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  • 1
    Electronic Resource
    Electronic Resource
    O(2,1)-like little group for spacelike four-momenta and localized light waves in continuous media (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3190-3196 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: While a light wave travels in a nonvacuum medium with speed less than the speed of light in vacuum, its energy-momentum four-vector is spacelike. Thus the little group for this light wave is locally isomorphic to O(2,1). It is shown that the transformation of this little group produces observable effects on the light wave, in contrast to the case of the E(2)-like little group for photons in vacuum. It is also shown that the little group can be defined for a localized light wave consisting of a superposition of waves with different frequencies traveling in the same direction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529537
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  • 2
    Electronic Resource
    Electronic Resource
    Space-time geometry of relativistic particles (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 55-60 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A three-dimensional space-time geometry of relativistic particles is constructed within the framework of the little groups of the Poincaré group. Since the little group for a massive particle is the three-dimensional rotation group, its relevant geometry is a sphere. For massless particles and massive particles in the infinite-momentum limit, it is shown that the geometry is that of a cylinder and a two-dimensional plane. The geometry of a massive particle continuously becomes that of a massless particle as the momentum/mass becomes large. The geometry of relativistic extended particles is also considered. It is shown that the cylindrical geometry leads to the concept of gauge transformations, while the two-dimensional Euclidean geometry leads to a deeper understanding of the Lorentz condition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528827
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  • 3
    Electronic Resource
    Electronic Resource
    Symmetries of two-mode squeezed states (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 5493-5508 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is known that the symmetry of two-mode squeezed states is governed by the group Sp(4) which is locally isomorphic to the O(3,2) de Sitter group. It is shown that this complicated ten-parameter group can be regarded as a product of two three-parameter Sp(2) groups. It is shown also that two coupled harmonic oscillators serve as a physical basis for the symmetry decomposition. It is shown further that the concept of entropy is needed when one of the two modes is not observed. The entropy is zero when the system is uncoupled. The system reaches thermal equilibrium when the entropy becomes maximal.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530318
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  • 4
    Electronic Resource
    Electronic Resource
    E(2)-symmetric two-mode sheared states (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1237-1246 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is noted that the symmetry of two-mode squeezed states of light is governed by the group Sp(4) that is locally isomorphic to O(3,2). This group has subgroups that are locally isomorphic to the two-dimensional Euclidean group. Two-mode states having the E(2) symmetry are constructed. The translation-like transformations of this symmetry group shear the Wigner distribution function defined over the four-dimensional phase space consisting of two pairs of canonical variables. Sheared states are constructed in the Schrödinger picture of quantum mechanics and in the Fock space for photon numbers. It is shown that the Wigner phase-space picture is a convenient representation of quantum mechanics for calculating measurable quantities of the sheared states.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529701
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  • 5
    Electronic Resource
    Electronic Resource
    Space-time geometry of relativistic particles in four-dimensional phase space (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1998-2006 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Wigner phase-space picture of Dirac's two-oscillator representation of O(3,2) is given. This constitutes a real representation of Sp(4) which allows us to study the symmetry of the O(3,2) de Sitter group using canonical transformations in four-dimensional phase space. It is also possible to study subgroups of O(3,1) in this phase space. The phase-space picture is given for the two-oscillator model of van Dam, Ng, and Biedenharn [Phys. Lett. B 158, 227 (1985)] for the little groups for massive and massless particles. In this formalism, Lorentz transformations can be described in terms of canonical transformations in phase space. It is particularly convenient for studying infinite-momentum/zero-mass limit of the O(3)-like little group for a massive particle. It is shown that the trivial representation of the E(2)-like little group for a massless particle emerges from this limiting process. The origin of gauge degree of freedom is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529220
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  • 6
    Electronic Resource
    Electronic Resource
    Highly efficient separate-confinement PpinN GaAs/AlGaAs waveguide phase modulator (1989)
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 55 (1989), S. 1865-1867 
    Details
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We report a high-efficiency PpinN GaAs/AlGaAs waveguide phase modulator for high-speed operations. By introducing p- and n-GaAs layers beside the intrinsic GaAs layer of a P-i-N double heterostructure, the absorption edge-related effect, hardly used in P-i-N phase modulators, is utilized. We demonstrate a high phase shift efficiency of 37.5°/V mm at 1.3 μm wavelength. Although this corresponds to the highest expeirmental value reported for reverse-biased GaAs/AlGaAs phase modulators, our device operates with a low junction and a very low dynamic capacitance.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.102155
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  • 7
    Electronic Resource
    Electronic Resource
    Parallel and vertical morphologies in block copolymers of cylindrical domain (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 1253-1256 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present a theoretical result on the ordering of cylindrical morphology in diblock and triblock copolymers. The equilibrium morphology of A–B diblock and A–B–A triblock copolymer films is shown to have the cylinders oriented parallel or vertical to the surface, depending on the film thickness and surface tensions. A criterion is derived that can be used to determine the conditions under which the orientation is parallel or vertical. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.475487
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  • 8
    Electronic Resource
    Electronic Resource
    Cylindrical group and massless particles (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 1175-1179 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the representation of the E(2)-like little group for photons can be reduced to the coordinate transformation matrix of the cylindrical group, which describes movement of a point on a cylindrical surface. The cylindrical group is isomorphic to the two-dimensional Euclidean group. As in the case of E(2), the cylindrical group can be regarded as a contraction of the three-dimensional rotation group. It is pointed out that the E(2)-like little group is the Lorentz-boosted O(3)-like little group for massive particles in the infinite-momentum/zero-mass limit. This limiting process is shown to be identical to that of the contraction of O(3) to the cylindrical group. Gauge transformations for free massless particles can thus be regarded as Lorentz-boosted rotations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527824
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  • 9
    Electronic Resource
    Electronic Resource
    Decomposition of Lorentz transformations (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 2373-2378 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that every Lorentz transformation can be decomposed into a helicity-preserving transformation that changes the momentum of a free particle and a helicity-changing transformation that leaves the momentum invariant. Since momentum-preserving transformations constitute a subgroup of the Lorentz group, helicity-preserving transformations form a coset space. It is shown further that, for massive particles, every Lorentz transformation can be decomposed into the Wigner rotation and helicity-preserving transformations. For massless particles, every Lorentz transformation can be decomposed into the gauge transformation and helicity-preserving transformation. The gauge transformation in this case is a Lorentz-boosted Wigner rotation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527773
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  • 10
    Electronic Resource
    Electronic Resource
    Eulerian parametrization of Wigner's little groups and gauge transformations in terms of rotations in two-component spinors (1986)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 2228-2235 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A set of rotations and Lorentz boosts is presented for studying the three-parameter little groups of the Poincaré group. This set constitutes a Lorentz generalization of the Euler angles for the description of classical rigid bodies. The concept of Lorentz-generalized Euler rotations is then extended to the parametrization of the E(2)-like little group and the O(2,1)-like little group for massless and imaginary-mass particles, respectively. It is shown that the E(2)-like little group for massless particles is a limiting case of the O(3)-like or O(2,1)-like little group. A detailed analysis is carried out for the two-component SL(2,c) spinors. It is shown that the gauge degrees of freedom associated with the translationlike transformation of the E(2)-like little group can be traced to the SL(2,c) spins that fail to align themselves to their respective momenta in the limit of large momentum and/or vanishing mass.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526994
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