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1

Escalante, Alberto, and Prihel Cavildo-Sánchez. "Symplectic Approach of Three-Dimensional Palatini Theory Plus a Chern-Simons Term." Advances in Mathematical Physics 2018 (2018): 1–7. http://dx.doi.org/10.1155/2018/3474760.

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Using the symplectic framework of Faddeev-Jackiw, the three-dimensional Palatini theory plus a Chern-Simons term [P-CS] is analyzed. We report the complete set of Faddeev-Jackiw constraints and we identify the corresponding generalized Faddeev-Jackiw brackets. With these results, we show that although P-CS produces Einstein’s equations, the generalized brackets depend on a Barbero-Immirzi-like parameter. In addition, we compare our results with those found in the canonical analysis showing that both formalisms lead to the same results.
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2

MANAVELLA, EDMUNDO C. "FADDEEV–JACKIW FORMALISM FOR CONSTRAINED SYSTEMS WITH GRASSMANN DYNAMICAL FIELD VARIABLES." International Journal of Modern Physics A 27, no. 24 (2012): 1250145. http://dx.doi.org/10.1142/s0217751x1250145x.

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The Faddeev–Jackiw canonical quantization formalism for constrained systems with Grassmann dynamical variables within the framework of the field theory is reviewed. First, by means of a iterative process, the symplectic supermatrix is constructed and their associated constraints are found. Next, by taking into account the phase space of the system, the constraint structure is considered. It is found that, if there are no auxiliary dynamical field variables, the supermatrix whose elements are the Bose–Fermi brackets between the constraints associated with the independent dynamical field variabl
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3

WOTZASEK, CLOVIS. "ON THE FADDEEV-JACKIW QUANTIZATION OF THE LINEAR CONSTRAINT CHIRAL BOSON." Modern Physics Letters A 08, no. 26 (1993): 2509–21. http://dx.doi.org/10.1142/s0217732393002841.

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The symplectic quantization method of Faddeev and Jackiw with true constraints is employed to study two-dimensional self-dual scalar fields with linear chiral constraints. A gauge invariant embedding of the previous model is explicitly obtained and investigated under Faddeev-Jackiw point of view.
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4

Anjali S and Saurabh Gupta. "Faddeev–Jackiw quantization of Christ–Lee model." Modern Physics Letters A 35, no. 10 (2020): 2050072. http://dx.doi.org/10.1142/s0217732320500728.

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We analyze the constraints of Christ–Lee model by means of modified Faddeev–Jackiw formalism in Cartesian as well as polar coordinates. Further, we accomplish quantization à la Faddeev–Jackiw by choosing appropriate gauge conditions in both the coordinate systems. Finally, we establish gauge symmetries of Christ–Lee model with the help of zero-modes of the symplectic matrix.
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5

Barcelos-Neto, J., and E. S. Cheb-Terrab. "Faddeev-Jackiw quantization in superspace." Zeitschrift für Physik C Particles and Fields 54, no. 1 (1992): 133–38. http://dx.doi.org/10.1007/bf01881716.

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6

BARCELOS-NETO, J., and C. WOTZASEK. "FADDEEV-JACKIW QUANTIZATION AND CONSTRAINTS." International Journal of Modern Physics A 07, no. 20 (1992): 4981–5003. http://dx.doi.org/10.1142/s0217751x9200226x.

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In a recent Letter, Faddeev and Jackiw have shown that the reduction of constrained systems into its canonical, first-order form, can bring some new insight into the research of this field. For sympletic manifolds the geometrical structure, called Dirac or generalized bracket, is obtained directly from the inverse of the nonsingular sympletic two-form matrix. In the cases of nonsympletic manifolds, this two-form is degenerated and cannot be inverted to provide the generalized brackets. This singular behavior of the sympletic matrix is indicative of the presence of constraints that have to be c
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7

Manavella, Edmundo C. "Composite particles within the Faddeev–Jackiw framework: Nonequivalence between the Dirac and Faddeev–Jackiw formalisms." International Journal of Modern Physics A 29, no. 15 (2014): 1450076. http://dx.doi.org/10.1142/s0217751x14500766.

