issue=1–4 | pages= 99–107 | year=2002 |

doi= 10.1016/S0370-2693(02)01320-5|arxiv = hep-ph/0201296 |bibcode = 2002PhLB..530...99B |s2cid=13446844 }}</ref>

Light-front quantization is thus the natural framework for the

Line 290:

title=Nonperturbative QCD: A Weak coupling treatment on the light front |

journal=[[Physical Review D]] | volume= 49 |issue=12 | pages= 6720–6766 | year=1994 |

doi= 10.1103/PhysRevD.49.6720|pmid=10016996 |arxiv = hep-th/9401153 |bibcode = 1994PhRvD..49.6720W }}</ref>

Light-front considerations of the vacuum as well as

the problem of achieving full [[Lorentz covariance|covariance]] in LFQCD require close

Line 331:

journal=[[Physical Review D]] | volume= 38 |

issue=10 | pages= 3277–3286 | year=1988 |

doi= 10.1103/PhysRevD.38.3277 |
pmid=9959077 |bibcode = 1988PhRvD..38.3277G }}</ref>

<ref name="Marisqq">{{ cite journal |author1=P. Maris |author2=C. D. Roberts |author3=P. C. Tandy |

title=Pion mass and decay constant |

journal=[[Physics Letters B]] | volume= 420 |issue=3–4 | pages= 267–273 | year=1998 |

doi= 10.1016/S0370-2693(97)01535-9|arxiv = nucl-th/9707003 |bibcode = 1998PhLB..420..267M |s2cid=16778465 }}</ref>

<ref name="Brodsky:2012ku">{{ cite journal |author1=S. J. Brodsky |author2=C. D. Roberts |author3=R. Shrock |author4=P. C. Tandy |

title= Confinement contains condensates |

journal=[[Physical Review C]] | volume= 85 |issue=6 | page= 065202 | year=2012 |

doi= 10.1103/PhysRevC.85.065202|arxiv = 1202.2376 |bibcode = 2012PhRvC..85f5202B |s2cid=118373670 }}</ref>

<ref name="CasherSusskind">{{ cite journal |author1=A. Casher |author2=L. Susskind |

title=Chiral magnetism (or magnetohadrochironics) |

Line 380 ⟶ 381:

doi= 10.2307/1968551|bibcode = 1939AnMat..40..149W |

jstor=1968551 |

s2cid=121773411 |

url=https://semanticscholar.org/paper/e7a88a5d0617b5adbefcedccb5e52a12725de6bf }}</ref>

and Bargmann<ref name="bargmann:1954">{{ cite journal |

Line 605 ⟶ 607:

journal=[[Physical Review C]] | volume= 82 |

issue=6 | page= 064001 | year=2010 |

doi= 10.1103/PhysRevC.82.064001|arxiv = 1008.5222 |bibcode = 2010PhRvC..82f4001P }}</ref>|

s2cid=26711947 }}</ref>

demonstrated that

relativistic quantum theories based on different forms of dynamics are

Line 665 ⟶ 668:

title=Quantum field theory on lightlike slabs |

journal=[[Nuovo Cimento]] | volume= A66 |issue=3 | pages= 536–554 | year=1970 |

doi= 10.1007/BF02826338|bibcode = 1970NCimA..66..536L |s2cid=124546775 }}</ref>

<ref name="ullrich:2006">{{ cite journal |author1=P. Ullrich |author2=E. Werner |

title=On the problem of mass-dependence of the two-point function of the real scalar free massive field on the light cone |

journal=[[Journal of Physics A]] | volume= 39 |issue=20 | pages= 6057–6068 | year=2006 |

doi= 10.1088/0305-4470/39/20/029|arxiv = hep-th/0503176 |bibcode = 2006JPhA...39.6057U |s2cid=32919998 }}</ref>

=== Rotational invariance ===

Line 706 ⟶ 709:

journal=[[Physical Review D]] | volume= 41 |

issue=2 | pages= 534–549 | year=1990 |

doi= 10.1103/PhysRevD.41.534 |
pmid=10012359 |bibcode = 1990PhRvD..41..534F }}</ref>

<ref name="fuda:1991">{{ cite journal |

author= M. Fuda |

Line 712 ⟶ 716:

journal=[[Physical Review D]] | volume= 44 |

issue=6 | pages= 1880–1890 | year=1991 |

doi= 10.1103/PhysRevD.44.1880|
pmid=10014068 |bibcode = 1991PhRvD..44.1880F }}</ref>

