Semiclassical analysis of Wigner 3<i>j</i>-symbol

Aquilanti, Vincenz̊o; Haggard, Hal M.; Littlejohn, Robert G.; Yu, Liang

doi:10.1088/1751-8113/40/21/013

Cited by 51 publications

(75 citation statements)

References 61 publications

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“…The remaining relevant large quantum numbers determine the Lagrangian manifolds. Once we fix the Lagrangian manifolds, the scalar WKB parts of the wave functions can be derived from a semiclassical analysis of these Lagrangian manifolds, following the procedure in [14,17]. The spinor parts of the wave functions at the intersection points of the Lagrangian manifolds are determined by the path used to calculate the action integral in the semiclassical analysis.…”

Section: Discussionmentioning

confidence: 99%

“…(17) and (18) in [16] that, when the configuration goes to its time-reversed image, that is, when all the vectors reverse their directions, the actions transform according to S (1) → −S (1) and S (2) → −S (2) + 2π ( 9 r=1 j r ) + 9π . As a result, the two terms cos(S (1) ) and sin(S (2) ) in the 9j formula (67) are invariant under timereversal symmetry.…”

Section: Lagrangian Manifolds and Actionsmentioning

confidence: 99%

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Semiclassical analysis of the Wigner12jsymbol with one small angular momentum

2011

Phys. Rev. A

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We derive an asymptotic formula for the Wigner 12j symbol, in the limit of one small and 11 large angular momenta. There are two kinds of asymptotic formulas for the 12j symbol with one small angular momentum. We present the first kind of formula in this paper. Our derivation relies on the techniques developed in the semiclassical analysis of the Wigner 9j symbol [L. Yu and R. G. Littlejohn, Phys. Rev. A 83, 052114 (2011)], where we used a gauge-invariant form of the multicomponent WKB wave functions to derive asymptotic formulas for the 9j symbol with small and large angular momenta. When applying the same technique to the 12j symbol in this paper, we find that the spinor is diagonalized in the direction of an intermediate angular momentum. In addition, we find that the geometry of the derived asymptotic formula for the 12j symbol is expressed in terms of the vector diagram for a 9j symbol. This illustrates a general geometric connection between asymptotic limits of the various 3nj symbols. This work contributes an asymptotic formula for the 12j symbol to the quantum theory of angular momentum, and serves as a basis for finding asymptotic formulas for the Wigner 15j symbol with two small angular momenta.

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Section: Discussionmentioning

confidence: 99%

Section: Lagrangian Manifolds and Actionsmentioning

confidence: 99%

Semiclassical analysis of the Wigner12jsymbol with one small angular momentum

2011

Phys. Rev. A

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“…This is discussed in Littlejohn (1990) and in Aquilanti et al (2007Aquilanti et al ( , 2012. In the case of the Ponzano-Regge formula, the relative phase between the two branches contained in cos(S+π/4) is 2S (dropping the π/4 which is irrelevant), which therefore is the integral of θ in (15) along a path starting on T 1 , running along the B-manifold to T 2 and then back along the A-manifold to the same point of T 1 .…”

Section: A Path For the Ponzano-regge Phasementioning

confidence: 96%

Symplectic and semiclassical aspects of the Schläfli identity

Hedeman

Kur

Littlejohn

et al. 2015

J. Phys. A: Math. Theor.

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Abstract. The Schläfli identity, which is important in Regge calculus and loop quantum gravity, is examined from a symplectic and semiclassical standpoint in the special case of flat, 3-dimensional space. In this case a proof is given, based on symplectic geometry. A series of symplectic and Lagrangian manifolds related to the Schläfli identity, including several versions of a Lagrangian manifold of tetrahedra, are discussed. Semiclassical interpretations of the various steps are provided. Possible generalizations to 3-dimensional spaces of constant (nonzero) curvature, involving Poisson-Lie groups and q-deformed spin networks, are discussed.

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“…The many kinds of molecular processes involve gasphase chemistry, surface chemistry, low and ultralow temperature chemistry as well as high temperatures, suprathermal atoms and molecules. 14 The theoretical treatments need to be developed by using ab initio molecular calculations, and classical, semi-classical 15,16 and quantum dynamics 17 approaches. (See also refs.…”

Section: Dynamics Of Elementary Processesmentioning

confidence: 99%

The Astrochemical Observatory: Molecules in the Laboratory and in the Cosmos

Palazzetti

Maciel

Lombardi

et al. 2012

J Chinese Chemical Soc

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Astrochemistry is a discipline consolidated recently, although its roots extend back to the dawn of early civilization with the observation and mapping of the sky. The way to the understanding of the common natural laws on earth and in space paved by Galilei's observations by the telescope, has been extended in the last decades, by new technologies such as radioastronomy and space missions. Plenty of new chemistry was surprisingly discovered. Extreme rich information on the chemical "composition" of the universe is being obtained, either from the other planets and satellites in the Solar System, from meteorites and comets, or from the interstellar space. In this article we will present selected topics regarding the chemical structures and reactions being discovered. Particular attention will be devoted to aspects considered as relevant for the prebiotic processes on earth, such as those involving chirality and its role played in the origin and evolution of life.

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Semiclassical analysis of Wigner 3j-symbol

Cited by 51 publications

References 61 publications

Semiclassical analysis of the Wigner12jsymbol with one small angular momentum

Semiclassical analysis of the Wigner12jsymbol with one small angular momentum

Symplectic and semiclassical aspects of the Schläfli identity

The Astrochemical Observatory: Molecules in the Laboratory and in the Cosmos

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