Library

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    Realizing 3-cocycles as obstructions (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 2605-2620 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The occurrence of a 3-cocycle in quantum mechanics or quantum field theory has been interpreted somewhat paradoxically as a breakdown of the Jacobi identity. The main result of this paper is that the 3-cocycle in chiral QCD arises as an obstruction which prevents the existence of a certain extension of one Lie algebra by another. This obstruction may be avoided by constructing a modified Lie algebra extension consisting of derivations on the algebra generated by the fields. However the 3-cocycle then appears when an attempt is made to implement these derivations by commutation with unbounded operators in the canonical equal-time formalism. Assuming the existence of these unbounded operators is what leads to the violation of the Jacobi identity. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531054
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    The Landau-Lifshitz equation, elliptic curves and the Ward transform (1993)
    Springer
    Communications in mathematical physics 154 (1993), S. 25-47 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The Landau-Lifshitz (LL) equation is studied from a point of view that is close to that of Segal and Wilson's work on KdV. The LL hierarchy is defined and shown to exist using a dressing transformation that involves parameters λ1, λ2, λ3 that live on an elliptic curve Σ. The crucial role of the groupK ≃ ℤ2 × ℤ2 of translations by the half-periods of Σ and its non-trivial central extension $$\tilde K$$ is brought out and an analogue of Birkhoff factorisation for $$\tilde K$$ -equivariant loops in Σ is given. This factorisation theorem is given two treatments, one in terms of the geometry of an infinite-dimensional Grassmannian, and the other in terms of the algebraic geometry of bundles over Σ. Further, a Ward-like transform between a class of holomorphic vector bundles on the total spaceZ of a line-bundle over Σ and solutions of LL is constructed. An appendix is devoted to a careful definition of the Grassmannian of the Frechet spaceC ∞(S 1).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02096830
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    The Landau-Lifshitz equation, elliptic curves and the ward transform (1993)
    Springer
    Communications in mathematical physics 158 (1993), S. 215-215 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02097238
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Riemann surfaces, Clifford algebras and infinite dimensional groups (1990)
    Springer
    Communications in mathematical physics 130 (1990), S. 217-236 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We introduce a class of Riemann surfaces which possess a fixed point free involution and line bundles over these surfaces with which we can associate an infinite dimensional Clifford algebra. Acting by automorphisms of this algebra is a “gauge” group of meromorphic functions on the Riemann surface. There is a natural Fock representation of the Clifford algebra and an associated projective representation of this group of meromorphic functions in close analogy with the construction of the basic representation of Kac-Moody algebras via a Fock representation of the Fermion algebra. In the genus one case we find a form of vertex operator construction which allows us to prove a version of the Boson-Fermion correspondence. These results are motivated by the analysis of soliton solutions of the Landau-Lifshitz equation and are rather distinct from recent developments in quantum field theory on Riemann surfaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02473351
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    Riemann surfaces, Clifford algebras and infinite dimensional groups (1991)
    Springer
    Communications in mathematical physics 139 (1991), S. 217-236 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We introduce a class of Riemann surfaces which possess a fixed point free involution and line bundles over these surfaces with which we can associate an infinite dimensional Clifford algebra. Acting by automorphisms of this algebra is a “gauge” group of meromorphic functions on the Riemann surface. There is a natural Fock representation of the Clifford algebra and an associated projective representation of this group of meromorphic functions in close analogy with the construction of the basic representation of Kac-Moody algebras via a Fock representation of the Fermion algebra. In the genus one case we find a form of vertex operator construction which allows us to prove a version of the Boson-Fermion correspondence. These results are motivated by the analysis of soliton solutions of the Landau-Lifshitz equation and are rather distinct from recent developments in quantum field theory on Riemann surfaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02102954
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    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
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    Induced representations, reproducing kernels and the conformal group (1977)
    Springer
    Communications in mathematical physics 52 (1977), S. 77-101 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The properties of “induced” (or multiplier) representations of groups which act in Hilbert spaces with a reproducing kernel are investigated. A resumé of earlier work is followed by a discussion of criteria for the irreducibility of such representations. The notions of reproducing kernel and positive definite spherical function are found to overlap. As a result, functional equations (analogous to those of Godement for spherical functions) are found for the reproducing kernel. The abstract theory is illustrated by certain discrete series representations of the conformal group and by their “limit points”. In particular the so-called ladder representations (which give rise to the conformal symmetry of zero mass particles) are analysed from this viewpoint.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01609072
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    Bounds on the coupling constant in two dimensional boson models (1981)
    Springer
    Communications in mathematical physics 82 (1981), S. 191-210 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider two dimensional boson field theories with an interaction potentialV (φ). We show how to define a cut-off, renormalised Hamiltonian for a certain class of non-polynomialV (φ), which are defined via an integral transform. We formulate precisely a variational argument devised by Coleman, obtaining a constraint on the coupling constant of the theory with generalV (φ), and illustrate the argument with several examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02099916
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    A note on the boson-fermion correspondence and infinite dimensional groups (1985)
    Springer
    Communications in mathematical physics 98 (1985), S. 435-448 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We show how to construct irreducible projective representations of the infinite dimensional Lie group Map (S 1, $$\mathbb{T}$$ ), by embedding it into the group of Bogoliubov automorphisms of the CAR. Using techniques of G. Segal for extending certain representations of Map (S 1, SU(2)) we show that our representations extend to give representations of a certain infinite dimensional superalgebra. We relate our work to the well known boson-fermion correspondence which exists in 1+1 dimensions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01209324
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    The massless Thirring model: Positivity of Klaiber'sn-point functions (1985)
    Springer
    Communications in mathematical physics 99 (1985), S. 347-364 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We present a simple solution to the problem of proving positivity of Klaiber'sn-point functions for the massless Thirring model. The corresponding fields are obtained as strong limits of explicitly given approximate fields, obviating reconstruction. By invoking recent results on the boson-fermion correspondence it is shown how the model can be formulated on the charged fermion Fock space. It is pointed out that the question of cyclicity of the vacuum is open, and that an affirmative answer is necessary to confirm the superselection sector picture of the model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01240352
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...