Universal unfolding of Hamiltonian systems: From symplectic structure to fiber bundles

Zaccaria, F.; Sudarshan, E. C. G.; Nilsson, Jonas; Mukunda, N.; Marmo, Giuseppe; Balachandran, A. P.

doi:10.1103/physrevd.27.2327

Cited by 31 publications

(29 citation statements)

References 9 publications

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“…As a matter of fact, the lhs of Eq. (2.43) is the field of a Dirac magnetic monopole (see, for example, Balachandran et al , 1983), and Eq. (2.43) defines 2 as its potential, which notoriously has a string of singularities (that can be put anywhere by a choice of gauge).…”

Section: T7mentioning

confidence: 99%

“…(3.18) or a theory with the usual interactions and the propagator Eo, but whose wave functions are subject to twisted boundary conditions. In the former case physical observables are modified because the added interaction may contribute to conserved quan4The theory of wave functions localized on paths has been developed by Zaccaria et al (1983) and Balachandran, Fromm, and Sorkin (1987). For an axiomatic (algebraic) approach see also Frohlich, Cxabbiani, and Marchetti (1989).…”

Section: B the Braid Groupmentioning

confidence: 99%

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Quantum mechanics and field theory with fractional spin and statistics

1992

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Planar systems admit quantum states that are neither bosons nor fermions, i.e. , whose angular momentum is neither integer nor half-integer. After a discussion of some examples of familiar mocfels in which fractional spin may arise, the relevant (nonrelativistic) quantum mechanics is developed from first principles.The appropriate generalization of statistics is also discussed. Some physical efFects of fractional spin and statistics are worked out explicitly. The group theory underlying relativistic models with fractional spin and statistics is then introduced and applied to relativistic particle mechanics and field theory. Fieldtheoretical models in 2+1 dimensions are presented which admit solitons that carry fractional statistics, and are discussed in a semiclassical approach, in the functional integral approach, and in the canonical approach. Finally, fundamental field theories whose Pock states carry fractional spin and statistics are discussed.

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Section: T7mentioning

confidence: 99%

Section: B the Braid Groupmentioning

confidence: 99%

Quantum mechanics and field theory with fractional spin and statistics

1992

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“…The classical symmetry group is SO(3), while the quantum symmetry group for some quantizations is SU(2); see [8,27]. An electron in the field of a magnetic monopole is also a good example; see [6,Chapter 7] and [11,35].…”

Section: The Set Of Path Components Ofmentioning

confidence: 99%

Untitled

2007

St. Petersburg Math. J.

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Abstract. The configuration space of a nonlinear sigma model is the space of maps from one manifold to another. This paper reviews the authors' work on nonlinear sigma models with target a homogeneous space. It begins with a description of the components, fundamental group, and cohomology of such configuration spaces, together with the physical interpretations of these results. The topological arguments given generalize to Sobolev maps. The advantages of representing homogeneousspace-valued maps by flat connections are described, with applications to the homotopy theory of Sobolev maps, and minimization problems for the Skyrme and Faddeev functionals. The paper concludes with some speculation about the possibility of using these techniques to define new invariants of manifolds.

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“…Dirac's ideas lead naturally to consideration of a quantum mechanics in which the wave function has a nonintegrable (or path-dependent) phase factor. This formalism has been developed by various authors (see, for example [23,24,25,26,27,28,29,30,31] and references therein). In general, the path-depndent wave function can be written as…”

Section: Nonassociative Gauge Transformationsmentioning

confidence: 99%