Realization of compact Lie algebras in Kahler manifolds

Bar-Moshe, David; Marinov, M. S.

doi:10.1088/0305-4470/27/18/035

Cited by 17 publications

(15 citation statements)

References 18 publications

(25 reference statements)

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“…A discussion of deformation quantization of coadjoint orbits of a Lie group, which again exhibits an intimate relationship to group representations and the Kirillov orbit method, can be found e.g. in Vogan [256], Landsman [160], Bar-Moshe and Marinov [24], Lledo [166], and Fioresi and Lledo [91]. A gauge-invariant quantization method which, in the authors' words, "synthesizes the geometric, deformation and Berezin quantization approaches", was proposed by Fradkin and Linetsky [95] and Fradkin [94].…”

Section: Deformation Quantizationmentioning

confidence: 99%

Quantization Methods: A Guide for Physicists and Analysts

2005

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This survey is an overview of some of the better known quantization techniques (for systems with finite numbers of degrees-of-freedom) including in particular canonical quantization and the related Dirac scheme, introduced in the early days of quantum mechanics, Segal and Borel quantizations, geometric quantization, various ramifications of deformation quantization, Berezin and Berezin–Toeplitz quantizations, prime quantization and coherent state quantization. We have attempted to give an account sufficiently in depth to convey the general picture, as well as to indicate the mutual relationships between various methods, their relative successes and shortcomings, mentioning also open problems in the area. Finally, even for approaches for which lack of space or expertise prevented us from treating them to the extent they would deserve, we have tried to provide ample references to the existing literature on the subject. In all cases, we have made an effort to keep the discussion accessible both to physicists and to mathematicians, including non-specialists in the field.

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Section: Deformation Quantizationmentioning

confidence: 99%

Quantization Methods: A Guide for Physicists and Analysts

2005

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“…In the parametrization we use, the principal covariant symbols have the property that their restriction to the largest Schubert cell Σ s ⊂ G/T is polynomial in the affine coordinates of Σ s [5,6]. The reproduction property of is expressed through the relation:…”

Section: The Quantization Space In Berezin Theorymentioning

confidence: 99%

“…Berezin quantization (in its generalized version on spaces of sections of line bundles [18]) leads to the realization of π λ [5] in terms of the Berezin symbols [8] which act as integration kernels on Γ hol (L λ ).…”

Section: Introductionmentioning

confidence: 99%

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A Method for Weight Multiplicity Computation Based on Berezin Quantization

Bar-Moshe¹

2009

SIGMA

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Abstract. Let G be a compact semisimple Lie group and T be a maximal torus of G. We describe a method for weight multiplicity computation in unitary irreducible representations of G, based on the theory of Berezin quantization on G/T . Let Γ hol (L λ ) be the reproducing kernel Hilbert space of holomorphic sections of the homogeneous line bundle L λ over G/T associated with the highest weight λ of the irreducible representation π λ of G. The multiplicity of a weight m in π λ is computed from functional analytical structure of the Berezin symbol of the projector in Γ hol (L λ ) onto subspace of weight m. We describe a method of the construction of this symbol and the evaluation of the weight multiplicity as a rank of a Hermitian form. The application of this method is described in a number of examples.

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“…In a different context this construction was used in [13,14]. A physical scalar field of unit mass dimension and U(1) weight r is obtained by taking: H (r) = S r /f ; the D-term of the real superfield ∆K H = Y r /f 2 defines its kinetic action.…”

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confidence: 99%

Matter coupling and anomaly cancellation in supersymmetric σ-models

Nibbelink

Holten

1998

Physics Letters B

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Generalized matter couplings to four-dimensional supersymmetric sigma models on general Kähler manifolds are presented, preserving all holomorphic symmetries. Our generalization allows assignment of arbitrary U (1) charges to additional matter fermions, in all representations of (the holomorphic part of) the isometry group. This can be used to eliminate unwanted γ 5 anomalies, in particular for the U(1) symmetry arising from the complex structure of the target space. A consistent gauging of this isometry group, or any of its subgroups, then becomes possible. When gauged in the presence of a chiral scalar multiplet, the U(1) symmetry is broken spontaneously, generating a mass for the U(1) vector multiplet via the supersymmetric Higgs effect. As an example we discuss the case of the homogeneous coset space E 6 /SO(10) × U (1).

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Realization of compact Lie algebras in Kahler manifolds

Cited by 17 publications

References 18 publications

Quantization Methods: A Guide for Physicists and Analysts

Quantization Methods: A Guide for Physicists and Analysts

A Method for Weight Multiplicity Computation Based on Berezin Quantization

Matter coupling and anomaly cancellation in supersymmetric σ-models

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