14379054
Covariant Model of Relativistic Extended Particles based on the Oscillator Representation of the Poincaré Group
While internal space-time symmetries of relativistic particles are dictated by the little groups of the Poincaré group, it is possible to construct representations of the little group for massive particles starting from harmonic oscillator wave functions for the quark model. The resulting oscillator wave functions are covariant and can be Lorentz-boosted. It is thus possible to obtain the parton model by boosting the quark model. A review of Wigner's theory of the little groups is given. It is shown that the covariant oscilla-tor wave functions become squeezed as as the system becomes boosted. It is shown also that the Lorentz-squeezed quark distribution exhibits the peculiarities of Feynman's parton model including the lack of coherence in the calculation of cross sections. A historical review of the concept of covariance is given.
1673726
Symmetries Shared by the Poincaré Group and the Poincaré Sphere
Henri Poincare formulated the mathematics of Lorentz transformations, known as the Poincare group. He also formulated the Poincare sphere for polarization optics. It is shown that these two mathematical instruments can be derived from the two-by-two representations of the Lorentz group. Wigner’s little groups for internal space-time symmetries are studied in detail. While the particle mass is a Lorentz-invariant quantity, it is shown to be possible to address its variations in terms of the decoherence mechanism in polarization optics.
73571003
Time separation as a hidden variable to the Copenhagen school of quantum mechanics
The Bohr radius is a space‐like separation between the proton and electron in the hydrogen atom. According to the Copenhagen school of quantum mechanics, the proton is sitting in the absolute Lorentz frame. If this hydrogen atom is observed from a different Lorentz frame, there is a time‐like separation linearly mixed with the Bohr radius. Indeed, the time‐separation is one of the essential variables in high‐energy hadronic physics where the hadron is a bound state of the quarks, while thoroughly hidden in the present form of quantum mechanics. It will be concluded that this variable is hidden in Feynman’s rest of the universe. It is noted first that Feynman’s Lorentz‐invariant differential equation for the bound‐state quarks has a set of solutions which describe all essential features of hadronic physics. These solutions explicitly depend on the time separation between the quarks. This set also forms the mathematical basis for two‐mode squeezed states in quantum optics, where both photons are observable,...
668406
Quantization of electromagnetic fields in a circular cylindrical cavity
We present a quantization procedure for the electromagnetic field in a circular cylindrical cavity with perfectly conducting walls, which is based on the decomposition of the field. A new decomposition procedure is proposed; all vector mode functions satisfying the boundary conditions are obtained with the help of this decomposition. After expanding the quantized field in terms of the vector mode functions, it is possible to derive the Hamiltonian for this quantized system.
14939249
Coupled Harmonic Oscillators and Feynman's Rest of the Universe
According to Feynman, the universe consists of two parts - the system in which we are interested and the rest of the universe which our measurement process does not reach. Feynman then formulates the density matrix in terms of the observable world and the rest of the universe. It is shown that coupled harmonic oscillators can serve as an illustrative example for Feynman's ``rest of the universe.'' It is pointed out that this simple example has far-reaching consequences in many branches of physics, including statistical mechanics, measurement theory, information theory, thermo-field dynamics, quantum optics, and relativistic quantum mechanics. It is shown that our ignorance of the rest of the universe increases the uncertainty and entropy in the system in which we are interested.
1320799
Wigner rotations and Iwasawa decompositions in polarization optics.
Wigner rotations and Iwasawa decompositions are manifestations of the internal space-time symmetries of massive and massless particles, respectively. It is shown to be possible to produce combinations of optical filters which exhibit transformations corresponding to Wigner rotations and Iwasawa decompositions. This is possible because the combined effects of rotation, phase-shift, and attenuation filters lead to transformation matrices of the six-parameter Lorentz group applicable to Jones vectors and Stokes parameters for polarized light waves. The symmetry transformations in special relativity lead to a set of experiments which can be performed in optics laboratories.
111325925
Reduction of ripple fields in DC magnet using an auxiliary winding
This paper presents a simple method to achieve 10−6 level of ripple fields in a large current DC magnet which is excited by a power supply of moderate ripple current content (10−4–10−5). A theory of the ripple field in a magnet with an auxiliary winding is derived and the conditions for ripple field reduction are obtained. When the resistance of the auxiliary circuit is much smaller than the reactance of that circuit, the ripple field bucking ratio is proportional to the quality factor of the auxiliary winding. To compare the theory with the experiment, a dipole magnet with an auxiliary winding was used. The auxiliary winding was either short-circuited or loaded with a resistor and the ripple fields were measured with a pickup coil placed in the magnet gap. When the auxiliary winding was short-circuited, a ripple field bucking ratio greater than 40 was achieved with a high output impedance power supply. This experimental result agrees well with the theory, and indicates that an auxiliary winding of a large cross-sectional area, instead of a large turn-number, is desired for an efficient ripple field reduction.