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Some time ago, the Faddeev–Jackiw canonical quantization formalism for constrained systems with Grassmann dynamical variables in the field theory context was reviewed. In the present work, the resulting formalism is applied to a classical nonrelativistic U(1) ×U(1) gauge field model that describes the electromagnetic interaction of composite particles in 2+1 dimensions. The model contains a Chern–Simons U(1) field and the electromagnetic field, and it uses either a composite boson system or a composite fermion one. The obtained results are compared with the ones corresponding to the implementa
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8

GARCÍA, J. ANTONIO, and JOSEP M. PONS. "FADDEEV-JACKIW APPROACH TO GAUGE THEORIES AND INEFFECTIVE CONSTRAINTS." International Journal of Modern Physics A 13, no. 21 (1998): 3691–710. http://dx.doi.org/10.1142/s0217751x98001736.

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The general conditions for the applicability of the Faddeev–Jackiw approach to gauge theories are studied. When the constraints are effective, a new proof in the Lagrangian framework of the equivalence between this method and the Dirac approach is given. We find, however, that the two methods may give different descriptions for the reduced phase space when ineffective constraints are present. In some cases the Faddeev–Jackiw approach may lose some constraints or some equations of motion. We believe that this inequivalence can be related to the failure of the Dirac conjecture (that says that th
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9

Manavella, E. C. "EXTENDED FADDEEV-JACKIW CANONICAL QUANTIZATION FOR THE (1+1)-DIMENSIONAL NONRELATIVISTIC ELECTRODYNAMICS." Anales AFA 31, no. 4 (2021): 127–34. http://dx.doi.org/10.31527/analesafa.2020.31.4.127.

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Some time ago, we proposed an extension of the usual Faddeev-Jackiw formalism for constrained systems with Grassmann dynamic variables in the field theory context. In the present work, we apply this extended formalism to the (1+1)-dimensional nonrelativistic electrodynamics. By comparing the obtained results with those corresponding to the implementation of Dirac formalism on this model, we find the same constraints and generalized brackets. In this way, we can conclude that the extended Faddeev-Jackiw and the Dirac formalisms can be considered equivalent, at least for this model. On the contr
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10

Pimentel, B. M., and G. E. R. Zambrano. "Faddeev-Jackiw quantization of Proca Electrodynamics." Nuclear and Particle Physics Proceedings 267-269 (October 2015): 183–85. http://dx.doi.org/10.1016/j.nuclphysbps.2015.10.100.

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11

Long, Zheng-Wen, and Jian Jing. "Faddeev–Jackiw approach to the noncommutativity." Physics Letters B 560, no. 1-2 (2003): 128–32. http://dx.doi.org/10.1016/s0370-2693(03)00375-7.

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12

Wotzasek, C. "Faddeev-Jackiw Approach to Hidden Symmetries." Annals of Physics 243, no. 1 (1995): 76–89. http://dx.doi.org/10.1006/aphy.1995.1091.

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13

BAZEIA, D. "REMARKS ON CHIRAL BOSONIZATION." Modern Physics Letters A 05, no. 30 (1990): 2497–502. http://dx.doi.org/10.1142/s0217732390002900.

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We use the first-order Lagrangian formalism of Faddeev and Jackiw to give some comments concerning chiral bosonization in the recent literature. In particular, after considering the fact that the Abelian formulation of Siegel's model reduces naturally to a gauged version of Floreanini and Jackiw's model, we introduce a method for understanding the bosonic description of the minimal chiral Schwinger model.
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14

SHIRZAD, A., and M. MOJIRI. "CONSTRAINT STRUCTURE IN MODIFIED FADDEEV–JACKIW METHOD." Modern Physics Letters A 16, no. 38 (2001): 2439–48. http://dx.doi.org/10.1142/s021773230100593x.

