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  • 1
    Electronic Resource
    Electronic Resource
    Finite-dimensional algebraic representations of the infinite phylon group (1992)
    Springer
    Acta applicandae mathematicae 28 (1992), S. 219-252 
    Details
    ISSN: 1572-9036
    Keywords: 53A55 ; 20G05 ; 58A20 ; Derivative string ; differential string ; D-matrix ; jets ; phyla ; phylon group
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The concept of phylon is introduced as a generalisation of derivative strings, differential strings and new tensors. The behaviour of phyla under change of coordinates is given by finite-dimensional algebraic representations of a very large group, the infinite phylon group. These representations are studied from both the general and the matrix points of view. Various examples of phyla are given, mainly from a statistical context. The basic structure of these representations is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00047088
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  • 2
    Electronic Resource
    Electronic Resource
    Holonomy and the Wess-Zumino term (1986)
    Springer
    Letters in mathematical physics 12 (1986), S. 323-327 
    Details
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The concept of a holonomy term in a Lagrangian is introduced. It unifies the idea of the interaction term in the Dirac monopole and the Wess-Zumino term. In particular, it provides a dynamical interpretation of the Kac-Moody cocycle on a loop group.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00402666
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  • 3
    Electronic Resource
    Electronic Resource
    Faddeev's anomaly and bundle gerbes (1996)
    Springer
    Letters in mathematical physics 37 (1996), S. 29-36 
    Details
    ISSN: 1573-0530
    Keywords: 81T50 ; 22E65 ; Faddeev's anomaly ; bundle gerbes ; Dixmier-Douady class ; infinite-dimensional Lie groups
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We show that transgression of the Dixmier-Douady class coming from the natural gerbe arising in the discussion of Faddeev's anomaly is the Faddeev-Mickelsson 2-cocycle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00400136
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  • 4
    Electronic Resource
    Electronic Resource
    Spectral curves and the ADHM method (1988)
    Springer
    Communications in mathematical physics 114 (1988), S. 463-474 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract For a general monopole the algebraic curves defined by Nahm are shown to be the same as the spectral curves.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01242139
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  • 5
    Electronic Resource
    Electronic Resource
    Another construction of the central extension of the loop group (1988)
    Springer
    Communications in mathematical physics 116 (1988), S. 73-80 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract By considering the geometry of the central extension of the loop group as a principal bundle it is shown that it must be the quotient of a larger group. This group is a central extension of the group of paths in the loop group and its cocycle is constructed as the holonomy around a certain path. Conversely it is shown that this definition of a cocycle gives a method of constructing the central extension. The Wess-Zumino term plays an important role in these constructions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01239026
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  • 6
    Electronic Resource
    Electronic Resource
    Why instantons are monopoles (1989)
    Springer
    Communications in mathematical physics 121 (1989), S. 85-90 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that instantons are hyperbolic monopoles for the loop group with non-maximal symmetry breaking at infinity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01218625
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  • 7
    Electronic Resource
    Electronic Resource
    Kac-Moody monopoles and periodic instantons (1988)
    Springer
    Communications in mathematical physics 120 (1988), S. 335-351 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that calorons, or periodic instantons are the same as monopoles with the loop group as their structure group. Their twistor correspondences and spectral data are defined. The spectral data is shown to determine the general caloron.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01217968
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  • 8
    Electronic Resource
    Electronic Resource
    Monopoles and spectral curves for arbitrary Lie groups (1983)
    Springer
    Communications in mathematical physics 90 (1983), S. 263-271 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The definition of the spectral curve of a monopole is extended to any connected, compact, simple Lie groupK. It is found there are rankK curves whose degrees are related to the topological weights of the monopole.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01205507
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  • 9
    Electronic Resource
    Electronic Resource
    Non-Abelian magnetic monopoles (1984)
    Springer
    Communications in mathematical physics 96 (1984), S. 539-565 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that a general, irreducible, SU(n), Sp(n), SO(2n) monopole with maximal symmetry breaking is determined by its spectral data. For SU(n) with minimal symmetry breaking the spectral data is defined and also shown to determine the monopole.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01212534
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  • 10
    Electronic Resource
    Electronic Resource
    String structures and the path fibration of a group (1991)
    Springer
    Communications in mathematical physics 141 (1991), S. 441-452 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We use the realisation of the universal bundle for the loop group as the path fibration of the group to investigate the string class, that is the obstruction to a loop group bundle lifting to a Kac-Moody group bundle. In the case that the loop group bundle is constructed by taking loops into a principal bundle we show that the classifying map is the holonomy around loops and give an explicit formula for the string class relating it to the Pontrjangin class of the principal bunble.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02102809
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