Hamiltonian embedding of the massive Yang-Mills theory and the generalized Stückelberg formalism

Banerjee, Rabin; Barcelos-Neto, J.

doi:10.1016/s0550-3213(97)00296-4

Cited by 50 publications

(59 citation statements)

References 34 publications

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“…Finally, we would like to comment on the interesting work recently done by Banerjee and Barcelos-Neto [29]. After finishing our work, we have found that their work is similar to our work.…”

Section: B Lagrangian From the Hamilton's Equation Of Motionsupporting

confidence: 66%

Non-Abelian Proca Model Based on the Improved BFT Formalism

Park

1998

Int. J. Mod. Phys. A

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We present the newly improved Batalin-Fradkin-Tyutin (BFT) Hamiltonian formalism and the generalization to the Lagrangian formulation, which provide the much more simple and transparent insight to the usual BFT method, with application to the non-Abelian Proca model which has been an difficult problem in the usual BFT method. The infinite terms of the effectively first class constraints can be made to be the regular power series forms by ingenious choice of X αβ and ω αβ -matrices. In this new method, the first class Hamiltonian, which also needs infinite correction terms is obtained simply by replacing the original variables in the original Hamiltonian with the BFT physical variables. Remarkably all the infinite correction terms can be expressed in the compact exponential form. We also show that in our model the Poisson brackets of the BFT physical variables in the extended phase space are the same structure as the Dirac brackets of the original phase space variables. With the help of both our newly developed Lagrangian formulation and Hamilton's equations of motion, we obtain the desired classical Lagrangian corresponding to the first class Hamiltonian which can be reduced to the generalized Stückelberg Lagrangian which is non-trivial conjecture in our infinitely many terms involved in Hamiltonian and Lagrangian.

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“…Finally, we would like to comment on the interesting work recently done by Banerjee and Barcelos-Neto [29]. After finishing our work, we have found that their work is similar to our work.…”

Section: B Lagrangian From the Hamilton's Equation Of Motionsupporting

confidence: 66%

Non-Abelian Proca Model Based on the Improved BFT Formalism

Park

1998

Int. J. Mod. Phys. A

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“…The method also permit us to obtain any involutive quantity that has zero Poisson brackets with all the constraints. The embedding Hamiltonian can be obtained in this way, starting from the initial canonical Hamiltonian and iteratively calculating the corresponding corrections.There is another manner to obtain an embedding Hamiltonian, which consists in using the BFFT method to obtain involutive coordinates [4]. The canonical Hamiltonian is then rewritten in terms of these new coordinates that automatically give it the involutive condition.…”

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confidence: 99%

“…The transformation of constraints from second to first-class is achieved after extending the phase space by means of auxiliary variables under the general rule that there is one pair of canonical variables for each second class constraint. The method is iterative and can stop in the first step [3] or can go on indefinitely [4,5]. In any case, after all constraints have been transformed into first-class, it is necessary to look for the Hamiltonian corresponding to this new theory.…”

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confidence: 99%

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A superspace embedding of the Wess–Zumino model

Barcelos-Neto

2001

Eur. Phys. J. C

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We embed the Wess-Zumino (WZ) model in a wider superspace than the one described by chiral and anti-chiral superfields.1. There is a systematic and interesting formalism for embedding, developed by Batalin, Fradkin, Fradkina, and Tyutin (BFFT) [1], where theories with second-class constraints [2] are transformed into more general (gauge) theories where all constraints become first-class. The transformation of constraints from second to first-class is achieved after extending the phase space by means of auxiliary variables under the general rule that there is one pair of canonical variables for each second class constraint. The method is iterative and can stop in the first step [3] or can go on indefinitely [4,5]. In any case, after all constraints have been transformed into first-class, it is necessary to look for the Hamiltonian corresponding to this new theory. The method also permit us to obtain any involutive quantity that has zero Poisson brackets with all the constraints. The embedding Hamiltonian can be obtained in this way, starting from the initial canonical Hamiltonian and iteratively calculating the corresponding corrections.There is another manner to obtain an embedding Hamiltonian, which consists in using the BFFT method to obtain involutive coordinates [4]. The canonical Hamiltonian is then rewritten in terms of these new coordinates that automatically give it the involutive condition. Of course, the embedding Hamiltonians obtained from these two different ways are not necessarily equal. This means that for some specific theory there may exist more than one possible embeddings. It is also opportune to say, on the other hand, that there are theories which cannot be embedded [6].One of the interesting problem that the BFFT method could be addressed is the covariant quantization of superparticles and superstrings, that remained opened for a long time. This problem has been solved in a embedding procedure but differently of the BFFT method [7]. In fact, the meaning of embedding in field theory can be taken as much wider than the cases described by the BFFT method. The important point is that the embedding theory contains all the physics of the embedded one.We mention, for example, even the general procedure of supersymmetrization is an example of embedding.We would like to address the present paper to this point of view of considering the embedding procedure in a wider way. We concentrate on the WZ model [8] in superfield language [9,10]. Conventionally, the WZ model is always developed in terms of chiral and antichiral superfields, that are examples of irreducible superfields. We shall consider here a kind of embedding where we describe the WZ model by using a more general superfield representation. We shall see that, contrarily to the bosonic nature of the chiral and antichiral superfields, the general superfield we have to use is fermionic. We shall also see that there are two possible terms that can figure in the Lagrangian and having a relative parameter between them. The consistency of th...

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“…Note that in the usual BFT Hamiltonian embedding of the model we would have identified two auxiliary fields with a pair of conjugate fields as coordinate and momenta [6,7,[9][10][11].…”

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confidence: 99%

Symplectic structure-free Chern-Simons theory

Kim¹,

Park²

1999

J. Phys. A: Math. Gen.

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The second class constraints algebra of the abelian Chern-Simons theory is rigorously studied in terms of the Hamiltonian embedding in order to obtain the first class constraint system. The symplectic structure of fields due to the second class constraints disappears in the resulting system. Then we obtain a new type of Chern-Simons action which has an infinite set of the irreducible first class constraints and exhibits new extended local gauge symmetries implemented by these first class constraints. PACS number(s):

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Hamiltonian embedding of the massive Yang-Mills theory and the generalized Stückelberg formalism

Cited by 50 publications

References 34 publications

Non-Abelian Proca Model Based on the Improved BFT Formalism

Non-Abelian Proca Model Based on the Improved BFT Formalism

A superspace embedding of the Wess–Zumino model

Symplectic structure-free Chern-Simons theory

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