14420331
Harmonic Oscillators as Bridges between Theories: Einstein, Dirac, and Feynman
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of two-by-two matrices. If two oscillators are coupled, the problem combines both two-by-two matrices and harmonic oscillators. This method then becomes a powerful research tool to cover many different branches of physics. Indeed, the concept and methodology in one branch of physics can be translated into another through the common mathematical formalism. Coupled oscillators provide clear illustrative examples for some of the current issues in physics, including entanglement, decoherence, and Feynman's rest of the universe. In addition, it is noted that the present form of quantum mechanics is largely a physics of harmonic oscillators. Special relativity is the physics of the Lorentz group which can be represented by the group of by two-by-two matrices commonly called $SL(2,c)$. Thus the coupled harmonic oscillators can therefore play the role of combining quantum mechanics with special relativity. Both Paul A. M. Dirac and Richard P. Feynman were fond of harmonic oscillators, while they used different approaches to physical problems. Both were also keenly interested in making quantum mechanics compatible with special relativity. It is shown that the coupled harmonic oscillators can bridge these two different approaches to physics.
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.
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.
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.
119291756
Gluino Stransverse Mass
We introduce a new observable, ’gluino stransverse mass’, which is an application of the Cambridge mT2 variable to the process where gluinos are pair produced in proton-proton collision and each gluino subsequently decays into two quarks and one LSP, i.e. g̃g̃ → qqχ̃01 qqχ̃ 0 1. We show that the gluino stransverse mass can be utilized to measure the gluino mass and the lightest neutralino mass separately, and also the 1st and 2nd generation squark masses if squarks are lighter than gluino, thereby providing a good first look at the pattern of sparticle masses experimentally.
124194266
Operation of single GEM, GEM + MWPC, and GEM + MSGC detectors
122988282
A method of closed orbit correction under constraint conditions
We have developed the correction algorithm of the closed orbit distortion (COD) under the constraint condition where beam positions at particular points are not changed. The new algorithm is based on the modified PSINOM algorithm including the regularization process in order to avoid the inversion problem of the ill-posed response matrices. We have confirmed that the COD is well corrected with no orbit leak in the simulation and is in good agreement with the experiment.
9733106
Microlensing Detections of Planets in Binary Stellar Systems
We demonstrate that microlensing can be used for detecting planets in binary stellar systems. This is possible because in the geometry of planetary binary systems, in which the planet orbits one of the binary components and the other binary star is located at a large distance, both planet and secondary companion produce perturbations in a common region around the planet-hosting binary star, and thus the signatures of both planet and binary companion can be detected in the light curves of high-magnification lensing events. We find that identifying planets in binary systems is optimized when the secondary is located within a certain range that depends on the type of the planet. The proposed method can detect planets with masses down to one-tenth of the Jupiter mass in binaries with separations 100 AU. These ranges of planet masses and binary separations are not covered by other methods, and thus microlensing would be able to make the planetary binary sample richer.
1457184
The Vector and Axial-Vector Susceptibilities and Effective Degrees of Freedom in the Vector Manifestation
The question as to what the relevant degrees of freedom are at the thermal chiral phase transition is addressed in terms of the “vector manifestation (VM)” of chiral symmetry à la Harada and Yamawaki. We find that both the vector susceptibility χV and the axial-vector susceptibility χA at the chiral transition could receive contributions from other degrees of freedom than pions in the chiral limit. The possible candidates are zero-mass vector mesons and quasiquarks. In the presence of these degrees of freedom, hidden local symmetry (HLS) theory with vector manifestation predicts that χV equals χA in consistency with chiral invariance and that both the time component f t π and the space component f s π of the pion decay constant vanish at the chiral phase transition. With the VM, the pion velocity vπ proportional to f s π/f t π at T = Tc is predicted to be equal to 1. These results are obtained in the leading order in power counting but we expect them to hold more generally in the chiral limit thanks to the VM point. and Department of Physics and Astronomy, University of South Carolina, Columbia, SC 29208 and School of Physics, Korea Institute for Advanced Study, Seoul 130-012, Korea.