117221789
Lorentz group in Feynman's world
R. P. Feynman was quite fond of inventing new physics. It is shown that some of his physical ideas can be supported by the mathematical instruments available from the Lorentz group. As a consequence, it is possible to construct a Lorentz-covariant picture of the parton model. It is shown first how the Lorentz group can be used for studying the internal space-time symmetries of relativistic particles. These symmetries are dictated by Wigner's little groups, whose transformations leave the energy-momentum four-vector of a given particle invariant. The symmetry of massive particles is like the three-dimensional rotation group, while the symmetry of massless particles is locally isomorphic to the two-dimensional Euclidean group. It is noted that the E(2)-like symmetry of massless particles can be obtained as an infinite-momentum and/or zero-mass limit of the O(3)-like little group for massive particles. It is shown that the formalism can be extended to cover relativistic particles with space-time extensions, such as heavy ions and hadrons in the quark model. It is possible to construct representations of the little group using harmonic oscillators, which Feynman et al. used for studying relativistic extended hadrons. This oscillator formalism allows us to show that Feynman's parton model is a Lorentz-boosted quark model. The formalism also allows us to explain in detail Feynman's rest of the universe which is contained in his parton picture.
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.
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.
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,...
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.
32058981
Development of FTK Architecture: A Fast Hardware Track Trigger for the ATLAS Detector
The Fast Tracker (FTK) is a proposed upgrade to the ATLAS trigger system that will operate at full Level-1 output rates and provide high quality tracks reconstructed over the entire detector by the start of processing in Level-2. FTK solves the combinatorial challenge inherent to tracking by exploiting the massive parallelism of Associative Memories (AM) that can compare inner detector hits to millions of pre-calculated patterns simultaneously. The tracking problem within matched patterns is further simplified by using pre-computed linearized fitting constants and leveraging fast DSP's in modern commercial FPGA's. Overall, FTK is able to compute the helix parameters for all tracks in an event and apply quality cuts in approximately one millisecond. By employing a pipelined architecture, FTK is able to continuously operate at Level-1 rates without deadtime. The system design is defined and studied using ATLAS full simulation. Reconstruction quality is evaluated for single muon events with zero pileup, as well as WH events at the LHC design luminosity. FTK results are compared with the tracking capability of an offline algorithm.
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.
117312086
Search for fast particles produced at large lab angles at NAL
An experiment is proposed to look for charged particles emitted at large lab angles that are normally forbidden kinematically. These particles if found would correspond to hitherto unobserved events such as the production of particles with imaginary mass values (''tachyons''). Also, they wish to look for fractionally-charged particles produced at these angles. These particles, if found, would correspond to strongly-bound quark-quark states formed in a dissociation of the target nucleon. The detection system will consist of wire-chambers, dE/dx and time-of-flight counters. The basic hardware is under construction and the final system will be ready for test runs at a lower-energy machine in six months. The detection telescope will view interactions of the primary proton beam from backward (in lab) directions and the first choice experimental site is the straight section B with a thin internal target. They would like to use the highest available beam at NAL and since the beam transport and intensity requirements are very minimal, they will be able to run parasitically during the tuning periods of the NAL machine in the next year. The machine time required for this experiment is about three months.
55335409
New design and development of 13 MeV PET cyclotron in Korea
Since 1997 design studies have been in progress in a joint collaboration between the Korea Cancer Center Hospital (KCCH) and the Pohang University of Science and Technology (POSTECH) for a 13 MeV PET (Positron Emission Tomography) cyclotron. It will accelerate H/sup -/ (negatively charged hydrogen) ions, which, after acceleration, will be stripped of its electrons by a stripping foil and then, on entering the target chamber, interact with the target material to produce positron emitters such as /sup 18/F, /sup 15/O, /sup 13/N and /sup 11/C. In this paper we describe the main features of the cyclotron.