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  • 1
    Electronic Resource
    Electronic Resource
    Deconstructing supersymmetry (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 736-750 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Two supersymmetric classical mechanical systems are discussed. Concrete realizations are obtained by supposing that the dynamical variables take values in the Grassmann algebra B2 with two generators. The equations of motion are explicitly solved, and the action of the supergroup on the space of solutions is elucidated. The Lie algebra of the supergroup is the even part of the tensor product B2⊗G, where G is the super Lie algebra of supersymmetries and time translations. For each system, the solutions with zero energy need to be constructed separately. For these Bogomolny-type solutions, the orbit of the supergroup is smaller than in the generic case. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532682
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  • 2
    Electronic Resource
    Electronic Resource
    Thermodynamics of vortices in the plane (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1171-1184 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The thermodynamics of vortices in the critically coupled Abelian Higgs model, defined on the plane, are investigated by placing N vortices in a region of the plane with periodic boundary conditions: a torus. It is noted that the moduli space for N vortices, which is the same as that of N indistinguishable points on a torus, fibrates into a CPN−1 bundle over the Jacobi manifold of the torus. The volume of the moduli space is a product of the area of the base of this bundle and the volume of the fiber. These two values are determined by considering two 2-surfaces in the bundle corresponding to a rigid motion of a vortex configuration, and a motion around a fixed center of mass. The partition function for the vortices is proportional to the volume of the moduli space, and the equation of state for the vortices is P(A−4π N)=NT in the thermodynamic limit, where P is the pressure, A the area of the region of the plane occupied by the vortices, and T the temperature. There is no phase transition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530633
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  • 3
    Electronic Resource
    Electronic Resource
    On the Constraints Defining BPS Monopoles (2000)
    Springer
    Communications in mathematical physics 212 (2000), S. 219-243 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: We discuss the explicit formulation of the transcendental constraints defining spectral curves of SU(2) BPS monopoles in the twistor approach of Hitchin, following Ercolani and Sinha. We obtain an improved version of the Ercolani–Sinha constraints, and show that the Corrigan–Goddard conditions for constructing monopoles of arbitrary charge can be regarded as a special case of these. As an application, we study the spectral curve of the tetrahedrally symmetric 3-monopole, an example where the Corrigan–Goddard conditions need to be modified. A particular 1-cycle on the spectral curve plays an important rôle in our analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002200000208
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  • 4
    Electronic Resource
    Electronic Resource
    Geometry of Skyrmions (1987)
    Springer
    Communications in mathematical physics 111 (1987), S. 469-478 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A Skyrmion may be regarded as a topologically non-trivial map from one Riemannian manifold to another, minimizing a particular energy functional. We discuss the geometrical interpretation of this energy functional and give examples of Skyrmions on various manifolds. We show how the existence of conformal transformations can cause a Skyrmion on a 3-sphere to become unstable, and how this may be related to chiral symmetry breaking.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01238909
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  • 5
    Electronic Resource
    Electronic Resource
    Geometry and kinematics of two Skyrmions (1993)
    Springer
    Communications in mathematical physics 153 (1993), S. 391-422 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract In Skyrme's soliton model of baryons, a single Skyrmion has six degrees of freedom, so it is expected that two-Skyrmion dynamics at modest energies can be modelled by motion on a 12-dimensional space of Skyrme fields. A candiate for this space is generated by the gradient flow of the potential energy function, descending from the unstable, baryon number two, hedgehog solutions of the Skyrme field equation. An apparently very similar space is obtained by restricting the gradient flow to the Skyrme fields derived fromSU(2) Yang-Mills instantons of charge two. On both of these spaces, one may quotient out by the group of translations and isospin rotations. Hartshorne's geometrical description of charge two instantons leads us to a conjecture for the global structure of the 6-dimensional quotient space. The conjectured structure is that of complex projective 3-space, with complex conjugate points on one projective plane identified and the real points in this plane removed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02096649
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  • 6
    Electronic Resource
    Electronic Resource
    Universal scaling behaviour for iterated maps in the complex plane (1983)
    Springer
    Communications in mathematical physics 89 (1983), S. 555-570 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract According to the theory of Schröder and Siegel, certain complex analytic maps possess a family of closed invariant curves in the complex plane. We have made a numerical study of these curves by iterating the map, and have found that the largest curve is a fractal. When the winding number of the map is the golden mean, the fractal curve has universal scaling properties, and the scaling parameter differs from those found for other types of maps. Also, for this winding number, there are universal scaling functions which describe the behaviour asn→∞ of theQ n th iterates of the map, whereQ n is then th Fibonacci number.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01214743
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  • 7
    Electronic Resource
    Electronic Resource
    Space-time symmetries in gauge theories (1980)
    Springer
    Communications in mathematical physics 72 (1980), S. 15-35 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A general definition of symmetries of gauge fields is proposed and a method developed for constructing symmetric fields for an arbitrary gauge group. Scalar fields occur naturally in the formalism and the pure gauge theory reduces to a Higgs model in lower dimensions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01200108
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  • 8
    Electronic Resource
    Electronic Resource
    Volume of Vortex Moduli Spaces (1999)
    Springer
    Communications in mathematical physics 199 (1999), S. 591-604 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: A gas of N Bogomol'nyi vortices in the Abelian Higgs model is studied on a compact Riemann surface of genus g and area A. The volume of the moduli space is computed and found to depend on N, g and A, but not on other details of the shape of the surface. The volume is then used to find the thermodynamic partition function and it is shown that the thermodynamical properties of such a gas do not depend on the genus of the Riemann surface.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002200050513
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  • 9
    Electronic Resource
    Electronic Resource
    Connections on discrete fibre bundles (1987)
    Springer
    Communications in mathematical physics 113 (1987), S. 341-351 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A new approach to gauge fields on a discrete space-time is proposed, in which the fundamental object is a discrete version of a principal fibre bundle. If the bundle is twisted, the gauge fields are topologically non-trivial automatically.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01223516
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  • 10
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    Monopole planets and galaxies (2012)
    American Physical Society
    Details
    Publication Date: 2012-02-15
    Print ISSN: 1550-7998
    Electronic ISSN: 1550-2368
    Topics: Physics
    Published by American Physical Society
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