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doi= 10.1016/j.nuclphysbps.2014.05.004
|volume=251–252
|bibcode=2014NuPhS.251..165B|display-authors=etal}}</ref><ref name="Burkardt">{{
author=M. Burkardt |
title= 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 }}</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 }}</ref>
of [[Quantum field theory|quantum field theories]]
Line 29 ⟶ 30:
author= P. A. M. Dirac |
title= Forms of Relativistic Dynamics |
journal=[[Reviews of Modern Physics]] | volume= 21 |
issue= 3 | pages= 392–399 | year=1949 | doi= 10.1103/RevModPhys.21.392 | bibcode=1949RvMP...21..392D}}</ref>
where <math>x^+\equiv ct+z</math> plays the role of time and the corresponding spatial
Line 116 ⟶ 118:
author=K. G. Wilson |
title= Confinement of Quarks |
journal=[[Physical Review D]] | volume= 10 |
issue= 8 | pages= 2445–2459 | year=1974 | doi= 10.1103/PhysRevD.10.2445
| bibcode=1974PhRvD..10.2445W }}</ref>
Line 140 ⟶ 143:
author= R. P. Feynman |
title= Very high-energy collisions of hadrons |
journal=[[Physical Review Letters]] | volume= 23 |
issue= 24 | pages= 1415–1417 | year=1969 | doi= 10.1103/PhysRevLett.23.1415 | bibcode=1969PhRvL..23.1415F}}</ref>
<ref name="KogutSusskind">{{ cite journal |author1=J. B. Kogut |author2=L. Susskind |
title=The parton picture of elementary particles |
journal=[[Physics Reports]] | volume= 8 |issue=2 | pages= 75–172 | year=1973 |
doi= 10.1016/0370-1573(73)90009-4|bibcode = 1973PhR.....8...75K }}</ref>
(see [[#Infinite momentum frame]])
Line 153 ⟶ 157:
functions,<ref name="Brodsky:2003pw">{{ cite journal |author1=S. J. Brodsky |author2=J. R. Hiller |author3=D. S. Hwang |author4=V. A. Karmanov |
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 }}</ref>
the eigensolution of the light-front
Line 161 ⟶ 165:
(BFKL)<ref name="Fadin:1998py">{{ cite journal |author1=V. S. Fadin |author2=L. N. Lipatov |
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 }}</ref>
Regge behavior of structure functions can be
Line 169 ⟶ 173:
author= G. P. Salam |
title= An Introduction to leading and next-to-leading BFKL |
journal=[[Acta Physica Polonica B]] | volume= 30 |
issue= pages= arxiv=hep-ph/9910492|bibcode = 1999AcPPB..30.3679S }}</ref>
of structure functions and the
Line 175 ⟶ 181:
evolution<ref name="Lepage:1980fj">{{ cite journal |author1=G. P. Lepage |author2=S. J. Brodsky |
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}}</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 |
journal=[[Physics Letters B]] | volume= 94 |issue=2 | pages= 245–250 | year=1980 |
doi= 10.1016/0370-2693(80)90869-2 | bibcode=1980PhLB...94..245E}}</ref>
of distribution amplitudes
Line 189 ⟶ 195:
of light-front wave functions as in the Drell-Yan-West
formula.<ref name="Drell:1969km">{{ cite journal |author1=S. D. Drell |author2=T. -M. Yan |
title= Connection of Elastic Electromagnetic Nucleon Form-Factors at Large <math>Q^2</math>
journal=[[Physical Review Letters]] | volume= 24 |issue=4 | pages= 181–186 | year=1970 |
doi= 10.1103/PhysRevLett.24.181
| bibcode=1970PhRvL..24..181D}}</ref>
Line 196 ⟶ 202:
author= G. B. West |
title= Phenomenological model for the electromagnetic structure of the proton |
journal=[[Physical Review Letters]] | volume= 24 |
issue= 21 | pages= 1206–1209 | year=1970 | doi= 10.1103/PhysRevLett.24.1206 | bibcode=1970PhRvL..24.1206W}}</ref>
<ref name="Brodsky:1980zm">{{ cite journal |author1=S. J. Brodsky |author2=S. D. Drell |
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}}</ref>
