Classification of Constraints Using the Chain-by-Chain Method

Loran, Farhang; Shirzad, A.

doi:10.1142/s0217751x02009643

Cited by 22 publications

(43 citation statements)

References 12 publications

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“…In fact, this requires a special algorithm to be followed as given in Ref. [4]. Now let us see how the gauge can be fixed.…”

Section: Gauge Fixing In Chain Structurementioning

confidence: 99%

“…First, the level by level method [3] in which the equations concerning the consistency of constraints at a given level are solved simultaneously to find the constraints of the next level. Second, the chain by chain method [4] in which the consistency of every primary constraint produces the corresponding constraint chain up to the end. In the second method the constraints are organized in separate first and second class chains.…”

Section: Introductionmentioning

confidence: 99%

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Full and partial gauge fixing

Shirzad¹

2007

Journal of Mathematical Physics

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Gauge fixing may be done in different ways. We show that using the chain structure to describe a constrained system, enables us to use either a perfect gauge, in which all gauged degrees of freedom are determined; or an imperfect gauge, in which some first class constraints remain as subsidiary conditions to be imposed on the solutions of the equations of motion. We also show that the number of constants of motion depends on the level in a constraint chain in which the gauge fixing condition is imposed. The relativistic point particle, electromagnetism and the Polyakov string are discussed as examples and perfect or imperfect gauges are distinguished.

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“…In fact, this requires a special algorithm to be followed as given in Ref. [4]. Now let us see how the gauge can be fixed.…”

Section: Gauge Fixing In Chain Structurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Full and partial gauge fixing

Shirzad¹

2007

Journal of Mathematical Physics

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“…F (3) does not admit a new left null-eigenvector, therefore a problem appears to reach the last constraint φ (4) within this procedure. Therefore, using (4) we truncate the matrix F (3) as Hence, we found the last constraint φ (4) = −2z by continuing the procedure with the null-eigenvector v (3) .…”

Section: Examplementioning

confidence: 99%

“…Then, multiplying both sides of the associated equations of motion by the left null-eigenvectors of the symplectic tensor gives the next secondclass constraint and so on. This procedure leads us to a chain structure [3] of a second-class constraint set φ (1) , φ (2) , . .…”

Section: Introductionmentioning

confidence: 99%

Symplectic algorithm for systems with second-class constraints

Defterli

Băleanu

2006

Czech J Phys

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“…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 holds…”

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confidence: 99%

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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Classification of Constraints Using the Chain-by-Chain Method

Cited by 22 publications

References 12 publications

Full and partial gauge fixing

Full and partial gauge fixing

Symplectic algorithm for systems with second-class constraints

The BFT method with chain structure

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