<ref name="fuda:1994">{{ cite journal |

author= M. Fuda |

Line 724 ⟶ 729:

journal=[[Few Body Systems]] | volume= 27 |

issue=2 | pages= 57–72 | year=1999 |

doi=10.1007/s006010050122|bibcode = 1999FBS....27...57P }}</ref>|

s2cid=120699006 }}</ref>

and the kinematic representation of rotations

Line 799 ⟶ 805:

title=Spin in relativistic quantum theory |

journal=[[Few Body Systems]] | volume= 54 |issue=11 | pages= 1667–1704 | year=2013 |

doi= 10.1007/s00601-012-0526-8 |arxiv = 1208.5840 |bibcode = 2013FBS....54.1667P |s2cid=42925952 }}</ref>

it is only total angular

momentum that requires interactions; the total spin does not

Line 826 ⟶ 832:

title=Model Tests of Cluster Separability In Relativistic Quantum Mechanics |

journal=[[Physical Review C]] | volume= 86 |issue=1 | page= 014002 | year=2012 |

doi= 10.1103/PhysRevC.86.014002|arxiv = 1109.6575 |bibcode = 2012PhRvC..86a4002K |s2cid=41960696 }}</ref>

then the transverse components of

total spin necessarily have an interaction dependence. The result is

Line 972 ⟶ 978:

title=Quantum Electrodynamics and Renormalization Theory in the Infinite Momentum Frame |

journal=[[Physical Review D]] | volume= 8 |issue=12 | pages= 4574–4594 | year=1973 |

doi= 10.1103/PhysRevD.8.4574|bibcode = 1973PhRvD...8.4574B |osti=1442551 }}</ref>

The vacuum state in the instant form defined at fixed <math>t</math> is acausal

Line 1,019 ⟶ 1,025:

title=Explicitly covariant light front dynamics and relativistic few body systems |

journal=[[Physics Reports]] | volume= 300 |issue=5–6 | pages= 215–347 | year=1998 |

doi= 10.1016/S0370-1573(97)00090-2 |arxiv = nucl-th/9804029 |bibcode = 1998PhR...300..215C |s2cid=119329870 }}</ref>),

in which the state vector is defined on the light-front plane of

general orientation:

Line 1,151 ⟶ 1,157:

title=Angular conditions, relations between Breit and light front frames, and subleading power corrections |

journal=[[Physical Review D]] | volume= 67 |issue=11 | page= 116002 | year=2003 |

doi= 10.1103/PhysRevD.67.116002|arxiv = hep-ph/0301213 |bibcode = 2003PhRvD..67k6002C |s2cid=7978843 }}</ref>

<ref name="AC-spin1">{{ cite journal |author1=B. L. G. Bakker |author2=C.-R. Ji |

title=Frame dependence of spin one angular conditions in light front dynamics |

journal=[[Physical Review D]] | volume= 65 |issue=7 | page= 073002 | year=2002 |

doi= 10.1103/PhysRevD.65.073002|arxiv = hep-ph/0109005 |bibcode = 2002PhRvD..65g3002B |s2cid=17967473 }}</ref>

<ref name="AC-spin2">{{ cite journal |

author=B. L. G. Bakker, H.-M.Choi and C.-R. Ji |

Line 1,162 ⟶ 1,168:

issue=11 | page= 116001 | year=2002 |

doi= 10.1103/PhysRevD.65.116001

|arxiv = hep-ph/0202217 |bibcode = 2002PhRvD..65k6001B }}</ref>|

s2cid=55018990 }}</ref>

After satisfying it, the solution obtains the form of a unique superposition of

the states <math>\psi_{lma}(\vec{k},\hat{n})</math> with different eigenvalues

Line 1,206 ⟶ 1,213:

title=Comparison of quantum field perturbation theory for the light front with the theory in lorentz coordinates |

journal=[[Theoretical and Mathematical Physics]] | volume= 112 |issue=3 | pages= 1117–1130 | year=1997 |

doi= 10.1007/BF02583044|arxiv = hep-th/9901110 |bibcode = 1997TMP...112.1117P |s2cid=5441075 }}</ref><ref name="StPete2">{{ cite journal |author1=S.A. Paston |author2=V.A. Franke |author3=E.V. Prokhvatilov |

title=Constructing the light-front QCD Hamiltonian |

journal=[[Theoretical and Mathematical Physics]] | volume= 120 |issue=3 | pages= 1164–1181 | year=1999 |

