S{cyrillic}i{cyrillic}n{cyrillic}g{cyrillic}u{cyrillic}l{cyrillic}ya{cyrillic}r{cyrillic}n{cyrillic}o{cyrillic}s{cyrillic}t{cyrillic}i{cyrillic} v{cyrillic} k{cyrillic}v{cyrillic}a{cyrillic}n{cyrillic}t{cyrillic}o{cyrillic}v{cyrillic}o{cyrillic}i{cyrillic, short} t{cyrillic}ye{cyrillic}o{cyrillic}r{cyrillic}i{cyrillic}i{cyrillic} p{cyrillic}o{cyrillic}l{cyrillic}ya{cyrillic}

M. Danos, Johann Rafelski

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The short-range behaviour of certain Feynman integrals reveals mathematical properties which are not those of either functions or distributions-they contain terms which are more singular than distributions and possess inherent ambiguities. Two classes of singularities exist: To the first one belong all those singularities which have a physical meaning in the sense that in a convergent (regularized) quantum field theory they contribute to observable quantities, frequently as renormalization constants. Most of the singularities of the second, the spurious type, violate the symmetries of the Lagrangian. We demonstrate that they are associated with certain mathematical difficulties of unregularized theories. Much of our analysis deals with the isolation of singularities of this type and with the study of the properties of the singular products of distribution. We argue that the four-dimensional integration leading to the S-matrix in the perturbation expansion must be carried out over an open domain which leaves out the contributions from singularities of the contact type, that is terms proportional to δ4x-y.

Original languageEnglish (US)
Pages (from-to)326-367
Number of pages42
JournalIl Nuovo Cimento A
Volume49
Issue number3
DOIs
StatePublished - Feb 1979
Externally publishedYes

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ambiguity
leaves
isolation
perturbation
expansion
symmetry
products
matrices

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Nuclear and High Energy Physics
  • Astronomy and Astrophysics

Cite this

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title = "S{cyrillic}i{cyrillic}n{cyrillic}g{cyrillic}u{cyrillic}l{cyrillic}ya{cyrillic}r{cyrillic}n{cyrillic}o{cyrillic}s{cyrillic}t{cyrillic}i{cyrillic} v{cyrillic} k{cyrillic}v{cyrillic}a{cyrillic}n{cyrillic}t{cyrillic}o{cyrillic}v{cyrillic}o{cyrillic}i{cyrillic, short} t{cyrillic}ye{cyrillic}o{cyrillic}r{cyrillic}i{cyrillic}i{cyrillic} p{cyrillic}o{cyrillic}l{cyrillic}ya{cyrillic}",
abstract = "The short-range behaviour of certain Feynman integrals reveals mathematical properties which are not those of either functions or distributions-they contain terms which are more singular than distributions and possess inherent ambiguities. Two classes of singularities exist: To the first one belong all those singularities which have a physical meaning in the sense that in a convergent (regularized) quantum field theory they contribute to observable quantities, frequently as renormalization constants. Most of the singularities of the second, the spurious type, violate the symmetries of the Lagrangian. We demonstrate that they are associated with certain mathematical difficulties of unregularized theories. Much of our analysis deals with the isolation of singularities of this type and with the study of the properties of the singular products of distribution. We argue that the four-dimensional integration leading to the S-matrix in the perturbation expansion must be carried out over an open domain which leaves out the contributions from singularities of the contact type, that is terms proportional to δ4x-y.",
author = "M. Danos and Johann Rafelski",
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N2 - The short-range behaviour of certain Feynman integrals reveals mathematical properties which are not those of either functions or distributions-they contain terms which are more singular than distributions and possess inherent ambiguities. Two classes of singularities exist: To the first one belong all those singularities which have a physical meaning in the sense that in a convergent (regularized) quantum field theory they contribute to observable quantities, frequently as renormalization constants. Most of the singularities of the second, the spurious type, violate the symmetries of the Lagrangian. We demonstrate that they are associated with certain mathematical difficulties of unregularized theories. Much of our analysis deals with the isolation of singularities of this type and with the study of the properties of the singular products of distribution. We argue that the four-dimensional integration leading to the S-matrix in the perturbation expansion must be carried out over an open domain which leaves out the contributions from singularities of the contact type, that is terms proportional to δ4x-y.

AB - The short-range behaviour of certain Feynman integrals reveals mathematical properties which are not those of either functions or distributions-they contain terms which are more singular than distributions and possess inherent ambiguities. Two classes of singularities exist: To the first one belong all those singularities which have a physical meaning in the sense that in a convergent (regularized) quantum field theory they contribute to observable quantities, frequently as renormalization constants. Most of the singularities of the second, the spurious type, violate the symmetries of the Lagrangian. We demonstrate that they are associated with certain mathematical difficulties of unregularized theories. Much of our analysis deals with the isolation of singularities of this type and with the study of the properties of the singular products of distribution. We argue that the four-dimensional integration leading to the S-matrix in the perturbation expansion must be carried out over an open domain which leaves out the contributions from singularities of the contact type, that is terms proportional to δ4x-y.

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