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We show that in modified Faddeev–Jackiw formalism, first- and second-class constraints appear at each level, and the whole constraint structure is in exact correspondence with level by level method of Dirac formalism.
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15

Dengiz, Suat. "Note on soft photons and Faddeev–Jackiw symplectic reduction of quantum electrodynamics in the eikonal limit." International Journal of Modern Physics A 33, no. 25 (2018): 1830020. http://dx.doi.org/10.1142/s0217751x1830020x.

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In this note, we go over the recent soft photon model and Faddeev–Jackiw quantization of the massless quantum electrodynamics in the eikonal limit to some extent. Throughout our readdressing, we observe that the gauge potentials in both approaches become pure gauges and the associated eikonal Faddeev–Jackiw quantum bracket matches with the soft quantum bracket. These observations and the fact that the gauge fields in two cases localize in two-dimensional plane (even if it is spatial in soft photon case and (1[Formula: see text]+[Formula: see text]1)-dimensional Minkowski in the eikonal case) i
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16

MONTANI, H., and C. WOTZASEK. "FADDEEV-JACKIW QUANTIZATION OF NON-ABELIAN SYSTEMS." Modern Physics Letters A 08, no. 35 (1993): 3387–96. http://dx.doi.org/10.1142/s0217732393003810.

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The Faddeev and Jackiw procedure for the quantization of constrained gauge systems is used on the analysis of non-Abelian symmetries. The key point is that the gauge algebra of the non-Abelian constraints under generalized brackets can be reconstructed. This follows from the singular matrix that defines the basic geometric structure of the model and its corresponding zero-modes. The attainment of this algebra, not previously found in the Faddeev-Jackiw formalism for constrained theories, leads to the correct transformation properties for the gauge fields. This construction shows that the zero-
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17

Kulshreshtha, D. S., and H. J. W. Müller-Kirsten. "Faddeev-Jackiw quantization of self-dual fields." Physical Review D 45, no. 2 (1992): R393—R397. http://dx.doi.org/10.1103/physrevd.45.r393.

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18

Wotzasek, Clovis. "Faddeev-Jackiw quantization of Siegel's chiral oscillator." Physical Review D 46, no. 6 (1992): 2734–36. http://dx.doi.org/10.1103/physrevd.46.2734.

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19

Barcelos-Neto, J., and A. Cabo. "Faddeev-Jackiw quantization of massive tensor fields." Zeitschrift für Physik C 74, no. 4 (1997): 731. http://dx.doi.org/10.1007/s002880050439.

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20

DUVAL, C., and P. A. HORVÁTHY. "EXOTIC GALILEAN SYMMETRY AND THE HALL EFFECT." International Journal of Modern Physics B 16, no. 14n15 (2002): 1971–77. http://dx.doi.org/10.1142/s021797920201169x.

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The "Laughlin" picture of the Fractional Quantum Hall effect can be derived using the "exotic" model based on the two-fold centrally-extended planar Galilei group. When coupled to a planar magnetic field of critical strength determined by the extension parameters, the system becomes singular, and "Faddeev-Jackiw" reduction yields the "Chern-Simons" mechanics of Dunne, Jackiw, and Trugenberger. The reduced system moves according to the Hall law.
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21

Belhadi, Zahir, Alain Bérard, and Hervé Mohrbach. "Faddeev–Jackiw quantization of non-autonomous singular systems." Physics Letters A 380, no. 41 (2016): 3355–58. http://dx.doi.org/10.1016/j.physleta.2016.08.018.

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22

KOH*, Seoktae. "Faddeev-Jackiw Approach in Generalized Single Field Inflation." New Physics: Sae Mulli 65, no. 1 (2015): 102–9. http://dx.doi.org/10.3938/npsm.65.102.

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23

Lee, Chang-Yeong, and Dong Won Lee. "Faddeev-Jackiw analysis of topological mass-generating action." Journal of Physics A: Mathematical and General 31, no. 38 (1998): 7809–20. http://dx.doi.org/10.1088/0305-4470/31/38/016.

