Natural Hamiltonian formulation of composite higher derivative theories

Öttinger, Hans Christian

doi:10.1088/2399-6528/ab3634

Cited by 6 publications

(24 citation statements)

References 29 publications

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“…The basic idea of composite theories has been developed in the context of mechanical systems [1,2]. However, the finitedimensional systems have been taken so general that spatially discretized versions of the field theories we are interested in * hco@mat.ethz.ch; www.polyphys.mat.ethz.ch are included.…”

Section: Composite Theoriesmentioning

confidence: 99%

“…In this classical approach,q andq serve as configurational variables and the corresponding conjugate momenta involve second and third time derivatives ofq. A more elegant Hamiltonian formulation of composite theories can be based on q andq as configurational variables and the corresponding conjugate momenta p (from the workhorse theory) andp (containing third derivatives ofq) [2]. The resulting Hamiltonian is linear in the momentump.…”

Section: Composite Theoriesmentioning

confidence: 99%

“…By requiring dynamic consistency of the constraints, the primary constraints lead to secondary and successively higher constraints. The examples of [2] show that (i) the hierarchy of constraints ends with the constraints p = 0, and (ii) the entire set of constraints is so large that the composite theory has fewer degrees of freedom than the workhorse theory. The constraintsp = 0 make the Hamiltonian bounded from below and therefore eliminate all concerns about instabilities.…”

Section: Composite Theoriesmentioning

confidence: 99%

“…The structure constants can be specified as follows: f abc is 1 (−1) if (a, b, c) is an even (odd) permutation of (4,5,6), (1,3,5), (1,6,2), or (2,4,3) and vanishes otherwise. These structure constants satisfy the Jacobi identity…”

Section: B Lorentz Groupmentioning

confidence: 99%

“…The purpose of this work is to elaborate a composite field theory that is a natural candidate for an alternative theory of gravity. Composite theories are obtained by considering the independent variables of some given theory as functions of some more fundamental variables and their derivatives [1,2]. Such composite theories typically involve higher derivatives and are thus prone to instability.…”

Section: Introductionmentioning

confidence: 99%

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Composite higher derivative theory of gravity

Öttinger

2020

Phys. Rev. Research

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We investigate a higher derivative theory that belongs to the class of composite field theories. Starting from the Yang-Mills theory based on the Lorentz group, we express the gauge vector fields in terms of the tetrad decomposition of a space-time metric with a nontrivial coupling constant. The resulting composite gauge theory is a natural candidate for an alternative theory of pure gravity. In the limit of vanishing coupling constant, all classical high-precision tests for theories of gravity are passed. An exact static isotropic solution is found, which is less singular than the Schwarzschild solution of general relativity. Composite field theories come with a natural canonical Hamiltonian formulation and a natural set of constraints, so that they provide an ideal setting for future quantization. Finally, we propose possible couplings of the gravitational field to matter.

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Section: Composite Theoriesmentioning

confidence: 99%

Section: Composite Theoriesmentioning

confidence: 99%

Section: Composite Theoriesmentioning

confidence: 99%

Section: B Lorentz Groupmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Composite higher derivative theory of gravity

Öttinger

2020

Phys. Rev. Research

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Mathematical structure and physical content of composite gravity in weak-field approximation

Öttinger

2020

Phys. Rev. D

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The natural constraints for the weak-field approximation to composite gravity, which is obtained by expressing the gauge vector fields of the Yang-Mills theory based on the Lorentz group in terms of tetrad variables and their derivatives, are analyzed in detail within a canonical Hamiltonian approach. Although this higher derivative theory involves a large number of fields, only a few degrees of freedom are left, which are recognized as selected stable solutions of the underlying Yang-Mills theory. The constraint structure suggests a consistent double coupling of matter to both Yang-Mills and tetrad fields, which results in a selection among the solutions of the Yang-Mills theory in the presence of properly chosen conserved currents. Scalar and tensorial coupling mechanisms are proposed, where the latter mechanism essentially reproduces linearized general relativity. In the weak-field approximation, geodesic particle motion in static isotropic gravitational fields is found for both coupling mechanisms. An important issue is the proper Lorentz covariant criterion for choosing a background Minkowski system for the composite theory of gravity.

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Conserved currents for the gauge-field theory with Lorentz symmetry group and a composite theory of gravity

Öttinger¹

2023

EPL

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For the Yang-Mills-type gauge-field theory with Lorentz symmetry group, we propose and verify an explicit expression for the conserved currents in terms of the energy-momentum tensor. A crucial ingredient is the assumption that the gauge symmetry arises from the decomposition of a metric in terms of tetrad variables. The currents exist under the weak condition that the energy-momentum tensor and the Ricci tensor commute. We show how the conserved currents can be used to obtain a composite theory of gravity and discuss the static isotropic field around a point mass at rest.

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Natural Hamiltonian formulation of composite higher derivative theories

Cited by 6 publications

References 29 publications

Composite higher derivative theory of gravity

Composite higher derivative theory of gravity

Mathematical structure and physical content of composite gravity in weak-field approximation

Conserved currents for the gauge-field theory with Lorentz symmetry group and a composite theory of gravity

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