Special Functions Connected with the Groups U(n), U(n−1,1) and IU(n−1)

Vilenkin, N. Ja.; Klimyk, A. U.

doi:10.1007/978-94-017-2883-6_3

Cited by 16 publications

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“…Exploiting this recurrence relation we now have a methodology for writing down the kernel for any SU (N ) differential volume element. Recalling equation (19) and the A(k, j(m)) term we see that in general…”

Section: Procedures For Calculating the Haar Measure And Group Volumentioning

confidence: 96%

“…Notice that even though we restricted ourselves to N > 2 for the Cartan decomposition, equation (19) is valid for N ≥ 2. For our purposes it is enough to note that this parametrization is special unitary by construction and can be shown to cover the group by modifying the ranges that follow and substituting them into the parametrization of the characters [11].…”

Section: Deriving the Euler Angle Parametrization For Su (N )mentioning

confidence: 99%

“…Taking the Euler angle parametrization given by equation (19) we now develop the differential volume element, also known as the Haar measure, for the group. We proceed by using the method originally given in [15] and developed for SU (3) in [9,10] and for SU (4) in [1]; take a generic U ∈ SU (N ) and find the matrix…”

Section: Procedures For Calculating the Haar Measure And Group Volumentioning

confidence: 99%

“…For example, when one looks at the parametrization of the group and matches the trigonometric function in the differential volume element kernel with its corresponding e iλ2αm component, one sees sin(2α m ) terms showing up. It is plain to see then that, in general, the differential volume kernel is made up of trigonometric functions that correspond to group elements that are of the form e iλ (k−1) 2 +1 α 2(k−1)+j(m) and where j(m) is given in equation (19). Therefore, there should be a general expression for the differential volume element kernel for SU (N ) that can be written down via inspection of the Euler angle parametrization.…”

Section: Procedures For Calculating the Haar Measure And Group Volumentioning

confidence: 99%

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Generalized Euler angle parametrization forSU(N)

Tilma¹,

Sudarshan²

2002

J. Phys. A: Math. Gen.

111

173

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In a previous paper [1] an Euler angle parametrization for SU (4) was given. Here we present the derivation of a generalized Euler angle parametrization for SU (N ). The formula for the calculation of the Haar measure for SU (N ) as well as its relation to Marinov's volume formula for SU (N ) [2, 3] will also be derived. As an example of this parametrization's usefulness, the density matrix parametrization and invariant volume element for a qubit/qutrit, three qubit, and two three-state systems, also known as two qutrit systems [4], will also be given. *

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Section: Procedures For Calculating the Haar Measure And Group Volumentioning

confidence: 96%

Section: Deriving the Euler Angle Parametrization For Su (N )mentioning

confidence: 99%

Section: Procedures For Calculating the Haar Measure And Group Volumentioning

confidence: 99%

Section: Procedures For Calculating the Haar Measure And Group Volumentioning

confidence: 99%

See 2 more Smart Citations

Generalized Euler angle parametrization forSU(N)

Tilma¹,

Sudarshan²

2002

J. Phys. A: Math. Gen.

111

173

View full text Add to dashboard Cite

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“…It is known that the Clebsch-Gordan coefficients for highest weight representations of SU(1, 1) may be identified with three classical systems of orthogonal polynomials, namely, the Jacobi polynomials, the Hahn polynomials, and the continuous Hahn polynomials [41]. They correspond to the three conjugacy classes of one-parameter subgroups of SU (1,1).…”

Section: Introductionmentioning

confidence: 99%

Multivariable q‐Hahn polynomials as coupling coefficients for quantum algebra representations

Rosengren

2001

International Journal of Mathematics and Mathematical Sciences

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Weaving Commutators: Beyond Fock Space

Arzano

2015

The Frontiers Collection

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The symmetrization postulate and the associated Bose/Fermi (anti)-commutators for field mode operators are among the pillars on which local quantum field theory lays its foundations. They ultimately determine the structure of Fock space and are closely connected with the local properties of the fields and with the action of symmetry generators on observables and states. We here show that the quantum field theory describing relativistic particles coupled to three dimensional Einstein gravity as a topological defect must be constructed using a deformed algebra of creation and annihilation operators. This reflects a non-trivial group manifold structure of the classical momentum space and a modification of the Leibniz rule for the action of symmetry generators governed by Newton's constant. We outline various arguments suggesting that, at least at the qualitative level, these three-dimensional results could also apply to real four-dimensional world thus forcing us to re-think the ordinary multiparticle structure of quantum field theory and many of the fundamental aspects connected to it.

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Special Functions Connected with the Groups U(n), U(n−1,1) and IU(n−1)

Cited by 16 publications

References 0 publications

Generalized Euler angle parametrization forSU(N)

Generalized Euler angle parametrization forSU(N)

Multivariable q‐Hahn polynomials as coupling coefficients for quantum algebra representations

Weaving Commutators: Beyond Fock Space

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