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24

Escalante, Alberto, and Prihel Cavildo Sánchez. "Faddeev–Jackiw quantization of four dimensional BF theory." Annals of Physics 374 (November 2016): 375–94. http://dx.doi.org/10.1016/j.aop.2016.09.003.

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25

Foussats, A., C. Repetto, O. P. Zandron, and O. S. Zandron. "Supersymmetric Anyons in the Faddeev–Jackiw Quantization Picture." Annals of Physics 268, no. 2 (1998): 225–45. http://dx.doi.org/10.1006/aphy.1998.5823.

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26

NATIVIDADE, C. P., and H. BOSCHI-FILHO. "FADDEEV-JACKIW FORMALISM FOR A TOPOLOGICAL-LIKE OSCILLATOR IN PLANAR DIMENSIONS." Modern Physics Letters A 11, no. 01 (1996): 69–79. http://dx.doi.org/10.1142/s0217732396000096.

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The problem of a harmonic oscillator coupling to an electromagnetic potential plus a topological-like (Chern-Simons) massive term, in two-dimensional space, is studied in the light of the symplectic formalism proposed by Faddeev and Jackiw for constrained systems.
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27

Liao, Leng, and Yong Chang Huang. "Non-equivalence of Faddeev–Jackiw method and Dirac–Bergmann algorithm and the modification of Faddeev–Jackiw method for keeping the equivalence." Annals of Physics 322, no. 10 (2007): 2469–84. http://dx.doi.org/10.1016/j.aop.2006.11.013.

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28

Abreu, Everton M. C., Rafael L. Fernandes, Albert C. R. Mendes, Jorge Ananias Neto, and Rodrigo M. de Paula. "Faddeev–Jackiw approach of noncommutative space–time electromagnetic theories." International Journal of Modern Physics A 33, no. 28 (2018): 1850163. http://dx.doi.org/10.1142/s0217751x18501634.

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The interest in higher derivatives field theories has its origin mainly in their influence concerning the renormalization properties of physical models and to remove ultraviolet divergences. The noncommutative Podolsky theory is a constrained system that cannot be directly quantized by the canonical way. In this work, we have used the Faddeev–Jackiw method in order to obtain the Dirac brackets of the NC space–time Maxwell, Proca and Podolsky theories.
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29

Seiler, W. M. "Involution and constrained dynamics. II. The Faddeev-Jackiw approach." Journal of Physics A: Mathematical and General 28, no. 24 (1995): 7315–31. http://dx.doi.org/10.1088/0305-4470/28/24/026.

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30

Jin-huan, Jiang. "Electron-Phonon Model in the Faddeev-Jackiw Quantization Formalism." International Journal of Theoretical Physics 59, no. 9 (2020): 2741–50. http://dx.doi.org/10.1007/s10773-020-04523-z.

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31

Foussats, A., C. Repetto, O. P. Zandron, and O. S. Zandron. "Nonlinear sigma model in the Faddeev-Jackiw quantization formalism." International Journal of Theoretical Physics 36, no. 12 (1997): 2923–35. http://dx.doi.org/10.1007/bf02435718.

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32

Foussats, A., C. Repetto, O. P. Zandron, and O. S. Zandron. "Faddeev-Jackiw quantization method in conformal three-dimensional supergravity." International Journal of Theoretical Physics 36, no. 1 (1997): 55–65. http://dx.doi.org/10.1007/bf02435771.

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33

Müller-Kirsten, H. J. W., and Jian-zu Zhang. "Faddeev-Jackiw brackets and quantization conditions of constrained systems." Physics Letters A 202, no. 4 (1995): 241–45. http://dx.doi.org/10.1016/0375-9601(95)00332-w.

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34

Ramos, J. "On the equivalence and non-equivalence of Dirac and Faddeev–Jackiw formalisms for constrained systems." Canadian Journal of Physics 95, no. 3 (2017): 225–33. http://dx.doi.org/10.1139/cjp-2015-0547.

