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Gauge Invariant Fractional Electromagnetic Fields
Mathematical Physics · Submitted 17 Aug 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation.
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The abstract, sentence by sentence
Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. | background 1.00 | 0.03 | 0.02 | asserted 1.00 |
| s1 | In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. | gap 0.83 | 0.04 | 0.04 | asserted 1.00 |
| s2 | In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. | contribution 1.00 | 0.94 | 0.66 | asserted 0.99 |
| s3 | From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators. | result 0.54 | 0.92 | 0.19 | asserted 1.00 |
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The paper
Original abstract
Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators.
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How the literature uses it
3 arXiv papers cite this in 3 sentences
Papers citing it · 2 sentences without a confident label
Cites it as background 1 paper
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Relativistic quantum mechanics [ref] , field theories [ref] , and gravitation [ref] , have been considered in the context of fractional calculus.
The DuBois-Reymond Fundamental Lemma of the Fractional Calculus of Variations and an Euler-Lagrange Equation Involving only Derivatives of Caputo · Introduction · 0.89
What it cites · 1 sentence without a confident label
Cites as background 1 paper
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Relativistic quantum mechanics [ref] , field theories [ref] and gravitation [ref] has been also recently considered in the context of fractional calculus.
Riemann-Liouville Fractional Einstein Field Equations · Introduction · 0.90
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