doi= 10.1007/BF02557241|bibcode = 1999TMP...120.1164P |arxiv=hep-th/0002062 |s2cid=119099826 }}</ref> Glazek-Wilson similarity renormalization-group procedure for Hamiltonians,<ref name="Glazek-Wilson1">{{ cite journal |author1=S. D. Glazek |author2=K. G. Wilson |

title=Renormalization of Hamiltonians |

journal=[[Physical Review D]] | volume= 48 |issue=12 | pages= 5863–5872 | year=1993 |

doi= 10.1103/PhysRevD.48.5863|pmid=10016252 |bibcode = 1993PhRvD..48.5863G |arxiv=hep-th/9706149 |s2cid=39086918 }}</ref><ref name="Glazek-Wilson2">{{ cite journal |author1=S. D. Glazek |author2=K. G. Wilson |

journal=[[Physical Review D]] | volume= 49 |issue=8 | pages= 4214–4218 | year=1994 |

doi= 10.1103/PhysRevD.49.4214

| title=Perturbative renormalization group for Hamiltonians|pmid=10017426 |bibcode = 1994PhRvD..49.4214G }}</ref><ref name="Glazek-Wilson3">{{ cite journal |author1=S. D. Glazek |author2=K. G. Wilson |

journal=[[Physical Review D]] | volume= 57 |issue=6 | pages= 3558–3566 | year=1998 |

doi= 10.1103/PhysRevD.57.3558

| title=Asymptotic freedom and bound states in Hamiltonian dynamics|arxiv = hep-th/9707028 |bibcode = 1998PhRvD..57.3558G |s2cid=16805417 }}</ref> Mathiot-Grange test functions,<ref name="Mathiot-Grange">{{ cite journal |author1=P. Grange |author2=J.-F. Mathiot |author3=B. Mutet |author4=andE. Werner |

title=Taylor-Lagrange renormalization scheme, Pauli-Villars subtraction, and light-front dynamics |

journal=[[Physical Review D]] | volume= 82 |issue=2 | page= 025012 | year=2010 |

doi= 10.1103/PhysRevD.82.025012|arxiv = 1006.5282 |bibcode = 2010PhRvD..82b5012G |s2cid=118513433 }}</ref> Karmanov-Mathiot-Smirnov<ref name="kms2012">{{ cite journal |author1=V.A. Karmanov |author2=J.-F. Mathiot |author3=A.V. Smirnov |

title=Ab initio nonperturbative calculation of physical observables in light-front dynamics. Application to the Yukawa model |

journal=[[Physical Review D]] | volume= 86 |issue=8 | page= 085006 | year=2012 |

doi= 10.1103/PhysRevD.86.085006

| bibcode=2012PhRvD..86h5006K|arxiv = 1204.3257 |s2cid=119000243 }}</ref> realization of sector-dependent renormalization, and determine how to incorporate symmetry breaking in light-front quantization;<ref name="Bender">{{ cite journal |author1=C. M. Bender |author2=S. S. Pinsky |author3=B. van de Sande |

title=Spontaneous symmetry breaking of <math>\phi^4</math> in (1+1)-dimensions in light front field theory |

journal=[[Physical Review D]] | volume= 48 |issue=2 | pages= 816–821 | year=1993 |

doi= 10.1103/PhysRevD.48.816|pmid=10016310 |arxiv = hep-th/9212009 |bibcode = 1993PhRvD..48..816B |s2cid=14265514 }}</ref><ref name="Pinsky2">{{ cite journal |author1=S. S. Pinsky |author2=B. van de Sande |

title=Spontaneous symmetry breaking of (1+1)-dimensional <math>\phi^4</math> theory in light front field theory. 2 |

journal=[[Physical Review D]] | volume= 49 |issue=4 | pages= 2001–2013 | year=1994 |

doi= 10.1103/PhysRevD.49.2001|pmid=10017185 |arxiv = hep-ph/9309240 |bibcode = 1994PhRvD..49.2001P |s2cid=17165941 }}</ref><ref name="Pinsky3">{{ cite journal |author1=S. S. Pinsky |author2=B. van de Sande |author3=J.R. Hiller |

title=Spontaneous symmetry breaking of (1+1)-dimensional <math>\phi^4</math> theory in light front field theory. 3 |

journal=[[Physical Review D]] | volume= 51 |issue=2 | pages= 726–733 | year=1995 |

doi= 10.1103/PhysRevD.51.726|pmid=10018525 |arxiv = hep-th/9409019 |bibcode = 1995PhRvD..51..726P |s2cid=15291034 }}</ref><ref name="Rozowsky:2000gy">{{ cite journal |author1=J. S. Rozowsky |author2=C. B. Thorn |