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We present a comparative analysis between the Dirac method and the original Faddeev–Jackiw formalism for constrained systems, such as Dirac free field, Proca model, electromagnetism coupled to matter, and source-free Maxwell field. We establish the possible differences between the approaches and show that they are not completely equivalent.
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35

ABREU, E. M. C., J. ANANIAS NETO, A. C. R. MENDES, C. NEVES, W. OLIVEIRA, and M. V. MARCIAL. "LAGRANGIAN FORMULATION FOR NONCOMMUTATIVE NONLINEAR SYSTEMS." International Journal of Modern Physics A 27, no. 09 (2012): 1250053. http://dx.doi.org/10.1142/s0217751x12500534.

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In this work we study Lagrangian formulations for the noncommutative versions of the SU(2) Skyrme model and O(3) nonlinear sigma model. These formulations will be obtained using the Faddeev–Jackiw symplectic formalism. Other noncommutative Lagrangian formulations can be proposed and different noncommutative versions for these nonlinear systems can be obtained.
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36

MONTANI, H. "SYMPLECTIC ANALYSIS OF CONSTRAINED SYSTEMS." International Journal of Modern Physics A 08, no. 24 (1993): 4319–37. http://dx.doi.org/10.1142/s0217751x93001764.

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The formal equivalence of the Dirac’s methods and the modified Faddeev-Jackiw approach, obtained by transferring the constraints from the coordinates to the velocities, is shown. The relation between internal and noninternal gauge symmetries, and first class constraints are analyzed in this framework. As a particular case, the reparametrization invariance is also discussed.
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37

BARCELOS-NETO, J., and E. S. CHEB-TERRAB. "SYMPLECTIC QUANTIZATION OF SUPERFIELDS." International Journal of Modern Physics A 09, no. 31 (1994): 5563–81. http://dx.doi.org/10.1142/s0217751x94002272.

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We show how the extension of the Faddeev-Jackiw symplectic quantization (including true constraints) can be used in superspace. We first deal with supersymmetric free field theory in the component language. After that, we consider the method applied to superfields, taken as canonical variables. We also use the formalism, directly in superfield formulation, for the supersymmetric nonlinear sigma model.
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38

GOVAERTS, JAN. "HAMILTONIAN REDUCTION OF FIRST-ORDER ACTIONS." International Journal of Modern Physics A 05, no. 18 (1990): 3625–40. http://dx.doi.org/10.1142/s0217751x90001574.

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The Hamiltonian structure associated to an arbitrary system described by a first-order action is considered in detail. The equivalence of two possible approaches is established in full generality. The first has been advocated recently by Faddeev and Jackiw. The second is based on the more standard methods of constrained dynamics. Some consequences of the general analysis are also discussed.
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39

Yi-Feng, Jia, Wu Ke, and Xu Zhi-Qiang. "New algorithms for constrained dynamics based on Faddeev–Jackiw approach." Chinese Physics 16, no. 12 (2007): 3581–88. http://dx.doi.org/10.1088/1009-1963/16/12/005.

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40

García, J. Antonio, and Josep M. Pons. "Equivalence of Faddeev–Jackiw and Dirac Approaches for Gauge Theories." International Journal of Modern Physics A 12, no. 02 (1997): 451–64. http://dx.doi.org/10.1142/s0217751x97000505.

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The equivalence between the Dirac method and Faddeev–Jackiw analysis for gauge theories is proven. In particular we trace out, in a stage-by-stage procedure, the standard classification of first and second class constraints of Dirac's method in the F–J approach. We also find that the Darboux transformation implied in the F–J reduction process can be viewed as a canonical transformation in Dirac approach. Unlike Dirac's method, the F–J analysis is a classical reduction procedure. The quantization can be achieved only in the framework of reduce and then quantize approach with all the known probl
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41

Jun, Jin Woo, and Changkeun Jue. "Faddeev-Jackiw quantization and the light-cone zero-mode problem." Physical Review D 50, no. 4 (1994): 2939–41. http://dx.doi.org/10.1103/physrevd.50.2939.