3194304
Kaon Condensation and Enforced Charge Neutrality of the Color-Flavor Locked Phase
We investigate the influence of charged kaon condensation in hadronic sector on the formation of the electron-free charge neutral quark matter of equipartition of three light flavors, i.e., a phenomenon called ``enforced electrical neutrality" of the color-flavor locked (CFL) phase. We employ the chiral quark model which is assumed to be applicable, "bottom-up," toward chiral restoration while accessible to kaon condensation in the hadronic sector. Approaching "bottom-up" the high density regime is more appropriate in addressing the properties of compact stars than approaching "top-down" from asymptotic QCD. It turns out that the presence of hadronic kaon condensation makes the electron-free charge-neutral CFL phase energetically more favorable with a relatively small color-superconducting gap $\Delta_0\sim 20$ MeV compared to $\Delta_0\sim 70$ MeV required in the absence of such kaon condensation.
2251108
Competition Between Induced Symmetry Breaking, Cooper Pairing and Chiral Condensate at Finite Density
We study the competition between induced symmetry breaking (ISB), 
Cooper pairing (superconductivity) and chiral condensation at finite non-asymptotic density. Using a quantum mechanical model studied recently by Ilieva and Thirring, we analyze the expectation value of the fermion number density $\la a^*a\ra$ in the presence of chemical potential and discuss relevance of the ISB phenomenon in the model. By Bogoliubov transformation, we obtain the ground state energy and find that a phase with both superconducting and mean field gap is a true ground state. We also study the effective potentials of a two-dimensional field theory model for competitions between $\la\bar\psi\psi\ra$, $\la\psi\psi\ra$ and $\la\psi^\dagger\psi\ra$. We find that in the regime $\mu \mu_c$ the system sits in the mixed phase characterized by 
$\la \psi^\dagger\psi\ra\neq 0$ and $\la \psi\psi\ra\neq 0$ as long as the renormalization point, $M_0$, corresponding to a superconducting gap is not zero, $M_0\neq 0$.
119962841
Photoelectron angular distributions from the subshells of high-Z elements
Numerical predictions are obtained, within a relativistic multipole central-field approximation calculation, for the radial matrix elements and resulting angular distributions of photoelectrons ejected from inner through outer subshells of uranium and for photoelectron energies from near threshold (1 eV) to 100 keV. Some data are also presented for outer subshells of mercury. We confirm that for inner shells higher-multipole effects persist to low energies, while we find that for outer shells such effects become small. For uranium inner ns subshells the asymmetry parameter ..beta../sub n/s differs from its nonrelativistic value 2, but not more than 30% (for n .. epsilonp/sub 1/2/ and ns ..-->.. epsilonp/sub 3/2/ transitions for these inner shells are similar). For outer s subshells relativistic spin-orbit splittings cause large deviations from the nonrelativistic predictions which can be understood from the magnitudes, zeros, and splittings of the two radial matrix elements. For U 6p/sub 1/2/ and 6p/sub 3/2/, ..beta../sub 6p/ has the same qualitative features found in nonrelativistic calculations for outer p shells of other high-Z elements, but the angular distributions from the two states do differ in detail. Such differences in angular distributions of themore » photoelectrons from the two j substates of given l become smaller for inner p shells. For outer d and f subshells the asymmetry parameter oscillates with photoelectron energy in a manner similar to that found by Manson in nonrelativistic dipole d-subshell calculations, and no qualitatively important relativistic effects have been identified; this is due to the decrease of the fine-structure-splitting interval with increasing angular momentum.« less
119341368
A Schematic model for rho - a(1) mixing at finite density and in-medium effective Lagrangian
Based on schematic two-level models extended to a{sub 1}-meson degrees of freedom, we investigate possible mechanisms of chiral restoration in the vector-axial-vector channels in cold nuclear matter. In the first part of this article we employ the massive Yang-Mills framework to construct an effective chiral Lagrangian based on low-energy mesonic modes at finite density. The latter are identified through nuclear collective excitations of ''meson''-sobar type such as {pi}{r_reversible}[{delta}(1232)N{sup -1}]{identical_to}{pi}, {rho}{r_reversible}[N{sup *}(1520)N{sup -1}]{identical_to}{rho}, etc. In a mean-field type treatment the in-medium gauge coupling g, the (axial-)vector meson masses and f{sub {pi}} are found to decrease with density indicating the approach towards chiral restoration in the language of in-medium effective fields. In the second part of our analysis we evaluate the (first) in-medium Weinberg sum rule which relates vector and axial-vector correlators to the pion decay constant. Using in-medium {rho}/a{sub 1} spectral functions (computed in the two-level model) also leads to a substantial reduction of the pion decay constant with increasing density. (c) 2000 The American Physical Society.