QuantumSU(2) andE(2) groups. Contraction procedure

1992 ◽  
Vol 149 (3) ◽  
pp. 637-652 ◽  
Author(s):  
S. L. Woronowicz
Keyword(s):  
Contraction Procedure

scholarly journals From osp(1|32)⊕osp(1|32) to the M-theory superalgebra: a contraction procedure

2017 ◽  
Vol 80 (2) ◽  
pp. 340-346
Author(s):  
J. J. Fernández ◽  
J. M. Izquierdo ◽  
M. A. del Olmo
Keyword(s):  
Contraction Procedure ◽  
M Theory

A Variation of the Sulfide Contraction Procedure for Synthesis of Corrinoid Systems

1973 ◽  
Vol 12 (11) ◽  
pp. 910-912 ◽  
Author(s):  
Erwin Götschi ◽  
Walter Hunkeler ◽  
Hans-Jakob Wild ◽  
Peter Schneider ◽  
Walter Fuhrer ◽  
...  
Keyword(s):  
Contraction Procedure ◽  
Sulfide Contraction

scholarly journals Carroll contractions of Lorentz-invariant theories

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Marc Henneaux ◽  
Patricio Salgado-Rebolledo
Keyword(s):  
Equations Of Motion ◽  
Action Principle ◽  
Hamiltonian Form ◽  
Speed Of Light ◽  
Hamiltonian Action ◽  
Canonical Variables ◽  
Higher Spin ◽  
Contraction Procedure ◽  
Ultrarelativistic Limit ◽  
The One

Abstract We consider Carroll-invariant limits of Lorentz-invariant field theories. We show that just as in the case of electromagnetism, there are two inequivalent limits, one “electric” and the other “magnetic”. Each can be obtained from the corresponding Lorentz-invariant theory written in Hamiltonian form through the same “contraction” procedure of taking the ultrarelativistic limit c → 0 where c is the speed of light, but with two different consistent rescalings of the canonical variables. This procedure can be applied to general Lorentz-invariant theories (p-form gauge fields, higher spin free theories etc) and has the advantage of providing explicitly an action principle from which the electrically-contracted or magnetically-contracted dynamics follow (and not just the equations of motion). Even though not manifestly so, this Hamiltonian action principle is shown to be Carroll invariant. In the case of p-forms, we construct explicitly an equivalent manifestly Carroll-invariant action principle for each Carroll contraction. While the manifestly covariant variational description of the electric contraction is rather direct, the one for the magnetic contraction is more subtle and involves an additional pure gauge field, whose elimination modifies the Carroll transformations of the fields. We also treat gravity, which constitutes one of the main motivations of our study, and for which we provide the two different contractions in Hamiltonian form.

Cyclophanes. VI. The synthesis of [2,2](3,3')biphenylparacyclophanedienes

1976 ◽  
Vol 29 (6) ◽  
pp. 1267 ◽  
Author(s):  
PJ Jessup ◽  
JA Reiss
Keyword(s):  
Ring Opening ◽  
Ring System ◽  
Ring Contraction ◽  
Stevens Rearrangement ◽  
Ring Opening Reaction ◽  
Disubstituted Benzene ◽  
Contraction Procedure

The preparations of [2,2](3,3')biphenylparacyclophane-1,9-dine (19) and a dimethyl derivative (20) synthesized by a ring-contraction procedure of the corresponding dithiacyclophanes (11) and (12) are reported. Both dienes (19) and (20) photocyclized under oxidative conditions to the benzo[ghi]- perylenes (21) and (22). Difficulties associated with the Stevens rearrangement in cyclophanes containing a para-disubstituted benzene moiety have been rationalized in terms of a competing ring- opening reaction. Several other reactions of the biphenylparacylophane ring system are reported, and the stereochemistry of the macrocycle is discussed.

scholarly journals A polynomial class of u(2) algebras

2015 ◽  
Vol 12 (08) ◽  
pp. 1560025
Author(s):  
Mohammed Daoud ◽  
Won Sang Chung
Keyword(s):  
Hilbert Space ◽  
Polynomial Algebra ◽  
Heisenberg Algebra ◽  
Parameter Family ◽  
Unitary Representations ◽  
Contraction Procedure ◽  
Bargmann Representation ◽  
Polynomial Class

A r-parameter u{κ1,κ2,…,κr}(2) algebra is introduced. Finite unitary representations are investigated. This polynomial algebra reduces via a contraction procedure to the generalized Weyl–Heisenberg algebra 𝒜{κ1,κ2,…,κr} [M. Daoud and M. Kibler, J. Phys. A: Math. Theor.45 (2012) 244036]. A pair of nonlinear (quadratic) bosons of type 𝒜κ ≡ 𝒜{κ1=κ,κ2=0,…,κr=0} is used to construct, à la Schwinger, a one parameter family of (cubic) uκ(2) algebra. The corresponding Hilbert space is constructed. The analytical Bargmann representation is also presented.