title= Spontaneous symmetry breaking at infinite momentum without P+ zero modes |

journal=[[Physical Review Letters]] | volume= 85 |issue=8 | pages= 1614–1617 | year=2000 |

doi= 10.1103/PhysRevLett.85.1614 | bibcode=2000PhRvL..85.1614R|arxiv = hep-th/0003301 | pmid=10970571|s2cid=17968437 }}</ref><ref name="Chakrabarti:2003tc">{{ cite journal |author1=D. Chakrabarti |author2=A. Harindranath |author3=L. Martinovic |author4=G. B. Pivovarov |author5=J. P. Vary |

title= Ab initio results for the broken phase of scalar light front field theory |

journal=[[Physics Letters B]] | volume= 617 |issue=1–2 | pages= 92–98 | year=2005 |

doi= 10.1016/j.physletb.2005.05.012|arxiv = hep-th/0310290 |bibcode = 2005PhLB..617...92C |s2cid=119370407 }}</ref><ref name="Kim:2003ha">{{ cite journal |author1=V. T. Kim |author2=G. B. Pivovarov |author3=J. P. Vary |

title= Phase transition in light front <math>\phi^4_{1+1}</math> |

journal=[[Physical Review D]] | volume= 69 |issue=8 | page= 085008 | year=2004 |

doi= 10.1103/PhysRevD.69.085008|arxiv = hep-th/0310216 |bibcode = 2004PhRvD..69h5008K |s2cid=119524638 }}</ref><ref name="Dskulsh">{{ cite journal |author1=U. Kulshreshtha |author2=D. S. Kulshreshtha |author3=J. P. Vary|title= Hamiltonian, Path Integral and BRST Formulations of Large N Scalar $QCD_{2}$ on the Light-Front and Spontaneous Symmetry Breaking |journal=[[Eur. Phys. J. C]]| volume= 75|issue= 4 |page= 174 | year=2015| doi=10.1140/epjc/s10052-015-3377-x|arxiv=1503.06177 | bibcode=2015EPJC...75..174K|s2cid=119102254 }}</ref> this is likely to require an analysis of zero modes and in-hadron condensates.<ref name="Wilson" /><ref name="Nambu" /><ref name="GOR" /><ref name="tHooftVeltman" /><ref name="SVZ" /><ref name="FeynmanQCD2" /><ref name="SSbreaking" /><ref name="GasserLeutwyler" /><ref name="condensates" /><ref name="Marisqq" /><ref name="Brodsky:2012ku" /><ref name="CasherSusskind" />

* Develop computer codes which implement the regularization and renormalization schemes.

Line 1,257 ⟶ 1,264:

title=Solving field theory in one space one time dimension |

journal=[[Physical Review D]] | volume= 32 |issue=8 | pages= 1993–2000 | year=1985 |

doi= 10.1103/PhysRevD.32.1993|pmid=9956373 |bibcode = 1985PhRvD..32.1993P }}</ref>

<ref name="DLCQ2">{{ cite journal |author1=H.-C. Pauli |author2=S. J. Brodsky |

title=Discretized light cone quantization: Solution to a field theory in one space one time dimensions |

journal=[[Physical Review D]] | volume= 32 |issue=8 | pages= 2001–2013 | year=1985 |

doi= 10.1103/PhysRevD.32.2001|pmid=9956374 |bibcode = 1985PhRvD..32.2001P }}</ref>

finite elements, function

expansions,<ref name="Vary:2009gt">{{ cite journal |author1=J. P. Vary |author2=H. Honkanen |author3=J. Li |author4=P. Maris |author5=S. J. Brodsky |author6=A. Harindranath |author7=G. F. de Teramond |author8=P. Sternberg |

title= Hamiltonian light-front field theory in a basis function approach |

journal=[[Physical Review C]] | volume= 81 |issue=3 | page= 035205 | year=2010 |

doi= 10.1103/PhysRevC.81.035205|arxiv = 0905.1411 |bibcode = 2010PhRvC..81c5205V |s2cid=33206182 }}</ref>

and the complete orthonormal wave functions obtained from

AdS/QCD. This will build on

Line 1,325 ⟶ 1,332:

title= Hadronic spectrum of a holographic dual of QCD |

journal=[[Physical Review Letters]] | volume= 94 |issue=20 | page= 201601 | year=2005 |

