Stable interactions in higher derivative field theories of derived type

Abakumova, V. A.; Lyakhovich, S. L.; Kaparulin, D. S.

doi:10.1103/physrevd.99.045020

Cited by 29 publications

(55 citation statements)

References 38 publications

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“…The explicit control of the DoF number in the involutive closure allows one to consistently include interactions in the covariant form for the second class systems, see (5), ( 6), (7). This method has been first proposed in the article [11] (for applications of the method in specific models see, for example, [12][13][14][15]). The original proposal of [11] allows one to find all the consistent vertices in the field equations, including non-Lagrangian one, without distinctions between variational and non-variational interactions.…”

Section: Discussionmentioning

confidence: 99%

“…For applications of this scheme of inclusion of interactions, see, for example, [11][12][13][14][15]. While non-Lagrangian vertices may have their own advantages, in particular they can be stable in higher derivative field theories [14,16], it seems interesting to have a method of identifying all the consistent Lagrangian vertices. The way to construct all the consistent Lagrangian vertices is briefly noticed in the next section as a side remark.…”

Section: Introductionmentioning

confidence: 99%

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General method for including Stueckelberg fields

Lyakhovich

2021

Eur. Phys. J. C

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A systematic procedure is proposed for inclusion of Stueckelberg fields. The procedure begins with the involutive closure when the original Lagrangian equations are complemented by all the lower order consequences. The Stueckelberg field is introduced for every consequence included into the closure. The generators of the Stueckelberg gauge symmetry begin with the operators generating the closure of original system. These operators are not assumed to be a generators of gauge symmetry of any part of the original action, nor are they supposed to form an on shell integrable distribution. With the most general closure generators, the consistent gauge invariant theory is iteratively constructed, without obstructions at any stage. The Batalin–Vilkovisky form of inclusion of the Stueckelberg fields is worked out and the existence theorem for the Stueckelberg action is proven.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

General method for including Stueckelberg fields

Lyakhovich

2021

Eur. Phys. J. C

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“…In this set, the quantities (T p ) μν , p = 0,…,n-2, are independent, while We mention this fact to illustrate possible dependence among conserved quantities in the class of gauge models. We also notice that the set of the conserved currents of the extended Chern-Simons model (87) was introduced in the work [25], while the compact form (91-94) is proposed in [34].…”

Section: Extended Chern-simons Modelmentioning

confidence: 99%

Conservation Laws and Stability of Field Theories of Derived Type

Kaparulin

2019

Symmetry

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We consider the issue of correspondence between symmetries and conserved quantities in the class of linear relativistic higher-derivative theories of derived type. In this class of models the wave operator is a polynomial in another formally self-adjoint operator, while each isometry of space-time gives rise to the series of symmetries of action functional. If the wave operator is given by n-th-order polynomial then this series includes n independent entries, which can be explicitly constructed. The Noether theorem is then used to construct an n-parameter set of second-rank conserved tensors. The canonical energy-momentum tensor is included in the series, while the other entries define independent integrals of motion. The Lagrange anchor concept is applied to connect the general conserved tensor in the series with the original space-time translation symmetry. This result is interpreted as existence of multiple energy-momentum tensors in the class of derived systems. To study stability we seek for bounded-conserved quantities that are connected with the time translations. We observe that the derived theory is stable if its wave operator is defined by a polynomial with simple and real roots. The general constructions are illustrated by the examples of the Pais-Uhlenbeck oscillator, higher-derivative scalar field, and extended Chern-Simons theory.

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“…charged scalar field constructed in [15] preserve one representative in the series of Hamiltonian formulations, and the theory remains stable at the interacting level.…”

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confidence: 99%

“…After excluding all the variables, equations(15)and(16)reproduce spatial and temporal part of the equations of motion (2), respectively. Let us note that in the first-order formalism the quantity Θ (16) does not involve time derivatives and can be considered as a constraint.The first-order system of equations (13) -(15) is Hamiltonian if there exists the Hamiltonian H(α , β) and Poisson brackets { , } α,β such that…”

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confidence: 99%

Stable Interactions Between the Extended Chern-Simons Theory and a Charged Scalar Field with Higher Derivatives: Hamiltonian Formalism

2019

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We consider constrained multi-Hamiltonian formulation for the extended Chern-Simons theory with higher derivatives of arbitrary finite order. The order n extension of the theory admits (n − 1)-parametric series of conserved tensors. The 00component of any representative of the series can be chosen as Hamiltonian. The theory admits a series of Hamiltonian formulations, including the canonical Ostrogradski formulation. The Hamiltonian formulations with different Hamiltonians are not connected by canonical transformations. Also, we demonstrate the inclusion of stable interactions with charged scalar field that preserves one specified Hamiltonian from the series. IntroductionThe Hamiltonian formulations for theories with higher derivatives have been discussed once and again for decades since the work of Ostrogradski [1]. The procedure for constructing such Hamiltonian formulation for degenerate theories was originally proposed in [2]. This procedure and its modifications can be applied to study different gauge theories, including gravity (see [3,4]). The canonical Ostrogradski Hamiltonian used in all these methods is not bounded. It leads to the wellknown stability problem and difficulties with constructing of quantum theory [5][6][7].The alternative Hamiltonian formulation was first introduced in the Pais-Uhlenbeck theory [8,9]. In the work [10], it was noticed that a wide class of theories with higher derivatives admits the series of Hamiltonians and the Poisson brackets that are not connected with each other by canonical transformations. The canonical Ostrogradski Hamiltonian is included in the series. The series of non-canonical Hamiltonian formulations was constructed explicitly in [11,12] for the extended Chern-Simons theory [13] of the third and fourth order.In the present work, we consider the Hamiltonian formulation for the extended Chern-Simons of arbitrary finite order. At free level, the theory of order n admits (n − 1)-parametric series of Hamiltonian formulations with Hamiltonian being the 00-component of any conserved tensor from the series [14]. We demonstrate that non-Lagrangian interaction vertices with * abakumova@phys.tsu.ru † dsc@phys.tsu.ru ‡ sll@phys.tsu.ru

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Stable interactions in higher derivative field theories of derived type

Cited by 29 publications

References 38 publications

General method for including Stueckelberg fields

General method for including Stueckelberg fields

Conservation Laws and Stability of Field Theories of Derived Type

Stable Interactions Between the Extended Chern-Simons Theory and a Charged Scalar Field with Higher Derivatives: Hamiltonian Formalism

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