scholarly journals Quantum E(2) groups for complex deformation parameters

2021 ◽  
pp. 2150021
Author(s):  
Atibur Rahaman ◽  
Sutanu Roy
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Locally Compact ◽  
Complex Deformation ◽  
Circle Group ◽  
Deformation Parameters ◽  
Quantum Analogue ◽  
Group Contraction ◽  
Contraction Procedure ◽  
Matrix Formula

We construct a family of [Formula: see text] deformations of E(2) group for nonzero complex parameters [Formula: see text] as locally compact braided quantum groups over the circle group [Formula: see text] viewed as a quasitriangular quantum group with respect to the unitary [Formula: see text]-matrix [Formula: see text] for all [Formula: see text]. For real [Formula: see text], the deformation coincides with Woronowicz’s [Formula: see text] groups. As an application, we study the braided analogue of the contraction procedure between [Formula: see text] and [Formula: see text] groups in the spirit of Woronowicz’s quantum analogue of the classic Inönü–Wigner group contraction. Consequently, we obtain the bosonization of braided [Formula: see text] groups by contracting [Formula: see text] groups.

THE JORDAN-SCHWINGER REALIZATION OF TWO-PARAMETRIC QUANTUM GROUP slq,s(2)

1993 ◽  
Vol 08 (06) ◽  
pp. 543-548 ◽  
Author(s):  
SICONG JING
Keyword(s):  
Harmonic Oscillator ◽  
Quantum Group ◽  
Commutation Relations ◽  
Deformed Oscillator ◽  
Contraction Procedure

The Jordan-Schwinger realization of two-parametric quantum group sl q,s(2), is presented by introducing two-parametric deformed harmonic oscillator. The Heisenberg commutation relations of the two-parametric deformed oscillator are derived by virtue of the Schwinger’s contraction procedure.

Cyclophanes. XII* The Synthesis of [2,2](3,3')Biphenylo(3,6)-phenanthrenophanes and Attempted Conversions into Hepta[8]circulene

1979 ◽  
Vol 32 (2) ◽  
pp. 361 ◽  
Author(s):  
DN Leach ◽  
JA Reiss
Keyword(s):  
Ring Contraction ◽  
Factors Affecting ◽  
Spectral Evidence ◽  
Saturated Compound ◽  
Contraction Procedure

[2,2](3,3')Biphenylo(3,6)phenanthrenophane-1,15-diene (6) has been synthesized by a ring-contraction procedure from the dithiacyclophane (10). The corresponding saturated compound (5) was prepared by pyrolysis of the sulfone (12). The stereochemistry of both (5) and (6) in solution has been determined to be syn from spectral evidence and neither compound shows any evidence of conformational ring-flipping or extensive mobility. Several attempts to convert the diene (6) into hepta[8]circulene are recorded. The factors affecting the photochemical ring-closures of cyclophanedienes are discussed.

scholarly journals THE SURFACE CHARGE OF RAT LIVER MITOCHONDRIA AND THEIR MEMBRANES

1970 ◽  
Vol 46 (1) ◽  
pp. 137-150 ◽  
Author(s):  
Hans-G. Heidrich ◽  
Roland Stahn ◽  
Kurt Hannig
Keyword(s):  
Surface Charge ◽  
Electrophoretic Mobility ◽  
Mitochondrial Membrane ◽  
Krebs Cycle ◽  
Liver Mitochondria ◽  
Rat Liver Mitochondria ◽  
Outer Mitochondrial Membrane ◽  
Contraction Procedure ◽  
Matrix Fraction ◽  
Nadh Cytochrome

The surface charge of intact mitochondria and submitochondrial particles was examined by the technique of preparative free flow electrophoresis. When submitochondrial preparations obtained by a swelling-contraction procedure were examined with this technique, two fractions were observed. One of these fractions exhibited the same electrophoretic properties as intact mitochondria, which indicated that it was derived from the outer limiting membrane of the mitochondrion. This fraction was found to contain the enzymes monoamine oxidase and rotenone-insensitive NADH-cytochrome c reductase which have been reported to be localized in the outer mitochondrial membrane. The other fraction exhibited an electrophoretic mobility which was different from that of intact mitochondria, and this fraction contained enzymes characteristic of the inner membrane-matrix fraction such as soluble and particulate enzymes of the Krebs cycle. Microsomes exhibited an electrophoretic mobility which was almost identical with that of the outer mitochondrial membrane. In addition to resolving the localization of enzymes in mitochondrial membranes, these data indicate that the outer limiting membrane of the mitochondrion is the sole determinant of the surface charge of mitochondria.

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