Is this the Correct Solution for Functional Differential Equations?

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    Functional Integration
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Discussion Overview

The discussion revolves around the correctness of a proposed solution for a functional differential equation. Participants are examining the formulation and definitions involved in the equation, specifically focusing on the interpretation of symbols and terms used.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant proposes a solution to the functional differential equation involving a functional derivative and a measure of a functional integral.
  • Another participant questions the meaning of the symbol \(\delta\), suggesting it might refer to the Gâteaux derivative.
  • A subsequent reply clarifies that \(\delta\) refers to the functional derivative and that \(D[\phi]\) denotes the measure of a functional integral.
  • A later comment introduces a humorous remark about the initial misunderstanding, implying a lack of clarity in communication.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of the symbols used in the equation, indicating that multiple views remain regarding the definitions and implications of the terms.

Contextual Notes

The discussion highlights potential ambiguities in the notation and terminology related to functional differential equations, which may affect the understanding of the proposed solution.

eljose
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let be the next functional differential equation:

[tex]\delta{F[\phi]}=G[\phi,\partial{\phi}][/tex]

then its solution would be:

[tex]F[\phi]=\int{D[\phi]G[\phi,\partial{\phi}][/tex]

would it be correct?..thanks..
 
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What does [itex]\delta[/itex] stand for ? The Gâteaux derivative?

Daniel.
 
No,no Dextercioiby i meant with delta the functional derivative and D[] the meassure of a functional integral.
 
Damn, why wasn't he psychic? Bet he feels bad now.
 

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