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  • 1
    Electronic Resource
    Electronic Resource
    Unitary braid group representations (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 3126-3133 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A large class of braid group representations are proven unitary which means a Hermitian bilinear form left invariant by the representation under consideration exists. This generalizes and improves known results on the Burau and Gassner representations. The elementary methods are naturally suggested by the study of monodromy invariant Hermitian forms. Applications to conformal quantum field theory in two dimensions are mentioned. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531357
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  • 2
    Electronic Resource
    Electronic Resource
    Der Satz von Bochner-Schwartz für Ultradistributionen (1976)
    Springer
    Mathematische Zeitschrift 147 (1976), S. 175-180 
    Details
    ISSN: 1432-1823
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01164281
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  • 3
    Electronic Resource
    Electronic Resource
    Smeared and Unsmeared Chiral Vertex Operators (1999)
    Springer
    Communications in mathematical physics 200 (1999), S. 275-296 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: We prove unboundedness and boundedness of the unsmeared and smeared chiral vertex operators, respectively. We use elementary methods in bosonic Fock space, only. Possible applications to conformal two-dimensional quantum field theory, perturbation thereof, and to the perturbative construction of the sine-Gordon model by the Epstein-Glaser method are discussed. From another point of view the results of this paper can be looked at as a first step towards a Hilbert space interpretation of vertex operator algebras.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002200050530
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  • 4
    Electronic Resource
    Electronic Resource
    Boundary values of analytic functions (1968)
    Springer
    Communications in mathematical physics 7 (1968), S. 225-233 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is known that a complex — valued continuous functionS(x) as well as a Schwartz distribution on the real axis can be extended in the complex plane minus the support ofS to an analytic functionŜ(z). In the case of a continuous function the jump ofŜ(z) on the real axis represents exactlyS(x): $$\mathop {\lim }\limits_{\varepsilon \to 0 + } [\hat S(x + i\varepsilon ) - \hat S(x - i\varepsilon )] = S(x)$$ . We call regular a pointx on the support ofS such that $$\mathop {\lim }\limits_{\varepsilon \to 0 + } [\hat S(x + i\varepsilon ) - \hat S(x - i\varepsilon )]$$ exists. Conditions are found for the existence of regular points on the support of a distribution. It is possible to call this limit (if this exists) the valueS(x) of the distributionS in the pointx. Properties of this type occur in the theory of dispersion relations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01645665
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  • 5
    Electronic Resource
    Electronic Resource
    Boundary values of analytic functions. II (1968)
    Springer
    Communications in mathematical physics 8 (1968), S. 345-352 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is known that a complex-valued continuous functionS(x) and a Schwartz distribution can both be extended to an analytic functionŜ(z) in the complex plane minus the support ofS. Conditions are given for the existence of limits $$\mathop {\lim }\limits_{\varepsilon \to 0 + } \hat S(x + i\varepsilon )$$ Ŝ(x+iε), in the ordinary sense, at certain points of the support ofS, for the case in whichŜ(z) is the Cauchy representation. In this way we obtain “local” Plemelj and dispersion relations. Possible generalizations and applications are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01646274
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  • 6
    Electronic Resource
    Electronic Resource
    Generalized Cauchy determinant formula and its applications to Coulomb gas problems (1995)
    Springer
    Letters in mathematical physics 33 (1995), S. 195-206 
    Details
    ISSN: 1573-0530
    Keywords: 82B05 ; 82B21 ; 82D05 ; 81T40
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Using only elementary methods, we generalize the classical Cauchy determinant formula and indicate applications to two-dimensional systems including the neutral asymmetric Coulomb gas and conformal quantum field theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00749621
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  • 7
    Electronic Resource
    Electronic Resource
    Chiral Charged Fermions, One-Dimensional Quantum Field Theory and Vertex Algebras (2000)
    Springer
    Letters in mathematical physics 52 (2000), S. 113-126 
    Details
    ISSN: 1573-0530
    Keywords: chiral charged fermions ; vertex operators and algebras
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We give an explicit L 2-representation of chiral charged fermions using the Hardy–Lebesgue octant decomposition. In the ‘pure’ case such a representation has already been used by M. Sato in holonomic field theory. We study both ‘pure’ and ‘mixed’ cases. In the compact case, we rigorously define unsmeared chiral charged fermion operators inside the unit circle. Using chiral fermions, we orient our findings towards a functional analytic study of vertex algebras as one-dimensional quantum field theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007645720174
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  • 8
    Electronic Resource
    Electronic Resource
    Monodromy Groups and Bilinear Monodromy Invariant Combinations of Generalized Hypergeometric Type Integrals (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 257-285 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The problem of determining bilinear combinations of holomorphic and antiholomorphic generalized hypergeometric type integrals left invariant under the action of the monodromy groups of the integrals is studied. In the special cases of simple Pochhammer type integrals and of twofold hypergeometric type integrals the existence and uniqueness of the bilinear invariants are proved, and the bilinear invariants are explicitly computed. Preparing the tools it is shown how to linearize and iterate representations of the braid group Bn as automorphism groups of certain free subgroups of the braid group Bn+1, and how the resulting iterated linear representations of the braid group in a natural way provide an algorithm to compute the monodromy group of generalized hypergeometric type integrals. Explicit formulae for different types of integration contours are given in the case of simple and twofold integrals.
    Type of Medium: Electronic Resource
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