Classical Yang-Mills field theory with nonstandard Lagrangians

Алексеев, А. И.; Arbuzöv, B. A.

doi:10.1007/bf01028515

Cited by 63 publications

(47 citation statements)

References 2 publications

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“…As an example for the more complicated case of a non-abelian theory, we applied the second order gauge theory to the Alekssev-Arbuzov-Baikov effective Lagrangian valid in the infrared regime, demonstrating that the conserved current (49) and the one obtained in [10] differ by surface terms. In this way, we have shown that 1-loop effective terms in the action can be found from first-principle calculations imposing the gauge symmetry to second order Lagrangians.…”

Section: General Remarksmentioning

confidence: 99%

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Second order gauge theory

2007

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A gauge theory of second order in the derivatives of the auxiliary field is constructed following Utiyama's program. A novel field strength G = ∂F + f AF arises besides the one of the first order treatment, F = ∂A − ∂A + f AA. The associated conserved current is obtained. It has a new feature: topological terms are determined from local invariance requirements. Podolsky Generalized Eletrodynamics is derived as a particular case in which the Lagrangian of the gauge field is LP ∝ G 2 . In this application the photon mass is estimated. The SU (N ) infrared regime is analysed by means of Alekseev-Arbuzov-Baikov's Lagrangian.

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Section: General Remarksmentioning

confidence: 99%

“…Another probable feature is the impossibility of closing the number of derivatives (counterterms), as in the case of gravitational field. Some tentative works in this direction were undertaken in [10].…”

Section: B Geometrical Aspectsmentioning

confidence: 99%

Second order gauge theory

2007

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“…This theory was originally proposed as an attempt to eliminate the infrared divergences in SU (N ) theories [32][33][34]. In order to introduce some concepts, let us consider the U (1) electrodynamics in four dimensions, see (7),…”

Section: Su(n) Higher-derivative Yang-mills-utiyama Theorymentioning

confidence: 99%

“…The relative success of these achievements motivated some authors to propose finite extensions of Quantum Chromodynamics (QCD) [32][33][34] and also to advocate that higher order terms would be able to explain quark confinement. Our main goal here would be exactly to study both higher-derivative theories, Podolsky's electrodynamics and a non-Abelian [35,36] extension of the model, also known as the Alekseev-Arbuzov-Baikov effective Lagrangian [37] in the framework of the Faddeev-Jackiw symplectic approach.…”

Section: Introductionmentioning

confidence: 99%

Higher-derivative non-Abelian gauge fields via the Faddeev–Jackiw formalism

Bufalo

Pimentel

2014

Eur. Phys. J. C

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In this paper we analyze two higher-derivative theories, the generalized electrodynamics and the AlekseevArbuzov-Baikov effective Lagrangian from the point of view of the Faddeev-Jackiw symplectic approach. It is shown that the full set of constraints is obtained directly from the zeromode eigenvectors, and that they are in accordance with wellknown results from Dirac's theory, a recurrent issue in the literature. The method shows to be rather economical in relation to the Dirac one, obviating thus unnecessary classification and calculations. Afterwards, to conclude we construct the transition amplitude of the non-Abelian theory following a constrained BRST method.

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“…The theory of non-natural or non-standard Lagrangians (NSL) which are characterized by a deformed Lagrangian or deformed kinetic and potential energy terms have recently gained an increasing importance due to their wide applications in applied mathematics and theoretical physics [23][24][25][26][27][28][29]. However, this topic has not been treated in all science branches due to the difficult apparent meaning of physical quantities, e.g.…”

Section: Introductionmentioning

confidence: 99%

From Classical to Discrete Gravity through Exponential Non-Standard Lagrangians in General Relativity

El-Nabulsi

2015

Mathematics

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Abstract:Recently, non-standard Lagrangians have gained a growing importance in theoretical physics and in the theory of non-linear differential equations. However, their formulations and implications in general relativity are still in their infancies despite some advances in contemporary cosmology. The main aim of this paper is to fill the gap. Though non-standard Lagrangians may be defined by a multitude form, in this paper, we considered the exponential type. One basic feature of exponential non-standard Lagrangians concerns the modified Euler-Lagrange equation obtained from the standard variational analysis. Accordingly, when applied to spacetime geometries, one unsurprisingly expects modified geodesic equations. However, when taking into account the time-like paths parameterization constraint, remarkably, it was observed that mutually discrete gravity and discrete spacetime emerge in the theory. Two different independent cases were obtained: A geometrical manifold with new spacetime coordinates augmented by a metric signature change and a geometrical manifold characterized by a discretized spacetime metric. Both cases give raise to Einstein's field equations yet the gravity is discretized and originated from "spacetime discreteness". A number of mathematical and physical implications of these results were discussed though this paper and perspectives are given accordingly.

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Classical Yang-Mills field theory with nonstandard Lagrangians

Cited by 63 publications

References 2 publications

Second order gauge theory

Second order gauge theory

Higher-derivative non-Abelian gauge fields via the Faddeev–Jackiw formalism

From Classical to Discrete Gravity through Exponential Non-Standard Lagrangians in General Relativity

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