doi= 10.1103/PhysRevLett.94.201601 | bibcode=2005PhRvL..94t1601D|arxiv = hep-th/0501022 | pmid=16090235|s2cid=11006078 }}</ref><ref name="deTeramond:2008ht">{{ cite journal |author1=G. F. de Teramond |author2=S. J. Brodsky |

title= Light-Front Holography: A First Approximation to QCD |

journal=[[Physical Review Letters]] | volume= 102 | page= 081601 | year=2009 |

doi= 10.1103/PhysRevLett.102.081601 | pmid=19257731 | issue=8|arxiv = 0809.4899 |bibcode = 2009PhRvL.102h1601D |s2cid=33855116 }}</ref><ref name="Brodsky:2011sk">{{ cite journal |author1=S. J. Brodsky |author2=F. -G. Cao |author3=G. F. de Teramond |

title= AdS/QCD and Applications of Light-Front Holography |

journal= [[Communications in Theoretical Physics]] | volume= 57 |issue=4 | pages= 641–664 | year=2012 |

doi= 10.1088/0253-6102/57/4/21 | bibcode=2012CoTPh..57..641S|arxiv=1108.5718 |s2cid=73629251 }}</ref><ref name="Forkel">{{ cite journal |author1=H. Forkel |author2=M. Beyer |author3=T. Frederico |

title= Linear square-mass trajectories of radially and orbitally excited hadrons in holographic QCD |

journal= [[JHEP]] | volume= 0707 |issue=7 | page= 077 | year= 2007 |

doi= 10.1088/1126-6708/2007/07/077|arxiv = 0705.1857 |bibcode = 2007JHEP...07..077F |s2cid=5282022 }}</ref><ref name="Gutsche:2012wb">{{ cite journal |author1=T. Gutsche |author2=V. E. Lyubovitskij |author3=I. Schmidt |author4=A. Vega |

title= Nucleon resonances in AdS/QCD |

journal=[[Physical Review D]] | volume= 87 |issue=1 | page= 016017 | year=2013 |

doi= 10.1103/PhysRevD.87.016017 | bibcode=2013PhRvD..87a6017G|arxiv = 1212.6252 |s2cid=118685470 }}</ref><ref name="Gutsche:2012ez">{{ cite journal |author1=T. Gutsche |author2=V. E. Lyubovitskij |author3=I. Schmidt |author4=A. Vega |

title= Chiral Symmetry Breaking and Meson Wave Functions in Soft-Wall AdS/QCD |

journal=[[Physical Review D]] | volume= 87 |issue=5 | page= 056001 | year=2013 |

doi= 10.1103/PhysRevD.87.056001 | bibcode=2013PhRvD..87e6001G|arxiv = 1212.5196 |s2cid=118377538 }}</ref>

The approximate duality in the limit of massless

quarks motivates few-body analyses of meson and

Line 1,360 ⟶ 1,367:

title= Model of the AdS/QFT duality |

journal=[[Physical Review D]] | volume= 88 |issue=10 | page= 105025 | year=2013 |

doi= 10.1103/PhysRevD.88.105025|arxiv = 1307.2059 |bibcode = 2013PhRvD..88j5025G |s2cid=118455480 }}</ref>

can be used to introduce effective

degrees of freedom such as diquarks in

Line 1,381 ⟶ 1,388:

title= Neutrino oscillations in the front form of Hamiltonian dynamics |

journal=[[Physical Review D]] | volume= 87 |issue=2 | page= 025002 | year=2013 |

doi= 10.1103/PhysRevD.87.025002|arxiv = 1208.5255 |bibcode = 2013PhRvD..87b5002G |s2cid=119206502 }}</ref> can be resolved and the front form of Hamiltonian dynamics utilized in providing the foundation for qualitatively new (treating the vacuum differently) studies of neutrino mass generation mechanisms.

* If the renormalization group procedure for effective particles (RGPEP)<ref name="RGPEPrecent1">{{ cite journal |

Line 1,393 ⟶ 1,400:

journal=[[Physical Review D]] | volume= 87 |

issue=12 | page= 125032 | year=2013 |

doi= 10.1103/PhysRevD.87.125032 |arxiv = 1305.3702 |bibcode = 2013PhRvD..87l5032G |
s2cid=119222650 }}</ref> does allow one to study intrinsic charm, bottom, and glue in a systematically renormalized and convergent light-front Fock-space expansion, one might consider a host of new experimental studies of production processes using the intrinsic components that are not included in the calculations based on gluon and quark splitting functions.

== See also ==