Second-order nonlinear Lagrangian tensor field theories of gravitation in agreement with recent observations

Let [Formula: see text] be a pseudo-Riemannian manifold and [Formula: see text] be its second-order tangent bundle equipped with the deformed [Formula: see text]nd lift metric [Formula: see text] which is obtained from the [Formula: see text]nd lift metric by deforming the horizontal part with a symmetric [Formula: see text]-tensor field [Formula: see text]. In the present paper, we first compute the Levi-Civita connection and its Riemannian curvature tensor field of [Formula: see text]. We give necessary and sufficient conditions for [Formula: see text] to be semi-symmetric. Secondly, we show that [Formula: see text] is a plural-holomorphic [Formula: see text]-manifold with the natural integrable nilpotent structure. Finally, we get the conditions under which [Formula: see text] with the [Formula: see text]nd lift of an almost complex structure is an anti-Kähler manifold.

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Order Reduction, Projectability and Constraints of Second-Order Field Theories and Higher-Order Mechanics

Reports on Mathematical Physics ◽

10.1016/s0034-4877(17)30012-5 ◽

2016 ◽

Vol 78 (3) ◽

pp. 327-337 ◽

Cited By ~ 1

Author(s):

Jordi Gaset ◽

Narciso Román-Roy

Keyword(s):

Order Reduction ◽

Higher Order ◽

Second Order ◽

Field Theories

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p-BRANES AS COMPOSITE ANTISYMMETRIC TENSOR FIELD THEORIES

International Journal of Modern Physics A ◽

10.1142/s0217751x98000597 ◽

1998 ◽

Vol 13 (08) ◽

pp. 1263-1292 ◽

Cited By ~ 12

Author(s):

CARLOS CASTRO

Keyword(s):

Tensor Field ◽

Target Space ◽

Field Theories ◽

Antisymmetric Tensor ◽

Field Equations ◽

Light Cone Gauge ◽

Infinite Dimensional ◽

Dimensional Group ◽

Antisymmetric Tensor Field ◽

Covariant Action

p′-brane solutions to rank p+1 composite antisymmetric tensor field theories of the kind developed by Guendelman, Nissimov and Pacheva are found when the dimensionality of space–time is D=(p+1)+(p′+1). These field theories possess an infinite-dimensional group of global Noether symmetries, that of volume-preserving diffeomorphisms of the target space of the scalar primitive field constituents. Crucial in the construction of p′ brane solutions are the duality transformations of the fields and the local gauge field theory formulation of extended objects given by Aurilia, Spallucci and Smailagic. Field equations are rotated into Bianchi identities after the duality transformation is performed and the Clebsch potentials associated with the Hamilton–Jacobi formulation of the p′ brane can be identified with the duals of the original scalar primitive constituents. Explicit examples are worked out the analog of S and T duality symmetry are discussed. Different types of Kalb–Ramond actions are given and a particular covariant action is presented which bears a direct relation to the light cone gauge p-brane action.

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SECOND-ORDER LAGRANGIAN DYNAMICS IN THE PHASE-SPACE: SOME EXAMPLES

Modern Physics Letters A ◽

10.1142/s0217732312500629 ◽

2012 ◽

Vol 27 (10) ◽

pp. 1250062

Author(s):

CONSTANTIN BIZDADEA ◽

MARIA-MAGDALENA BÂRCAN ◽

MIHAELA TINCA MIAUTĂ ◽

SOLANGE-ODILE SALIU

Keyword(s):

Phase Space ◽

Scalar Field ◽

Finite Number ◽

Configuration Space ◽

Degrees Of Freedom ◽

Hamiltonian Formulation ◽

Second Order ◽

Lagrangian Formulation ◽

Field Theories ◽

Lagrangian Dynamics

By means of a class of nondegenerate models with a finite number of degrees of freedom, it is proved that given a Hamiltonian formulation of dynamics, there exists an equivalent second-order Lagrangian formulation whose configuration space coincides with the Hamiltonian phase-space. The above result is extended to scalar field theories in a Lorentz-covariant manner.

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Condensation of p-Branes and Generalized Higgs/Confinement Duality

International Journal of Modern Physics A ◽

10.1142/s0217751x97000955 ◽

1997 ◽

Vol 12 (06) ◽

pp. 1227-1235 ◽

Cited By ~ 8

Author(s):

Fernando Quevedo ◽

Carlo A. Trugenberger

Keyword(s):

Phase Transition ◽

Recent Work ◽

Finite Temperature ◽

Weak Coupling ◽

Tensor Field ◽

Low Energy ◽

Field Theories ◽

Antisymmetric Tensor ◽

Antisymmetric Tensor Field

We review our recent work on the low-energy actions and the realizations of strong-weak coupling dualities in non-perturbative phases of compact antisymmetric tensor field theories due to p-brane condensation. As examples we derive and discuss the confining string and confining membrane actions obtained from compact vector and tensor theories in 4D. We also mention the relevance of our results for the description of the Hagedorn phase transition of finite temperature strings.

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The hidden scalar Lagrangians within Horndeski theory

International Journal of Modern Physics D ◽

10.1142/s021827182043004x ◽

2020 ◽

Vol 29 (14) ◽

pp. 2043004

Author(s):

Gregory W. Horndeski

Keyword(s):

Scalar Field ◽

Generating Function ◽

Cotangent Bundle ◽

Tensor Field ◽

Scalar Fields ◽

Field Theories ◽

Metric Tensor ◽

Cosmological Solutions ◽

Different Types ◽

Vacuum Solutions

In this paper, I show that there exists a new way to obtain scalar–tensor field theories by combining a special scalar field on the cotangent bundle with a scalar field on spacetime. These two scalar fields act as a generating function for the metric tensor. When using these two scalar fields in the Horndeski Lagrangians, we discover, while seeking Friedmann–Lemaître–Robertson–Walker-type cosmological solutions, that hidden in the Horndeski Lagrangians are nondegenerate second-order scalar Lagrangians. In accordance with Ostrogradsky’s work, these hidden scalar Lagrangians lead to multiple vacuum solutions, and thereby predict the existence of the multiverse. The multiverse is comprised of numerous different types of individual universes. For example, some begin explosively, and then coast along exponentially forever at an accelerated rate, while others begin in that manner, and then stop expanding and contract.

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