Lagrangian formulation of massive fermionic totally antisymmetric tensor field theory in space

Buchbinder, I. L.; Krykhtin, V.A.; Ryskina, L. L.

doi:10.1016/j.nuclphysb.2009.04.014

Cited by 24 publications

(31 citation statements)

References 45 publications

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“…One should notice that the case of totally antisymmetric spin-tensors developed in Ref. [60] is contained in the general Lagrangian formulation for s 1 = s 2 = ... = s k = 3 2 , k = [(d − 1)/2]. As examples demonstrating the applicability of the general scheme, it is shown that it contains as a particular case the Lagrangian formulation for a mixed-symmetric spin-tensors subject to a Young tableaux with two rows, first developed in [59], as well as the new unconstrained Lagrangian formulation in (6.30)-(6.34) for mixed-symmetry fermionic HS fields with three groups of symmetric indices subject to a Young tableaux with three rows, obtained in the literature for the first time.…”

Section: Resultsmentioning

confidence: 99%

“…There exists another realization of all irreps be means of a different Fock space H as , generated by fermionic oscillators (antisymmetric basis)â m µ m (x),ân + ν n (x) with the anticommutation relations {â m µ m ,â n+ ν n } = −η µ m ν n δ mn , for m, n = 1, ..., n 1 , and one can complete the below procedure, which follows the prescription of[60] for totally antisymmetric spin-tensors for n 1 = n 2 = ... = n k .…”

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confidence: 99%

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General Lagrangian formulation for higher spin fields with arbitrary index symmetry. 2. Fermionic fields

Reshetnyak

2013

Nuclear Physics B

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We continue the construction of a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with an arbitrary Young tableaux having k rows, on a basis of the BRST-BFV approach suggested for bosonic fields in our first article (Nucl. Phys. B862 (2012) 270, [arXiv:1110). Starting from a description of fermionic mixed-symmetry higher-spin fields in a flat space of any dimension in terms of an auxiliary Fock space associated with a special Poincare module, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincare-group representations) into a system of first-class constraints. To do this, we find, in first time, by means of generalized Verma module the auxiliary representations of the constraint subsuperalgebra, to be isomorphic due to Howe duality to osp(1|2k) superalgebra, and containing the subsystem of second-class constraints in terms of new oscillator variables. We suggest a universal procedure of finding unconstrained gauge-invariant Lagrangians with reducible gauge symmetries, describing the dynamics of both massless and massive fermionic fields of any spin. It is shown that the space of BRST cohomologies with a vanishing ghost number is determined only by constraints corresponding to an irreducible Poincare-group representation. As examples of the general approach, we propose a method of Lagrangian construction for fermionic fields subject to an arbitrary Young tableaux having 3 rows, and obtain a gauge-invariant Lagrangian for a new model of a massless rank-3 spintensor field of spin (5/2, 3/2) with first-stage reducible gauge symmetries and a non-gauge Lagrangian for a massive rank-3 spin-tensor field of spin (5/2, 3/2). and fermionic fields of various spins, providing the consideration of higher-spin theory as a tool of investigating the structure of superstring theory. For the current progress in higher-spin field theory, see the reviews [1], whereas some recent directions in higher-spin theory, starting from the pioneering papers [2], [3], [4], are examined in [5]- [20].The dynamics of totally symmetric free higher-spin fields is currently the most well-developed area in the variety of unitary representations of the Poincare and AdS algebras [3], [4], [21], [22]. This situation is due to the fact that a 4d space-time does not admit any mixed-symmetry irreducible representations, except for dual theories. It is well-known that in higher space-time dimensions there arise mixed-symmetry representations, determined by spin-like parameters being more than one in number [23], [24], [25], whereas their field-theoretic description is not so well-developed as for totally symmetric representations. While the simplest mixed-symmetric HS bosonic fields were examined in [26], attempts to construct Lagrangian descriptions of free and interacting higher-spin field theories have met with consistency problems, which have not yet been completely solved. Unconstrained Lagrangians for half-integer H...

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Section: Resultsmentioning

confidence: 99%

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confidence: 99%

General Lagrangian formulation for higher spin fields with arbitrary index symmetry. 2. Fermionic fields

Reshetnyak

2013

Nuclear Physics B

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“…To derive the unconstrained formulation from the Lagrangian (2.28) we partially fix the gauge invariance as was done in [43][44][45][46][47][48][49][50][51][52] (putting there the curvature to zero, R = 0), except that we will not fix gauge invariance corresponding to the gauge parameter |ε (we remove only the dependence on b…”

Section: Partial Gauge Fixing and Different Lagrangian Formulationsmentioning

confidence: 99%

“…Our main aim is to derive the gauge invariant Lagrangian using the method of BRST construction [43][44][45][46][47][48][49][50][51][52] in the quadratic approximation in the field strength F μν of the external field. This method in fact yields a gauge invariant Lagrangian description for massive higher spin fields in extended Fock space and therefore the Lagrangian will contain, apart from the basic fields, some additional fields, such as Stückelberg fields.…”

Section: Introductionmentioning

confidence: 99%

Quartic interaction vertex in the massive integer higher spin field theory in a constant electromagnetic field

Buchbinder

Krykhtin

2015

Eur. Phys. J. C

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We consider the massive integer higher spin fields coupled to an external constant electromagnetic field in flat space of arbitrary dimension and find a gauge invariant quartic interaction vertex which is quadratic in a dynamical higher spin field and quadratic in the external field. The construction of the vertex is based on the BRST approach to higher spin field theory where no off-shell constraints on the fields and on the gauge parameters are imposed from the very beginning (unconstrained formulation).

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“…Within the metric-like approach totally antisymmetric fermionic fields were studied in [38] and [39]. The field potential is an antisymmetric spin-tensor φ µ 1 ...µp:α with the gauge transformations of the form…”

Section: One-column Fieldmentioning

confidence: 99%

Frame-like actions for massless mixed-symmetry fields in Minkowski space. Fermions

Skvortsov

Zinoviev²

2011

Nuclear Physics B

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Lagrangian formulation of massive fermionic totally antisymmetric tensor field theory in space

Cited by 24 publications

References 45 publications

General Lagrangian formulation for higher spin fields with arbitrary index symmetry. 2. Fermionic fields

General Lagrangian formulation for higher spin fields with arbitrary index symmetry. 2. Fermionic fields

Quartic interaction vertex in the massive integer higher spin field theory in a constant electromagnetic field

Frame-like actions for massless mixed-symmetry fields in Minkowski space. Fermions

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