Finite Order BFFT Method

Monemzadeh, M.; Shirzad, A.

doi:10.1142/s0217751x03016501

Cited by 12 publications

(16 citation statements)

References 16 publications

(20 reference statements)

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“…As it has been stated before [23,24], there are more than one solution for equation (12). Thus, for a given second class system, there are so many corresponding first class systems which divert to it after gauge fixing.…”

Section: Bft Methodsmentioning

confidence: 88%

First class models from linear and nonlinear second class constraints

et al. 2015

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Two models with linear and nonlinear second class constraints are considered and gauged by embedding in an extended phase space. These models are studied by considering a free non-relativistic particle on the hyper plane and hyper sphere in the configuration space. The gauged theory of the first model is obtained by converting the very second class system to the first class one, directly. In contrast, the first class system related to the free particle on the hyper sphere is derived with the help of the infinite BFT embedding procedure. We propose a practical formula, based on the simplified BFT method, which is practical in gauging linear and some nonlinear second class systems. As a result of gauging these two models, we show that in the conversion of second class constraints to the first class ones, the minimum number of phase space degrees of freedom for both systems is a pair of phase space coordinates. This pair is made up of a coordinate and its conjugate momentum for the first model, but the corresponding Poisson structure of the embedded non-relativistic particle on hyper sphere is a non-trivial one. We derive infinite correction terms for the Hamiltonian of the nonlinear constraints and an interacting gauged Hamiltonian is constructed by summing over them. At

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Section: Bft Methodsmentioning

confidence: 88%

First class models from linear and nonlinear second class constraints

et al. 2015

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“…In this way one can convert second class constraints to first class ones and then apply the well-known quantization method of gauge theories [4,5]. In our previous paper [6] we showed that if one chooses arbitrary parameters of the BFT method suitably then the power series of auxiliary fields for the embedded constraints and Hamiltonian could be truncated in some cases. In this Letter we want to preserve the chain structure of a second class system (except for the last element of the chain) during the BFT embedding.…”

mentioning

confidence: 99%

“…(14)-(16), respectively. We remind that [6], the aim is to choose a suitable solution for χ αβ in Eq. (17) such that the series for τ α andH truncates after a few steps.…”

mentioning

confidence: 99%

“…As explained in more details in [6] after embedding, the constraints remain linear with respect to the coordinates of the extended phase space. Moreover, if the original Hamiltonian is quadratic, it would remain quadratic after embedding.…”

mentioning

confidence: 99%

“…(25) satisfy the chain structure relation (1) where τ 1 is the primary constraint. The chiral Schwinger model has also been discussed in [6] where the set of first class constraints are the same as (25) while the embedded HamiltonianH is different. It is worth nothing that this Hamiltonian does not differ from that of the strongly involutive formulation by the mere addition of a suitable combination of the first class constraints.…”

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The BFT method with chain structure

Shirzad

Monemzadeh

2004

Physics Letters B

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We have constructed a modified BFT method that preserves the chain structure of constraints. This method has two advantages: first, it leads to less number of primary constraints such that the remaining constraints emerge automatically; and second, it gives less number of independent gauge parameters. We have applied the method for bosonized chiral Schwinger model. We have constructed a gauge invariant embedded Lagrangian for this model.  2004 Elsevier B.V. All rights reserved.Dirac as a pioneer, quantized classical gauge theories by converting Poisson brackets to quantum commutators [1]. However, for second class constraint systems it is necessary to replace Poisson brackets by Dirac brackets and then convert them to quantum commutators. Sometimes this process implies problems such as factor ordering which makes this approach improper. The BFT method, however, solves this ambiguity by embedding the phase space in a larger space including some auxiliary fields [2,3]. In this way one can convert second class constraints to first class ones and then apply the well-known quantization method of gauge theories [4,5]. In our previous paper [6] we showed that if one chooses arbitrary parameters of the BFT method suitably then the power series of auxiliary fields for the embedded constraints and Hamiltonian could be truncated in some cases. E-mail addresses: shirzad@ipm.ir (A. Shirzad), monemzadeh@sepahan.iut.ac.ir (M. Monemzadeh).In this Letter we want to preserve the chain structure of a second class system (except for the last element of the chain) during the BFT embedding. The main idea of the chain structure, as fully discussed in [7], is that it is possible to derive the constraints as commuting distinct chains such that within each chain the following iterative relation holds0 stand for primary constraints. The advantages of this method will be discussed afterward.Consider a second class constraint system described by the Hamiltonian H 0 and a set of second class constraints Φ α ; α = 1, . . ., N satisfying the algebrawhere ∆ is an antisymmetric and invertible matrix. For simplicity and without loss of generality we suppose that the second class constraints Φ α are elements of one chain. The results can be extended to multi-chain 0370-2693/$ -see front matter 

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