Line 223 ⟶ 230:
(a) the [[cluster decomposition theorem]]<ref name="Brodsky:1985gs">{{ cite journal |author1=S. J. Brodsky |author2=C.-R. Ji |
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|bibcode = 1986PhRvD..33.2653B }}</ref>
and (b) the vanishing
Line 229 ⟶ 236:
hadron;<ref name="Brodsky:2000ii">{{ cite journal |author1=S. J. Brodsky |author2=D. S. Hwang |author3=B.-Q. Ma |author4=I. Schmidt |
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 }}</ref>
one also can show that a nonzero
Line 236 ⟶ 243:
properties<ref name="Antonuccio:1997tw">{{ cite journal |author1=F. Antonuccio |author2=S. J. Brodsky |author3=S. Dalley |
title= Light cone wave functions at small <math>x</math> |
journal=[[Physics Letters B]] | volume= 412 |issue=1–2 | pages= 104–110 | year=1997 |
doi= 10.1016/S0370-2693(97)01067-8|arxiv = hep-ph/9705413 |bibcode = 1997PhLB..412..104A }}</ref>
of light-front time-ordered [[Perturbation theory (quantum mechanics)|perturbation theory]],
Line 243 ⟶ 250:
amplitudes.<ref name="Cruz-Santiago:2013vta">{{ cite journal |author1=C. A. Cruz-Santiago |author2=A. M. Stasto |
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 }}</ref>
The counting-rule<ref name="Brodsky:1994kg">{{ cite journal |author1=S. J. Brodsky |author2=M. Burkardt |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 }}</ref>
behavior of structure functions
Line 253 ⟶ 260:
duality<ref name="BloomGilman1">{{ cite journal |author1=E. Bloom |author2=F. Gilman |
title= Scaling, Duality, and the Behavior of Resonances in Inelastic electron-Proton Scattering |
journal=[[Physical Review Letters]] | volume= 25 |issue=16 | pages= 1140–1143 | year=1970 |
doi= 10.1103/PhysRevLett.25.1140 | bibcode=1970PhRvL..25.1140B|citeseerx=10.1.1.412.3968 }}</ref>
<ref name="BloomGilman2">{{ cite journal |author1=E. Bloom |author2=F. Gilman |
title= Scaling and the Behavior of Nucleon Resonances in Inelastic electron-Nucleon Scattering |
journal=[[Physical Review D]] | volume= 4 |issue=9 | pages= 2901–2916 | year=1971 |
doi= 10.1103/PhysRevD.4.2901|bibcode = 1971PhRvD...4.2901B |citeseerx=10.1.1.412.5779 }}</ref>
have also been derived in light-front QCD (LFQCD).
The existence of "lensing effects" at leading twist, such as the
Line 265 ⟶ 272:
methods.<ref name="Brodsky:2002cx">{{ cite journal |author1=S. J. Brodsky |author2=D. S. Hwang |author3=I. Schmidt |
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 }}</ref>
Line 280 ⟶ 287:
counting.<ref name="Wilsonetal">{{ cite journal |author1=K. G. Wilson |author2=T. S. Walhout |author3=A. Harindranath |author4=W.-M. Zhang |author5=R. J. Perry |author6=S. D. Glazek |
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|arxiv = hep-th/9401153 |bibcode = 1994PhRvD..49.6720W }}</ref>
Light-front considerations of the vacuum as well as
Line 287 ⟶ 294:
contributions.<ref name="Nambu">{{ cite journal |author1=Y. Nambu |author2=G. Jona-Lasinio |
title=Dynamical model of elementary particles based on an analogy with auperconductivity |
journal=[[Physical Review]] | volume= 122 |issue=1 | pages= 345–358 | year=1961 |
doi= 10.1103/PhysRev.122.345|bibcode = 1961PhRv..122..345N }}</ref>
<ref name="GOR">{{ cite journal |author1=M. Gell-Mann |author2=R. J. Oakes |author3=B. Renner |
title=Behavior of current divergences under SU(3) x SU(3) |
journal=[[Physical Review]] | volume= 175 |issue=5 | pages= 2195–2199 | year=1968 |
doi= 10.1103/PhysRev.175.2195|bibcode = 1968PhRv..175.2195G }}</ref>
