Phase space of mechanical systems with a gauge group

Prokhorov, L.V.; Shabanov, Sergei V.

doi:10.1070/pu1991v034n02abeh002339

Cited by 24 publications

(33 citation statements)

References 39 publications

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“…In the second step we will further transform the angular part of this measure into the measure in terms of the angular velocities. Some of the results in the first part of this section are already in the literature [11]. However, for the sake of completeness and also because our interpretation of some of the terms in the final measure is different (see footnote 8), we will reproduce them briefly below.…”

Section: Iid the Measurementioning

confidence: 99%

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Abelianization of SU(N) gauge theory with gauge invariant dynamical variables and magnetic monopoles

Giacomo

Mathur

1998

Nuclear Physics B

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It is shown that SU(N) gauge theory coupled to adjoint Higgs can be explicitly re-written in terms of SU(N) gauge invariant dynamical variables with local physical interactions. The resultant theory has a novel compact abelian U(1) (N −1) gauge invariance. The above abelian gauge invariance is related to the adjoint Higgs field and not to the gauge group SU(N). In this abelianized version the magnetic monopoles carrying the magnetic charges of (N − 1) types have a natural origin and therefore appear explicitly in the partition function as Dirac monopoles along with their strings. The gauge invariant electric and magnetic charges with respect to U(1) (N −1) gauge groups are shown to be vectors in root and co-root lattices of SU(N) respectively. Therefore, the Dirac quantization condition corresponds to SU(N) Cartan matrix elements being integers. We also study the effect of the θ term in the abelian version of the theory.

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Section: Iid the Measurementioning

confidence: 99%

“…In the Cartan basis [11], |ω(ρ)| = N 2 −N 2 α=1 ( ρ. K(α)) 2 , where the product over α runs only over the positive roots. Therefore, the Jacobian J(ρ, z) splits into the following radial and angular parts:…”

Section: Iid the Measurementioning

confidence: 99%

Abelianization of SU(N) gauge theory with gauge invariant dynamical variables and magnetic monopoles

Giacomo

Mathur

1998

Nuclear Physics B

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“…As a first example, consider the motion of a particle in two-dimensional space whose dynamics are governed by the Lagrangian [7,14] L(x i ,ẋ i , q) = 1 2ẋ …”

Section: The Christ-lee Modelmentioning

confidence: 99%

Gauge independent Hamiltonian reduction of constrained systems

Muslih

2002

Journal of Applied Mathematics

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“…Note that the G= SO(3) model of the paper belongs to this class, while for an arbitrary gauge group G, the case with d=1 has already been considered in Refs. [9,11].…”

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confidence: 97%

“…Likewise for dimensionally reduced nonabelian models, introducing a quadratic gauge invariant potential as in (2) turns the reduced model into a collection of anharmonic oscillators with an angular frequency | as a free regularisation parameter, while nevertheless, the quartic term may be removed altogether without spoiling the nonabelian gauge symmetry of the reduced system. The type of model defined by (1) has been considered previously in the literature [8,9,11], and quite recently again in Ref. [13].…”

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confidence: 98%