Fredholm's Minors of Arbitrary Order: Their Representations as a Determinant of Resolvents and in Terms of Free Fermions and an Explicit Formula for Their Functional Derivative

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dc.creatorFeinberg, Joshua
dc.date2004-02-11
dc.date2004-03-18
dc.date.accessioned2026-07-07T10:50:38Z
dc.date.available2026-07-07T10:50:38Z
dc.descriptionWe study the Fredholm minors associated with a Fredholm equation of the second type. We present a couple of new linear recursion relations involving the $n$th and $n-1$th minors, whose solution is a representation of the $n$th minor as an $n\times n$ determinant of resolvents. The latter is given a simple interpretation in terms of a path integral over non-interacting fermions. We also provide an explicit formula for the functional derivative of a Fredholm minor of order $n$ with respect to the kernel. Our formula is a linear combination of the $n$th and the $n\pm 1$th minors.
dc.description17 pages, Latex, no figures connection to supplementary compound matrices mentioned, references added, typos corrected
dc.identifierhttps://arxiv.org/abs/math-ph/0402029
dc.identifierhttp://arxiv.org/abs/math-ph/0402029
dc.identifierJ.Phys.A37:6299-6310,2004
dc.identifierdoi:10.1088/0305-4470/37/24/008
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/184597
dc.subjectMathematical Physics
dc.subjectOther Condensed Matter
dc.subjectHigh Energy Physics - Theory
dc.subject45B05 Fredholm integral equations
dc.titleFredholm's Minors of Arbitrary Order: Their Representations as a Determinant of Resolvents and in Terms of Free Fermions and an Explicit Formula for Their Functional Derivative
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