<ref name="tHooftVeltman">{{ cite journal |author1=G. 't Hooft |author2=M. Veltman |
title=Regularization and renormalization of gauge fields |
journal=[[Nuclear Physics B]] | volume= 44 |issue=1 | pages= 189–213 | year=1972 |
doi= 10.1016/0550-3213(72)90279-9|bibcode = 1972NuPhB..44..189T }}</ref>
<ref name="SVZ">{{ cite journal |author1=M. A. Shifman |author2=A.I. Vainshtein |author3=V. I. Zakharov |
title=QCD and Resonance Physics: Applications |
journal=[[Nuclear Physics B]] | volume= 147 |issue=5 | pages= 448–518 | year=1979 |
doi= 10.1016/0550-3213(79)90023-3|bibcode = 1979NuPhB.147..448S }}</ref>
<ref name="FeynmanQCD2">{{ cite journal |
author=R. P. Feynman |
title=The Qualitative Behavior of Yang-Mills Theory in (2+1)-Dimensions |
journal=[[Nuclear Physics B]] | volume= 188 |
issue=3 | pages= 479–512 | year=1981 | doi= 10.1016/0550-3213(81)90005-5|bibcode = 1981NuPhB.188..479F }}</ref>
<ref name="SSbreaking">{{ cite journal |
author=E. Witten |
title=Dynamical Breaking of Supersymmetry |
journal=[[Nuclear Physics B]] | volume= 188 |
issue=3 | pages= 513–554 | year=1981 | doi= 10.1016/0550-3213(81)90006-7|bibcode = 1981NuPhB.188..513W }}</ref>
<ref name="GasserLeutwyler">{{ cite journal |author1=J. Gasser |author2=H. Leutwyler |
title=Chiral Perturbation Theory to One Loop |
journal=[[Annals of Physics]] | volume= 158 |issue=1 | pages= 142–210 | year=1984 |
doi= 10.1016/0003-4916(84)90242-2 |bibcode = 1984AnPhy.158..142G }}</ref>
<ref name="condensates">{{ cite journal |
author=S. D. Glazek |
title=Light Front QCD in the Vacuum Background |
journal=[[Physical Review D]] | volume= 38 |
issue=10 | pages= 3277–3286 | year=1988 | doi= 10.1103/PhysRevD.38.3277 |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 }}</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 }}</ref>
<ref name="CasherSusskind">{{ cite journal |author1=A. Casher |author2=L. Susskind |
title=Chiral magnetism (or magnetohadrochironics) |
journal=[[Physical Review D]] | volume= 9 |issue=2 | pages= 436–460 | year=1974 |
doi= 10.1103/PhysRevD.9.436|bibcode = 1974PhRvD...9..436C }}</ref>
The truncation of the light-front
Line 363 ⟶ 373:
author=E.P. Wigner |
title=On unitary representations of the inhomogeneous Lorentz group |
journal=[[Annals of Mathematics]] | volume= 40 |
issue=1 pages=149–204 | year=1939 | doi= 10.2307/1968551|bibcode = 1939AnMat..40..149W
jstor=1968551 }}</ref>
and Bargmann<ref name="bargmann:1954">{{ cite journal |
author=V. Bargmann |
title=On unitary ray representations of continuous groups |
journal=[[Annals of Mathematics]] | volume= 59 |
issue= pages=1–46 | year=1954 | doi= 10.2307/1969831
jstor=1969831 }}</ref>
showed that this symmetry must be realized by a unitary representation of the
connected component of the Poincaré group on the Hilbert space of
Line 559 ⟶ 575:
simplifications of light-front quantum field theory are realized in
the infinite momentum
limit<ref name="fubini:1965">{{ cite journal |author1=S. Fubini |title=Renormalization effects for partially conserved currents |author2=G. Furlan |
journal=Physics | volume= 1 |issue=4 | page= 229 | year=1965 |doi=10.1103/PhysicsPhysiqueFizika.1.229 }}</ref>
<ref name="weinberg:1966">{{ cite journal |
author= S. Weinberg |
title= Dynamics at infinite momentum |
journal=[[Physical Review]] | volume= 150 |
issue= 4 | pages= 1313–1318 | year=1966 | doi= 10.1103/PhysRev.150.1313|bibcode = 1966PhRv..150.1313W }}</ref>
of ordinary canonical field theory (see [[#Infinite momentum frame]]).
