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  • 1
    Electronic Resource
    Electronic Resource
    Harmonic analysis on spannors (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 2826-2879 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The spannor representation of the universal covering group of the conformal group of Minkowski space–time is studied herein. It is an example of an indecomposable representation. Various parallelizations for spannors are described. Normalized K˜-finite basis fields for the spannors are introduced, and a computation of the actions of the scale generator and other generators of the conformal group on these basis fields is given. The irreducibility of all irreducible composition factors is established, and it is decided which ones are infinitesimally unitary. Two sets of generators for maximal Abelian subalgebras of the enveloping algebra of the conformal group are introduced. The action of one of the sets on K˜-finite basis fields in the spannor representation is studied; this is important for understanding of the problem of degeneracy in the spannor representation, since K˜ types occur with multiplicity 2. Many calculations make use of the lowest (highest) weight module structures of the unitarizable and positive (negative) energy, irreducible composition factors; and, thus, many of our results and techniques can be used to initiate a study of the quantum deformations of the associated Lie algebra representations. Results on the Poincaré content of the unitarizable, irreducible composition factors are stated, and unitary equivalences between certain of these factors are established. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531069
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  • 2
    Electronic Resource
    Electronic Resource
    An embedding of the Poincaré Lie algebra into an extension of the Lie field of SO0(1,4) (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 5320-5332 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The * isomorphism between algebraic extensions of the Lie fields of SO0(1,4) and the Poincaré group are considered herein. It is shown that the principal series of unitary ray representations of SO0(1,4) are associated, via the * isomorphism, with real mass, positive and negative energy representations of the Poincaré Lie algebra with arbitrary spin. Results on the most degenerate exceptional series of SO0(1,4) representations are also given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530307
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  • 3
    Electronic Resource
    Electronic Resource
    Unitary representations of the (4+1) de Sitter group on unitary irreducible representation spaces of the Poincaré group: Equivalence with their realizations as induced representations (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 29-40 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In a previous work we have constructed realizations of the principal continuous series of unitary irreducible representations of the simply connected covering group of the (4+1) de Sitter group on unitary irreducible representation spaces of the simply connected covering group of the Poincaré group. In this work we demonstrate the equivalence of the representations constructed in the previous work with their realizations as induced representations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526795
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  • 4
    Electronic Resource
    Electronic Resource
    On the integrability of certain symmetric representations of the Lie algebra of SO0(4,1) (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 365-374 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A proof of the existence of an essentially self-adjoint extension of a symmetric ∼(SO0(4,1)) Nelson operator, which is constructed out of the generators of a positive mass, arbitrary spin unitary irreducible representation of the Poincaré group, is presented. Our analysis of ∼(SO0(4,1)) and its Lie algebra provides us with an example of an observation of Harish-Chandra: There exist subspaces of the space of differentiable vectors of a representation of a noncompact group which are invariant under the Lie algebra, but the closures of the subspaces are not invariant under the group. The chief results of this paper should hold true for ∼(SO0(n,1)). In particular, we should have a realization of an arbitrary principal series irreducible unitary representation of SO0(n,1) on the direct sum of two identical unitary irreducible representation spaces of the motion group in an n-dimensional Minkowski space, which has one timelike dimension.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526669
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  • 5
    Electronic Resource
    Electronic Resource
    In vitro Ca deposition by rat matrix vesicles: Is the membrane association of alkaline phosphatase essential for matrix vesicle-mediated calcium deposition?
    Amsterdam : Elsevier
    International Journal of Biochemistry 25 (1988), S. 1737-1742 
    Details
    ISSN: 0020-711X
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Biology , Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://linkinghub.elsevier.com/retrieve/pii/0020-711X(88)90301-1
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  • 6
    Electronic Resource
    Electronic Resource
    Radiative reaction and quantum mechanics (1993)
    Springer
    International journal of theoretical physics 32 (1993), S. 2031-2035 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract According to the principles of quantum mechanics, the classical Lorentz-Dirac equations of the electron should follow from quantum electrodynamics in the classical limit. We show this is indeed true for the special case in which the charge does not radiate, provided the momentum operators in the Dirac theory are identified, in the classical limit, with the effective momenta of the Lorentz-Dirac equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00675015
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  • 7
    Electronic Resource
    Electronic Resource
    Embedding Euclidean Lie algebras into quantum structures (1997)
    Springer
    Czechoslovak journal of physics 47 (1997), S. 1251-1258 
    Details
    ISSN: 1572-9486
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We show that it is possible to express the basis elements of the Lie algebra of the Euclidean group, E(2), as simple irrational functions of certain q deformed expressions involving the generators of the quantum algebra U q(so(2, 1)). We consider implications of these results for the representation theory of the Lie algebra of E(2). We briefly discuss analogous results for U q(so(2, 2)).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022829700566
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  • 8
    Electronic Resource
    Electronic Resource
    Positive-energy irreps of the quantum anti de Sitter algebra (1996)
    Springer
    Czechoslovak journal of physics 46 (1996), S. 171-178 
    Details
    ISSN: 1572-9486
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We obtain positive-energy irreducible representations of theq-deformed anti de Sitter algebraU q (so(3, 2)) by deformation of the classical ones. When the deformation parameterq isN-th root of unity, all these irreducible representations become unitary and finite-dimensional. Generically, their dimensions are smaller than those of the corresponding finite-dimensional non-unitary representations ofso(3, 2). We discuss in detail the singleton representations, i.e. the Di and Rac. WhenN is odd, the Di has dimension 1/2(N 2−1) and the Rac has dimension 1/2(N 2+1), while ifN is even, both the Di and Rac have dimension 1/2N 2. These dimensions are classical only forN=3 when the Di and Rac are deformations of the two fundamental non-unitary representations ofso(3, 2).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01688808
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  • 9
    Electronic Resource
    Electronic Resource
    Representations of Lie algebras from representations of quantum groups (1998)
    Springer
    Czechoslovak journal of physics 48 (1998), S. 1457-1464 
    Details
    ISSN: 1572-9486
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In paper [*] (P. Moylan: Czech. J. Phys., Vol. 47 (1997), p. 1251) we gave an explicit embedding of the three dimensional Euclidean algebra ɛ(2) into a quantum structure associated with U q(so(2, 1)). We used this embedding to construct skew symmetric representations of ɛ(2) out of skew symmetric representations of U q(so(2, 1)). Here we consider generalizations of the results in [*] to a more complicated quantum group, which is of importance to physics. We consider U q(so(3, 2)), and we show that, for a particular representation, namely the “Rac” representation, many of the results in [*] carry over to this case. In particular, we construct representations of so(3, 2), P(2, 2), the Poincaré algebra in 2+2 dimensions, and the Poincaré algebra out of the Rac representation of U q(so(3, 2)). These results may be of interest to those working on exploiting representations of U q(so(3, 2)), like the Rac, as an example of kinematical confinement for particle constituents such as the quarks.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021625810591
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  • 10
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    Relativistic rotator. III. Contraction limits and experimental justification (1984)
    American Physical Society
    Details
    Publication Date: 1984-06-15
    Print ISSN: 0556-2821
    Electronic ISSN: 1089-4918
    Topics: Physics
    Published by American Physical Society
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