14578311
Dirac Matrices and Feynman's Rest of the Universe
There are two sets of four-by-four matrices introduced by Dirac. The first set consists of fifteen Majorana matrices derivable from his four $\gamma$ matrices. These fifteen matrices can also serve as the generators of the group $SL(4,r)$. The second set consists of ten generators of the $Sp(4)$ group which Dirac derived from two coupled harmonic oscillators. It is shown possible to extend the symmetry of $Sp(4)$ to that of $SL(4,r)$ if the area of the phase space of one of the oscillators is allowed to become smaller without a lower limit. While there are no restrictions on the size of phase space in classical mechanics, Feynman's rest of the universe makes this $Sp(4)$-to-$SL(4,r)$ transition possible. The ten generators are for the world where quantum mechanics is valid. The remaining five generators belong to the rest of the universe. It is noted that the groups $SL(4,r)$ and $Sp(4)$ are locally isomorphic to the Lorentz groups O(3,3) and O(3,2) respectively. This allows us to interpret Feynman's rest of the universe in terms of space-time symmetry.
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.
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.
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.
5119942
Measuring superparticle masses at hadron collider using the transverse mass kink
We present a detailed study of the collider observable mT2 applied for pair-produced superparticles decaying to visible particles and a pair of invisible lightest supersymmetric particles (LSPs). Analytic expressions of the maximum of mT2 over all events (mT2max) are derived. It is noticed that if the decay product of each superparticle involves more than one visible particle, mT2max being a function of the trial LSP mass mχ has a kink structure at mχ = true LSP mass, which can be used to determine the mother superparticle mass and the LSP mass simultaneously. To see how well mT2max can be constructed from collider data, a Monte-Carlo analysis of the gluino mT2 is performed for some superparticle spectra.
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}
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.
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.