Generalized Schwinger boson realizations and the oscillator-like coherent states of the rotation groups and the asymmetric top

1979 ◽  
Vol 57 (7) ◽  
pp. 998-1021 ◽  
Author(s):  
P. Gulshani
Keyword(s):  
Angular Momentum ◽  
Coherent States ◽  
Euler Angles ◽  
Boson Realization ◽  
Special Cases ◽  
Asymmetric Top ◽  
Rotation Groups ◽  
Angular Momentum Algebra

Various definitions of the coherent states of the angular momentum are shown to be special cases of the oscillator-like coherent states of the groups SU(2) and SO(3) obtained by Mikhailov on the basis of a generalized Schwinger boson realization of the angular momentum algebra. This realization is then generalized to that of the angular momentum algebra of an asymmetric top by means of a transformation from the Euler angles to the Cayley–Klein parameters. The oscillator-like coherent states of an asymmetric top, analogous to those of Mikhailov, are then constructed. It is, then, shown that Janssen's and Mostowski's definitions of the coherent states of a top are special cases of these.

First-order Theory of Fields with Arbitrary Spin

2020 ◽  
pp. 135-146
Author(s):  
Daniel Canarutto
Keyword(s):  
Order Theory ◽  
Arbitrary Spin ◽  
General Description ◽  
First Order ◽  
First Order Theory ◽  
Special Cases ◽  
Spinor Geometry ◽  
Theory Of Fields ◽  
Angular Momentum Algebra ◽  
Dirac Spinors

By exploiting the previously exposed results in 2-spinor geometry, a general description of fields of arbitrary spin is exposed and shown to admit a first-order Lagrangian which extends the theory of Dirac spinors. The needed bundle is the fibered direct product of a symmetric ‘main sector’—carrying an irreducible representation of the angular-momentum algebra—and an induced sequence of ‘ghost sectors’. Several special cases are considered; in particular, one recovers the Bargmann-Wigner and Joos-Weinberg equations.

scholarly journals Observations of Binaries and Evolutionary Implications

1984 ◽  
Vol 80 ◽  
pp. 199-227
Author(s):  
C. De Loore
Keyword(s):  
Mass Transfer ◽  
Angular Momentum ◽  
Mass Transfer Process ◽  
Transfer Phase ◽  
X Ray ◽  
Special Cases ◽  
Angular Momentum Loss ◽  
Spectral Ranges ◽  
X Ray Binaries

AbstractComparison of the characteristics of groups of stars in various evolutionary phases and the study of individual systems allow to make estimates of the parameters governing mass loss and mass transfer. Observations enable us in a few cases to determine geometric models for binaries during or after the mass transfer phase (disks, rings, common envelopes, symbiotics, interacting binaries, compact components).From spectra taken at different phases, radial velocity curves can be derived and masses and radii can be determined. In special cases spectra in different spectral ranges (visual, UV, X-ray) are required for the determination of the radial velocities of the two components (for X-ray binaries, for systems with hot and cool components). Information on parameters related to the mass transfer process enables us to consider non conservative evolution - i.e. the computation of evolutionary sequences with the assumption that mass and angular momentum not only are transferred from one of the components towards the other one, but that also mass and angular momentum can leave the system. Careful and detailed analysis of the observations allows in certain cases to determine the parameters governing this mass and angular momentum loss, and for contact phases, to determine the degree of contact.

Fredholm Approximations in the Scalar Bethe-Salpeter Equation

1974 ◽  
Vol 29 (6) ◽  
pp. 916-923
Author(s):  
W. Bauhoff
Keyword(s):  
Angular Momentum ◽  
Variational Methods ◽  
Vertex Function ◽  
Feynman Parameter ◽  
Special Cases

The Fredholm approximation is discussed in the framework of the scalar Bethe-Salpeter equation. The trace of the angular momentum decomposed kernel is expressed in terms of Feynman parameter integrals which shows the relation to the vertex function. A new derivation for this representation is given which is far more direct than the previous one. Using this representation, several general features of the eigenvalues are discussed. For special cases, the trace is computed explicitly, and the numerical values are compared with the exact ones, obtained by variational methods.

Coherent states and geometric phases of a generalized damped harmonic oscillator with time-dependent mass and frequency

2014 ◽  
Vol 28 (26) ◽  
pp. 1450177 ◽  
Author(s):  
I. A. Pedrosa ◽  
D. A. P. de Lima
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Classical Equation ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Quantum Invariant ◽  
Dynamical Phase ◽  
Special Cases ◽  
Berry Phases ◽  
Dependent Mass

In this paper, we study the generalized harmonic oscillator with arbitrary time-dependent mass and frequency subjected to a linear velocity-dependent frictional force from classical and quantum points of view. We obtain the solution of the classical equation of motion of this system for some particular cases and derive an equation of motion that describes three different systems. Furthermore, with the help of the quantum invariant method and using quadratic invariants we solve analytically and exactly the time-dependent Schrödinger equation for this system. Afterwards, we construct coherent states for the quantized system and employ them to investigate some of the system's quantum properties such as quantum fluctuations of the coordinate and the momentum as well as the corresponding uncertainty product. In addition, we derive the geometric, dynamical and Berry phases for this nonstationary system. Finally, we evaluate the dynamical and Berry phases for three special cases and surprisingly find identical expressions for the dynamical phase and the same formulae for the Berry's phase.

scholarly journals COHERENT STATES, SUPERPOSITIONS OF COHERENT STATES AND UNCERTAINTY RELATIONS ON A MÖBIUS STRIP

2013 ◽  
Vol 28 (15) ◽  
pp. 1350058 ◽  
Author(s):  
THIAGO PRUDÊNCIO ◽  
DIEGO JULIO CIRILO-LOMBARDO
Keyword(s):  
Angular Momentum ◽  
Coherent States ◽  
Continuous Variable ◽  
Uncertainty Relations ◽  
Topological Properties ◽  
Möbius Strip ◽  
Symmetry Properties ◽  
Potential Applications ◽  
Fermionic Fields ◽  
Mobius Strip

Since symmetry properties of coherent states (CS) on Möbius strip (MS) and fermions are closely related, CS on MS are naturally associated to the topological properties of fermionic fields. Here, we consider CS and superpositions of coherent states (SCS) on MS. We extend a recent propose of CS on MS (Cirilo-Lombardo, J. Phys. A: Math. Theor.45, 244026 (2012)), including the analysis of periodic behaviors of CS and SCS on MS and the uncertainty relations associated to angular momentum and the phase angle. The advantage of CS and SCS on MS with respect to the standard ones and potential applications in continuous variable quantum computation (CVQC) are also addressed.

Boson and differential realizations of polynomial angular momentum algebra

2001 ◽  
Vol 42 (6) ◽  
pp. 2718-2724 ◽  
Author(s):  
Dong Ruan ◽  
Yufeng Jia ◽  
Wei Ruan
Keyword(s):  
Angular Momentum ◽  
Angular Momentum Algebra
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