117203424
Diagonalization of Sp(2) matrices
The two-by-two Sp(2) matrix has three parameters with unit determinant. Yet, there are no established procedures for diagonalizing this matrix. It is shown that this matrix can be written as a similarity transformation of the two-by-two Wigner matrix, derivable from Wigner's little group which dictates the internal space-time symmetries of relativistic particles. The Wigner matrix can be diagonalized for massive and space-like particles, while it takes a triangular form with unit diagonal elements for light-like particles. The most immediate physical application can be made to repeated one-dimensional transfer matrices appearing in many different branches of physics. Another application of current interest could be the dis-entanglement of entangled systems.
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.
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.
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.
119099546
Quark number susceptibility with finite chemical potential in holographic QCD
We study the quark number susceptibility in holographic QCD with a finite chemical potential or under an external magnetic field at finite temperature. We first consider the quark number susceptibility with the chemical potential. We observe that approaching Tc from high temperature regime, χq/T2 develops a peak as we increase the chemical potential, which confirms recent lattice QCD results. We discuss this behavior in connection with the existence of the critical end point in the QCD phase diagram. We also consider the quark number susceptibility under the external magnetic field. We predict that the quark number susceptibility exhibits a blow-up behavior at low temperature as we raise the value of the magnetic field. We finally spell out some limitations of our study.
56039995
DEVELOPMENT OF BEAM PROFILE MONITOR FOR CYCLOTRON
A current sensor module was designed and fabricated to measure the beam profile of the cyclotron MC50 at KIRAMS. The sensors were made of a tungsten wire and they were assembled into an array type. The sensor wires were placed in parallel with the incident beam, while they were placed in the perpendicular direction to the incident beam in the conventional method. The current output of each sensor was amplified using a transresistance amplifier. The front-end stage of this amplifier was implemented using discrete circuit elements and can measure input current in the range of 1 pA to 1 μA. The amplifier had a resolution of ~ 20 fA and the temperature drift of ~ 0.5 pA/°C. Various test results of the amplifier and sensor module assembly are given in this paper. The measured current profiles of cyclotron beam line at KIRAMS are also given.
18064237
The effect of kaon condensation on quark-antiquark condensate in dense matter
Abstract Assuming that at sufficiently high densities the constituent quarks become relevant degrees of freedom, we study within the framework of a chiral quark model the influence of s -wave K − condensation on the quark–antiquark condensates. We find that, in linear density approximation, the presence of a K − condensate quenches the u ¯ u condensate, but that the d ¯ d condensate remains unaffected up to the chiral order under consideration. We discuss the implication of the suppressed u ¯ u condensate for flavor-dependent chiral symmetry restoration in dense matter.
5924990
BARYON DENSITY AND THE DILATED CHIRAL QUARK MODEL
We calculate perturbatively the effect of density on hadronic properties using the chiral quark model implemented by the QCD trace anomaly to see the possibility of constructing a Lorentz-invariant Lagrangian at finite density. We calculate the density-dependent masses of the constituent quark, the scalar field, and the pion in one-loop order using the technique of thermofield dynamics. In the chiral limit, the pion remains massless at finite density. It is found that the tadpole-type corrections lead to decreasing masses with increasing baryon density, while the radiative corrections induce Lorentz-symmetry-breaking terms. We found in the large N{sub c} limit with large scalar mass that the tadpoles dominate and the mean-field approximation is reliable, giving rise to a Lorentz-invariant Lagrangian with masses decreasing as the baryon density increases. {copyright} {ital 1997} {ital The American Physical Society}
123462298
Overlap of shape resonance and Cooper-minimum structure in photoionization
Examples of a Cooper minimum inside the range of a shape-resonance maximum of a photoionization cross section have been found in numerical calculations within a single-electron model in a relativistic Hartree-Fock-Slater potential. In these model calculations for the photoionization of tin and uranium we find relatively broad shape resonances in all the $d$ and $f$ subshells. In addition a Cooper minimum occurs in the outer subshells of these high-angular-momentum states within the region of the shape-resonance maximum. We examine the matrix elements for these subshells and the resulting cross sections and angular distributions.