120440944
A simple method for illustrating the difference between the homogeneous and inhomogeneous Lorentz groups
A method is proposed for illustrating the difference between the Poincare (inhomogeneous Lorentz) and homogeneous Lorentz groups. Representations of the Poincare group are constructed from solutions of the relativistic harmonic oscillator equation whose physical wave functions have been effective in describing basic high‐energy hadronic features in the relativistic quark model. It is shown that the Poincare group can be represented by solutions of the relativistic oscillator equation in a ’’moving cylindrical’’ coordinate system in which the time‐separation variable in the hadronic rest frame is treated separately. Representations which are diagonal in the Casimir operators of the homogeneous Lorentz group are also constructed from solutions of the same oscillator differential equation in a hyperbolic coordinate system. It is pointed out that the difference between the Poincare and homogeneous Lorentz groups mainfests itself in the coordinate systems in which the oscillator differential equation in separable.
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.
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.
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,...
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.
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.
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, $M_0\neq 0$.
119447142
Renormalization group analysis ofρ-meson properties at finite density
We calculate the density dependence of the $\rho$-meson mass and coupling constant($g_{\rho NN}$) for $\rho$-nucleon-nucleon vertex at one loop using the lagrangian where the $\rho$-meson is included as a dynamical gauge boson of a hidden local symmetry. From the condition that thermodynamic potential should not depend on the arbitrary energy scale, renormalization scale, one can construct a renormalization group equation for the thermodynamic potential and argue that the various renormalization group coefficients are functions of the density or temperature. We calculate the $\beta$-function for $\rho$-nucleon-nucleon coupling constant ($g_{\rho NN}$) and $\gamma$-function for $\rho$-meson mass ($\gamma_{m_\rho}$). We found that the $\rho$-meson mass and the coupling constant for $g_{\rho NN}$ drop as density increases in the low energy limit.
54616116
PRECISION FIELD MAPPING SYSTEM FOR CYCLOTRON MAGNET
This paper presents a Hall-probe mapping system for measuring the cyclotron magnet, which has been fabricated for the 13 MeV cyclotron at the Korea Institute of Radiological and Medical Sciences(KIRAMS). The Hall probe are mounted on the precision x-y stage, and maps the magnetic field in the Cartesian coordinates. To reduce the data-acquisition time, the system uses the “flying” mode field mapping method. The data acquisition time for mapping the whole gap-area of the cyclotron magnet is ~ 60 minutes. The relative random fluctuation error during the entire mapping process is under 0.01 %. The field measurement results after correction have indicated that the total phase excursion is less than ±15°.
67811641
ENERGY SPREAD ISSUE IN LASER UNDULATOR BASED XFELs
At the Center for the Exploration of Energy and Matter (CEEM) in Indiana University, we have been developing a new XFEL concept, which is based on inverse Compton scattering and a laser undulator instead of the conventional magnetic undulator. In this paper, we report an estimation of the energy spread growth in the electron storage ring due to the inverse Compton scattering itself and their impacts on the FEL lasing in the laser undulator based XFEL concept.
8523168
Fixed-Point Analysis of the Low-Energy Constants in the Pion-Nucleon Chiral Lagrangian
In the framework of heavy-baryon chiral perturbation theory, we investigate the fixed point structure of renormalization group equations (RGE) for the ratios of the renormalized low energy constants (LECs) that feature in the pion-nucleon chiral Lagrangian. The ratios of the LECs deduced from our RGE analysis are found to be in semi-quantitative agreement with those obtained from direct fit to the experimental data. The naturalness of this agreement is discussed using a simple dimensional analysis combined with Wilsonian RGEs.