Line 579 ⟶ 596:
Sokolov<ref name="sokolov:1978">{{ cite journal |author1=S. N. Sokolov |author2=A. N. Shatini |
journal=Theoreticheskya
<ref name="polyzou:2010">{{ cite journal |
author= W. N. Polyzou |
title=Examining the equivalence of Bakamjian-Thomas
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>
demonstrated that
Line 643 ⟶ 661:
variables.<ref name="leutwyler:1970">{{ cite journal |author1=H. Leutwyler |author2=J.R. Klauder |author3=L. Streit |
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 }}</ref>
<ref name="ullrich:2006">{{ cite journal |author1=P. Ullrich |author2=E. Werner |
title=On the problem of mass-dependence of the two-point
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 }}</ref>
Line 677 ⟶ 695:
author=M. Fuda |
title=A new picture for light front dynamics |
journal=[[Annals of Physics]] | volume= 197 |
issue=2 | pages= 265–299 | year=1990 | doi= 10.1016/0003-4916(90)90212-7|bibcode = 1990AnPhy.197..265F }}</ref>
<ref name="fuda:1990b">{{ cite journal |
author= M. Fuda |
title=Poincaré invariant Lee model |
journal=[[Physical Review D]] | volume= 41 |
issue=2 | pages= 534–549 | year=1990 | doi= 10.1103/PhysRevD.41.534 |bibcode = 1990PhRvD..41..534F }}</ref>
<ref name="fuda:1991">{{ cite journal |
author= M. Fuda |
title=Angular momentum and light front scattering theory |
journal=[[Physical Review D]] | volume= 44 |
issue=6 | pages= 1880–1890 | year=1991 | doi= 10.1103/PhysRevD.44.1880|bibcode = 1991PhRvD..44.1880F }}</ref>
<ref name="fuda:1994">{{ cite journal |
author= M. Fuda |
title=A new picture for light front dynamics. 2 |
journal=[[Annals of Physics]] | volume= 231 |
issue=1 | pages= 1–40 | year=1994 | doi= 10.1006/aphy.1994.1031|bibcode = 1994AnPhy.231....1F }}</ref>
<ref name="polyzou:1999">{{ cite journal |
author= W. N. Polyzou |
title=Left Coset Invariance and Relativistic Invariance |
journal=[[Few Body Systems]] | volume= 27 |
issue=2 | pages= 57–72 | year=1999 | doi=10.1007/s006010050122|bibcode = 1999FBS....27...57P }}</ref>
and the kinematic representation of rotations
Line 723 ⟶ 746:
<ref name="karmanov:1982a">{{ cite journal |
author= V.A. Karmanov |
title=Angular Condition Imposed On The State Vector Of
journal=[[Soviet Physics JETP Letters]] | volume= 35 | page= 276 | year=1982 }}</ref>
<ref name="karmanov:1982b">{{ cite journal |
author= V.A. Karmanov |
title=Complete System Of Equations For The State Vector
journal=[[Journal of Experimental and Theoretical Physics]] | volume= 56 | page= 1 | year=1982 }}</ref>
introduced a
Line 751 ⟶ 774:
rotations.<ref name="Melosh">{{ cite journal |
author=H. J. Melosh|
journal=[[Physical Review D]] | volume= 9 |
issue=4 | pages= 1095–1112 | year=1974 | doi= 10.1103/PhysRevD.9.1095
| title=Quarks: Currents and constituents|bibcode = 1974PhRvD...9.1095M }}</ref>
Line 770 ⟶ 794:
is more complicated,<ref name="glockle:2013">{{ cite journal |author1=W. N. Polyzou |author2=W. Glockle |author3=H. Witala |
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 }}</ref>
it is only total angular
Line 780 ⟶ 804:
<ref name="leutwyler:1977b">{{ cite journal |author1=H. Leutwyler |author2=J. Stern |
title=Covariant Quantum Mechanics on a Null Plane |
journal=[[Physics Letters B]] | volume= 69 |issue=2 | pages= 207–210 | year=1977 |
doi= 10.1016/0370-2693(77)90645-1|bibcode = 1977PhLB...69..207L }}</ref>
Line 797 ⟶ 821:
properties,<ref name="keister:2012">{{ cite journal |author1=B. D. Keister |author2=W. N. Polyzou |
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 }}</ref>
then the transverse components of
Line 809 ⟶ 833:
properties;<ref name="coester:1982">{{ cite journal |author1=F. Coester |author2=W. N. Polyzou |
title=Relativistic Quantum Mechanics Of Particles With Direct Interactions |
journal=[[Physical Review D]] | volume= 26 |issue=6 | pages= 1348–1367 | year=1982 |
doi= 10.1103/PhysRevD.26.1348 |bibcode = 1982PhRvD..26.1348C }}</ref>
these realizations all have additional
