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  • 1
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A class of completely solvable gauge field equations is investigated. These equations are shown to be closely analogous to the four-dimensional self-duality equations. A similar geometrical interpretation is exhibited, and a generalisation of the ADHM construction is shown to provide solutions.
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  • 2
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Ignoring the problem of sources and singularities, explicit expressions are constructed for the ansätze of Atiyah and Ward. These take an especially simple form in theR gauge of Yang. Some non-linear transformation properties of the self-duality equations in this gauge provide an inductive proof of the ansätze. There is a six-parameter family of these Bäcklund transformations. They take real SU(2) gauge fields into real SU(1, 1) gauge fields and vice versa.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 80 (1981), S. 575-587 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract An exact static monopole solution, possessingn units of magnetic charge and (4n-1) degrees of freedom, is constructed, generalising the recent work of Ward on two monopole solutions. The equations solved are those of anSU(2) gauge theory with adjoint representation Higgs field in the (BPS) limit of vanishing Higgs potential. The number of degrees of freedom is maximal for self-dual solutions. The construction is described in a deductive way, within the framework of the Atiyah-Ward formalism for self-dual gauge fields.
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  • 4
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We analyse further the algebraic structure of dependent fermions, namely ones interrelated by the vertex operator construction. They are associated with special sorts of lattice systems which are introduced and discussed. The explicit evaluation of the relevant cocycles leads to the result that the operator product expansion of the fermions is related in a precise way to one or another of the division algebras given by complex numbers, quaternions or octonions. The latter case is seen to be realised in the light cone formalism of superstring theory.
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  • 5
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract New representations of affine Lie algebras are constructed using symplectic bosons of the sort that occur naturally in the BRST treatment of fermionic string theories. These representations are shown to have analogous properties to the current algebra representations in terms of free fermion fields, though they do not act in a positive space. In particular, the condition for the Sugawara construction of the Virasoro algebra to equal the free one is the existence of a superalgebra with a quadratic Casimir operator, paralleling the symmetric space theorem for fermionic field constructions. Both results are seen to be particular cases of a more general super-symmetric space theorem, which arises from considering an affinisation of the superalgebras. These algebras are realised in terms of free fermions and symplectic bosons and lead to a super-Sugawara construction of the Virasoro algebra. The conditions for this to equal a Virasoro algebra obtained from the free fields are provided by the super-symmetric space theorem.
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  • 6
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A vertex operator construction is given for the level one representations of the affine Kac-Moody algebras associated with non-simply-laced finite-dimensional Lie algebras, using free boson and interacting fermion fields. The fermion fields are constructed explicitly and a detailed discussion is given of the theory of the cocycles necessary for this and other vertex operator constructions. The construction is related in detail to the folding of Dynkin diagrams and a generalisation of it yields Freudenthal's magic square.
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  • 7
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that a method previously given for constructing representations of the Virasoro algebra out of representations of affine Kac-Moody algebras yields the full discrete series of highest weight irreducible representations of the Virasoro algebra. The corresponding method for the super-Virasoro algebras (i.e. the Neveu-Schwarz and Ramond algebras) is described in detail and shown to yield the full discrete series of irreducible highest weight representations.
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  • 8
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted andZ 2-twisted theories, ℋ(Λ) and $$\tilde H(\Lambda )$$ respectively, which may be constructed from a suitable even Euclidean lattice Λ. Similarly, one may construct lattices $$\Lambda _C $$ and $$\tilde \Lambda _C $$ by analogous constructions from a doubly-even binary code $$C$$ . In the case when $$C$$ is self-dual, the corresponding lattices are also. Similarly, ℋ(Λ) and $$\tilde H(\Lambda )$$ are self-dual if and only if Λ is. We show that $$H(\Lambda _C )$$ has a natural “triality” structure, which induces an isomorphism $$H(\tilde \Lambda _C )$$ ≡ $$\tilde H(\Lambda _C )$$ and also a triality structure on $$\tilde H(\tilde \Lambda _C )$$ . For $$C$$ the Golay code, $$\tilde \Lambda _C $$ is the Leech lattice, and the triality on $$\tilde H(\tilde \Lambda _C )$$ is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories ℋ(Λ) and $$\tilde H(\Lambda )$$ with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code.
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  • 9
    ISSN: 1432-0614
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary The isolation of silver-resistant, silver-accumulating bacteria is reported. Following the screening of a number of environmental sources, silver-resistant Enterobacteriaceae were isolated from both sewage and photographic processing effluent. The level of resistance to silver and other heavy metals was determined for a selection of these isolates and, together with preliminary accumulation data derived from batch culture studies, one isolate, a strain of Citrobacter intermedius, was selected for further examination. The effect of silver concentration on batch culture growth of this organism was also investigated.
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  • 10
    ISSN: 1432-0614
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Accumulation of silver is reported for growing and non-growing populations of Citrobacter intermedius B6. In non-growing cultures a maximum uptake of 4.35% (w/w) was observed at an initial silver concentration of 2111.2 μmol Ag+ l-1. In contrast the maximum uptake of silver by growing bacteria was 2.81% (w/w) at an effective concentration of silver of 217.8 μmol·l-1. Silver accumulation rates in both resting (460 μmol Ag+ g-1 per hour) and continuously grown (41 μmol Ag+ g-1 per hour) bacteria are higher than previously reported. Cell fractionation and electron microscopy of continuously grown bacteria indicated that accumulation of silver was associated with the cell envelope, in the form of dense deposits of macromolecular proportions. This observation discounts simple surface adsorption as the process of accumulation in growing cultures.
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