Invariance properties of the Dirac monopole

Frenkel, A.; Hraskó, P.

doi:10.1016/0003-4916(77)90242-1

Cited by 14 publications

(11 citation statements)

References 14 publications

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“…and equations (15), (34) we find χ l (γ ′ ) = 1 for all γ ′ ∈ Γ ′ 1 and all l. Thus (69) is trivial to calculate in this case, and from (68), (55) we find…”

Section: Extension To Reflection Groupsmentioning

confidence: 72%

“…For the moment we deal with the easier, pure rotational case, g ∈ SO(3). Then the behaviour is an elementary consequence of the SU(2) group combination law and one has explicitly (Wu and Yang [8], Frenkel and Hraskó [15])…”

Section: Modes and Group Actions On The Full Spherementioning

confidence: 99%

“…should hold, and this can be checked directly from (7). The geometrical details are to be found in the useful article by Frenkel and Hraskó [15]. The magnetic rotation operator, T g , is defined, on scalars, by the action…”

Section: Modes and Group Actions On The Full Spherementioning

confidence: 99%

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Magnetic fields and factored two-spheres

Dowker

2001

Journal of Mathematical Physics

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A magnetic monopole is placed at the centre of a ball whose surface S 2 is tiled by the symmetry group, Γ, of a regular solid. The quantum mechanics on the two-dimensional quotient S 2 /Γ is developed and the monopole charge is found to be quantised in an expected manner. The heat-kernel and ζ-functions are evaluated and the Casimir energy is computed. Numerical approaches to the calculation of the derivative of the Barnes ζ-function are presented.

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“…and equations (15), (34) we find χ l (γ ′ ) = 1 for all γ ′ ∈ Γ ′ 1 and all l. Thus (69) is trivial to calculate in this case, and from (68), (55) we find…”

Section: Extension To Reflection Groupsmentioning

confidence: 72%

Section: Modes and Group Actions On The Full Spherementioning

confidence: 99%

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Magnetic fields and factored two-spheres

Dowker

2001

Journal of Mathematical Physics

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“…With this quantization condition, the (static part of the) quantum wave function of the electron in the static magnetic field of a monopole can be single valued. Later it was shown [4,5,17] that this condition actually ensures that the position of the string is defined up to a gauge transformation, which is equivalent to rotating the line of singularity S n . In other words, the direction of the Dirac string is not fixed and could be arbitrary, therefore its field is not physical.…”

Section: Quantum Theory Of the Charge-monopole Systemmentioning

confidence: 99%

On the gauge transformation for the rotation of the singular string in the Dirac monopole theory

Pan,

Chen,

et al. 2020

Preprint

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In the Dirac theory of the quantum-mechanical interaction of a magnetic monopole and an electric charge, the vector potential is singular from the origin to infinity along certain direction -the so called Dirac string. Imposing the famous quantization condition, the singular string attached to the monopole can be rotated arbitrarily by a gauge transformation, and hence is not physically observable. By deriving its analytical expression and analyzing its properties, we show that the gauge function χ(r) which rotates the string to another one has quite complicated behaviors depending on which side from which the position variable r gets across the plane expanded by the two strings. Consequently, some misunderstandings in the literature are clarified.

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“…where Ω(n, n ′ ; r) is the solid angle of the geodesic simplex with the vertices (n, n ′ ; r) [12,54,55]. Now returning to the transformation S κ n → S κ ′ n we obtain…”

Section: Jhep00(2005)000mentioning

confidence: 99%

Infinite-dimensional representations of the rotation group and Dirac monopole problem

Nesterov

Cruz

2008

Journal of Mathematical Physics

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Within the context of infinite-dimensional representations of the rotation group the Dirac monopole problem is studied in details. Irreducible infinite-dimensional representations, being realized in the indefinite metric Hilbert space, are given by linear unbounded operators in infinite-dimensional topological spaces, supplied with a weak topology and associated weak convergence. We argue that an arbitrary magnetic charge is allowed, and the Dirac quantization condition can be replaced by a generalized quantization rule yielding a new quantum number, the so-called topological spin, which is related to the weight of the Dirac string.

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Invariance properties of the Dirac monopole

Cited by 14 publications

References 14 publications

Magnetic fields and factored two-spheres

Magnetic fields and factored two-spheres

On the gauge transformation for the rotation of the singular string in the Dirac monopole theory

Infinite-dimensional representations of the rotation group and Dirac monopole problem

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