Line 873 ⟶ 897:
<ref name="leutwyler:1977a">{{ cite journal |author1=H. Leutwyler |author2=J. Stern |
title=Relativistic Dynamics on a Null Plane |
journal=[[Annals of Physics]] | volume= 112 |issue=1 | pages= 94–164 | year=1978 |
doi= 10.1016/0003-4916(78)90082-9|bibcode = 1978AnPhy.112...94L }}</ref>
given by ({{EquationNote|1}})
Line 942 ⟶ 966:
can be found in the work of Brodsky, Roskies and
Suaya.<ref name="IMF-QED">{{ cite journal |author1=S. J. Brodsky |author2=R. Roskies |author3=R. Suaya |
title=Quantum Electrodynamics and Renormalization Theory in the
journal=[[Physical Review D]] | volume= 8 |issue=12 | pages= 4574–4594 | year=1973 |
doi= 10.1103/PhysRevD.8.4574|bibcode = 1973PhRvD...8.4574B }}</ref>
Line 990 ⟶ 1,014:
et al.<ref name="cdkm">{{ cite journal |author1=J. Carbonell |author2=B. Desplanques |author3=V.A. Karmanov |author4=J.F. Mathiot |
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 }}</ref>),
in which the state vector is defined on the light-front plane of
Line 1,017 ⟶ 1,041:
author=V.G. Kadyshevsky |
title=Quasipotential type equation for the relativistic scattering amplitude |
journal=[[Nuclear Physics B]] | volume= 6 |
issue=2 | year=1968 | pages=125–148 | doi= 10.1016/0550-3213(68)90274-5|bibcode = 1968NuPhB...6..125K }}</ref>
By these rules, the light-front amplitudes are represented as the
Line 1,093 ⟶ 1,118:
author=V.A. Karmanov |
title=Relativistic Deuteron Wave Function On Light Front |
journal=[[Nuclear Physics A]] | volume= 362 |
issue=2 | pages= 331–348 | year=1981 | doi= 10.1016/0375-9474(81)90497-8|bibcode = 1981NuPhA.362..331K }}</ref>
Line 1,119 ⟶ 1,145:
condition<ref name="karmanov:1982a" /><ref name="karmanov:1982b" />
<ref name="CarlsonJi">{{ cite journal |author1=C. Carlson |author2=C.-R. Ji |
title=Angular conditions, relations between Breit and light front
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 }}</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 }}</ref>
<ref name="AC-spin2">{{ cite journal |
author=B. L. G. Bakker, H.-M.Choi and C.-R. Ji |
title=The vector meson form-factor analysis in light front dynamics |
journal=[[Physical Review D]] | volume= 65 |
issue=11 | page= 116001 | year=2002 | doi= 10.1103/PhysRevD.65.116001
|arxiv = hep-ph/0202217 |bibcode = 2002PhRvD..65k6001B }}</ref>
Line 1,145 ⟶ 1,172:
model.<ref name="carb-karm:1995">{{ cite journal |author1=J. Carbonell |author2=V.A. Karmanov |
title=Relativistic deuteron wave function in the light front dynamics |
journal=[[Nuclear Physics A]] | volume= 581 |issue=3–4 | pages= 625–653 | year=1995 |
doi= 10.1016/0375-9474(94)00430-U|bibcode = 1995NuPhA.581..625C }}</ref>
Line 1,175 ⟶ 1,202:
* Construct symmetry-preserving regularization and renormalization schemes for light-front QCD, to include the Pauli-Villars-based method of the St. Petersburg group,<ref name="StPete1">{{ cite journal |author1=S.A. Paston |author2=V.A. Franke |
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 }}</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 }}</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 |
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journal=[[Physical Review D]] | volume= 49 |issue=8 | pages= 4214–4218 | year=1994 |
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journal=[[Physical Review D]] | volume= 57 |issue=6 | pages= 3558–3566 | year=1998 |
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| title=Asymptotic freedom and bound states in Hamiltonian dynamics|arxiv = hep-th/9707028 |bibcode = 1998PhRvD..57.3558G }}</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 }}</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
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| bibcode=2012PhRvD..86h5006K|arxiv = 1204.3257 }}</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|arxiv = hep-th/9212009 |bibcode = 1993PhRvD..48..816B }}</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