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42

Escalante, Alberto, and C. Medel-Portugal. "Faddeev–Jackiw quantization of topological invariants: Euler and Pontryagin classes." Annals of Physics 391 (April 2018): 27–46. http://dx.doi.org/10.1016/j.aop.2018.02.003.

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43

Gupta, Saurabh, and Raju Roychowdhury. "Antiself-dual Yang–Mills, modified Faddeevs–Jackiw formalism and hidden BRS invariance." International Journal of Modern Physics A 31, no. 24 (2016): 1650138. http://dx.doi.org/10.1142/s0217751x16501384.

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We analyze the constraints for a system of antiself-dual Yang–Mills (ASDYM) equations by means of the modified Faddeev–Jackiw method in [Formula: see text] and [Formula: see text] gauges à la Yang. We also establish the Hamiltonian flow for ASDYM system through the hidden BRS invariance in both the gauges. Finally, we remark on the bi-Hamiltonian nature of ASDYM and the compatibility of the symplectic structures therein.
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44

CAO, ZHEN-BIN, and YI-SHI DUAN. "OPEN STRING IN pp-WAVE BACKGROUND WITH B-FIELD." Modern Physics Letters A 24, no. 10 (2009): 759–68. http://dx.doi.org/10.1142/s0217732309028217.

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The open string ending on a flat D-brane in the pp-wave background with a constant B-field is exactly solvable but will be controlled by a more mass parameter. In this paper we mainly quantize this open string theory canonically by employing the Faddeev–Jackiw symplectic quantization procedure, and find that the phase space of the string coordinate and canonical momentum becomes fully noncummutative, consistent with the results obtained previously.
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45

ZANDRON, O. S. "THE HUBBARD OPERATORS AND THE SLAVE-PARTICLES PATH-INTEGRAL REPRESENTATIONS DESCRIBING THE t-J MODEL." International Journal of Modern Physics B 21, no. 11 (2007): 1861–74. http://dx.doi.org/10.1142/s0217979207037077.

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In the present work it is shown that the family of first-order Lagrangians for the t-J model and the corresponding correlation generating functional previously found can be exactly mapped into the slave-fermion decoupled representation. Next, by means of the Faddeev-Jackiw symplectic method, a different family of Lagrangians is constructed and it is shown how the corresponding correlation generating functional can be mapped into the slave-boson decoupled representation.
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46

Abreu, E. M. C., A. C. R. Mendes, C. Neves, W. Oliveira, R. C. N. Silva, and C. Wotzasek. "Obtaining non-Abelian field theories via the Faddeev–Jackiw symplectic formalism." Physics Letters A 374, no. 35 (2010): 3603–7. http://dx.doi.org/10.1016/j.physleta.2010.07.006.

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47

Banerjee, N., D. Chatterjee, and Subir Ghosh. "Chiral bosons coupled to Liouville gravity in the Faddeev-Jackiw formalism." Physical Review D 46, no. 12 (1992): 5590–97. http://dx.doi.org/10.1103/physrevd.46.5590.

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48

Foussats, A., and O. S. Zandron. "About the supersymmetric extension of the symplectic Faddeev - Jackiw quantization formalism." Journal of Physics A: Mathematical and General 30, no. 15 (1997): L513—L517. http://dx.doi.org/10.1088/0305-4470/30/15/006.

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49

Müller-Kirsten, H. J. W., and Jian-zu Zhang. "Faddeev-Jackiw formalism, gauge fixing conditions and constraint induced effective potential." Physics Letters A 200, no. 3-4 (1995): 243–49. http://dx.doi.org/10.1016/0375-9601(95)00166-z.

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50

Paschalis, J. E., and P. I. Porfyriadis. "Application of the Faddeev-Jackiw formalism to the gauged WZW model." Physics Letters B 355, no. 1-2 (1995): 171–77. http://dx.doi.org/10.1016/0370-2693(95)00746-8.

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