journal=[[Physical Review D]] | volume= 49 |issue=4 | pages= 2001–2013 | year=1994 |
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title=Spontaneous symmetry breaking of (1+1)-dimensional <math>\phi^4</math> theory
journal=[[Physical Review D]] | volume= 51 |issue=2 | pages= 726–733 | year=1995 |
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title= Spontaneous symmetry breaking at infinite momentum without P+ zero modes |
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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 |
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title= Phase transition in light front <math>\phi^4_{1+1}</math> |
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Line 1,226 ⟶ 1,253:
(DLCQ),<ref name="DLCQ1">{{ cite journal |author1=H.-C. Pauli |author2=S. J. Brodsky |
title=Solving field theory in one space one time dimension |
journal=[[Physical Review D]] | volume= 32 |issue=8 | pages= 1993–2000 | year=1985 |
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<ref name="DLCQ2">{{ cite journal |author1=H.-C. Pauli |author2=S. J. Brodsky |
title=Discretized light cone quantization: Solution to
journal=[[Physical Review D]] | volume= 32 |issue=8 | pages= 2001–2013 | year=1985 |
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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 }}</ref>
and the complete orthonormal wave functions obtained from
Line 1,294 ⟶ 1,321:
* Explore the [[AdS/QCD correspondence]] and [[light front holography]].<ref name="deTeramond:2005su">{{ cite journal |author1=G. F. de Teramond |author2=S. J. Brodsky |
title= Hadronic spectrum of a holographic dual of QCD |
journal=[[Physical Review Letters]] | volume= 94 |issue=20 | page= 201601 | year=2005 |
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title= Light-Front Holography: A First Approximation to QCD |
Line 1,300 ⟶ 1,327:
doi= 10.1103/PhysRevLett.102.081601 | pmid=19257731 | issue=8|arxiv = 0809.4899 |bibcode = 2009PhRvL.102h1601D }}</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 |
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title= Linear square-mass trajectories of radially and orbitally excited hadrons in holographic QCD |
journal= [[JHEP]] | volume= 0707 |issue=7 | page= 077 | year= 2007 |
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title= Nucleon resonances in AdS/QCD |
journal=[[Physical Review D]] | volume= 87 |issue=1 | page= 016017 | year=2013 |
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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 }}</ref>
The approximate duality in the limit of massless
Line 1,329 ⟶ 1,356:
interpretation<ref name="Ehrenfest">{{ cite journal |author1=S. D. Glazek |author2=A. P. Trawinski |
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 }}</ref>
can be used to introduce effective
Line 1,350 ⟶ 1,377:
* Develop a light-front approach to the [[neutrino oscillation]] experiments possible at [[Fermilab]] and elsewhere, with the goal of reducing the energy spread of the neutrino-generating hadronic sources, so that the three-energy-slits interference picture of the oscillation pattern<ref name="Glazek:2012wp">{{ cite journal |author1=S. D. Glazek |author2=A. P. Trawinski |
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 }}</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 |
author=S. D. Glazek |
title=Perturbative Formulae for Relativistic Interactions of
journal=[[Acta Physica Polonica B]] | volume= 43 |
issue=9 | page= 1843 | year=2012 | doi= 10.5506/APhysPolB.43.1843}}</ref><ref name="RGPEPrecent2">{{ cite journal |
author=S. D. Glazek |
title=Fermion mass mixing and vacuum triviality in
journal=[[Physical Review D]] | volume= 87 |
issue=12 | page= 125032 | year=2013 | doi= 10.1103/PhysRevD.87.125032 |arxiv = 1305.3702 |bibcode = 2013PhRvD..87l5032G }}</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.
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