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.
120854919
Covariant harmonic oscillators and the parton picture
It is shown that the covariant-harmonic-oscillator wave function exhibits the peculiarities of the Feynman parton picture in the infinite-momentum frame.
122981620
Illustrative examples of the symplectic group
Simple illustrative examples are given for understanding the symplectic group. Transformation properties of the Sp(2) group are discussed in terms of the two‐dimensional geometry of circles and ellipses, two‐by‐two matrices, and in terms of a group‐theoretical language similar to that of the Pauli spin matrices. The isomorphism between the Sp(2) and SO(2,1) groups is discussed in detail. It is noted that this isomorphism is similar to that between the SU(2) and rotation groups. Simple illustrative physcial examples are given also for using the symplectic group in nuclear physics, statistical mechanics, and in high‐energy physics.
118455922
Quarks and Partons as Two Different Manifestations of One Covariant Entity
Unlike classical physics, modern physics depends heavily on observer’s state of mind or environment. Quantum mechanics depends on how we measure physical quantities, and this issue has not yet been completely settled. In relativity, observers in different Lorentz frames see the same physical system differently. The importance of the observer’s subjective viewpoint was emphasized by Immanuel Kant in his book entitled Kritik der reinen Vernunft whose first and second editions were published in 1781 and 1787 respectively. However, using his own logic, he ended up with a conclusion that there must be an absolute inertial frame, and that we only see the frames dictated by our subjectivity.
117540013
Theory and applications of the Poincaré group
I: Elements of Group Theory.- 1. Definition of a Group.- 2. Subgroups, Cosets, and Invariant Subgroups.- 3. Equivalence Classes, Orbits, and Little Groups.- 4. Representations and Representation Spaces.- 5. Properties of Matrices.- 6. Schur's Lemma.- 7. Exercises and Problems.- II: Lie Groups and Lie Algebras.- 1. Basic Concepts of Lie Groups.- 2. Basic Theorems Concerning Lie Groups.- 3. Properties of Lie Algebras.- 4. Properties of Lie Groups.- 5. Further Theorems of Lie Groups.- 6. Exercises and Problems.- III: Theory of the Poincare Group.- 1. Group of Lorentz Transformations.- 2. Orbits and Little Groups of the Proper Lorentz Group.- 3. Representations of the Poincare Group.- 4. Lorentz Transformations of Wave Functions.- 5. Lorentz Transformations of Free Fields.- 6. Discrete Symmetry Operations.- 7. Exercises and Problems.- IV: Theory of Spinors.- 1. SL(2, c) as the Covering Group of the Lorentz Group.- 2. Subgroups of SL(2, c).- 3. SU (2).- 4. 5L(2, c) Spinors and Four-Vectors.- 5. Symmetries of the Dirac Equation.- 6. Exercises and Problems.- V: Covariant Harmonic Oscillator Formalism.- 1. Covariant Harmonic Oscillator Differential Equations.- 2. Normalizable Solutions of the Relativistic Oscillator Equation.- 3. Irreducible Unitary Representations of the Poincare Group.- 4. Transformation Properties of Harmonic Oscillator Wave Functions.- 5. Harmonic Oscillators in the Four-Dimensional Euclidean Space.- 6. Moving O(4) Coordinate System.- 7. Exercises and Problems.- VI: Dirac's Form of Relativistic Quantum Mechanics.- 1. C-Number Time-Energy Uncertainty Relation.- 2. Dirac's Form of Relativistic Theory of "Atom ".- 3. Dirac's Light-Cone Coordinate System.- 4. Harmonic Oscillators in the Light-Cone Coordinate System.- 5. Lorentz-Invariant Uncertainty Relations.- 6. Exercises and Problems.- VII: Massless Particles.- 1. What is the E(2) Group?.- 2. E(2)-like Little Group for Photons.- 3. Transformation Properties of Photon Polarization Vectors.- 4. Unitary Transformation of Photon Polarization Vectors.- 5. Massless Particles with Spin 1/2.- 6. Harmonic Oscillator Wave Functions for Massless Composite Particles.- 7. Exercises and Problems.- VIII: Group Contractions.- 1. SE(2) Group as a Contraction of SO(3).- 2. E(2)-like Little Group as an Infinite-momentum/zero-mass Limit of the O(3)-like Little Group for Massive Particles.- 3. Large-momentum/zero-mass Limit of the Dirac Equation.- 4. Finite-dimensional Non-unitary Representations of the SE(2) Group.- 5. Polarization Vectors for Massless Particles with Integer Spin.- 6. Lorentz and Galilei Transformations.- 7. Group Contractions and Unitary Representations of SE(2).- 8. Exercises and Problems.- IX: SO(2, 1) and SU(1, 1).- 1. Geometry of SL(2, r) and Sp(2).- 2. Finite-dimensional Representations of SO(2, 1).- 3. Complex Angular Momentum.- 4. Unitary Representations of SU(1, 1).- 5. Exercises and Problems.- X: Homogeneous Lorentz Group.- 1. Statement of the Problem.- 2. Finite-dimensional Representations of the Homogeneous Lorentz Group.- 3. Transformation Properties of Electric and Magnetic Fields.- 4. Pseudo-unitary Representations for Dirac Spinors.- 5. Harmonic Oscillator Wave Functions in the Lorentz Coordinate System.- 6. Further Properties of the Homogeneous Lorentz Group.- 7. Concluding Remarks.- XI: Hadronic Mass Spectra.- 1. Quark Model.- 2. Three-particle Symmetry Classifications According to the Method of Dirac.- 3. Construction of Symmetrized Wave Functions.- 4. Symmetrized Products of Symmetrized Wave Functions.- 5. Spin Wave Functions for the Three-Quark System.- 6. Three-quark Unitary Spin and SU(6) Wave Functions.- 7. Three-body Spatial Wave Functions.- 8. Totally Symmetric Baryonic Wave Functions.- 9. Baryonic Mass Spectra.- 10. Mesons.- 11. Exercises and Problems.- XII: Lorentz-Dirac Deformation in High-Energy Physics.- 1. Lorentz-Dirac Deformation of Hadronic Wave Functions.- 2. Form Factors of Nucleons.- 3. Calculation of the Form Factors.- 4. Scaling Phenomenon and the Parton Picture.- 5. Covariant Harmonic Oscillators and the Parton Picture.- 6. Calculation of the Parton Distribution Function for the Proton.- 7. Jet Phenomenon.- 8. Exercises and Problems.- References.
120733750
Dirac’s form of relativistic quantum mechanics
It is shown that Dirac’s ’’instant form’’ dynamics provides a theoretical framework in which models of relativistic quantum mechanics can be constructed. The convariant harmonic oscillator formalism discussed in previous papers is shown to be such a model. Dirac’s ’’point’’ and ’’front’’ forms are shown to generate a space‐time geometry convenient for describing Lorentz deformation properties of relativistic extended hadrons.
43997367
New generation digital longitudinal feedback system for Duke FEL and HIγS facilities
To cure harmful longitudinal coupled-bunch mode beam instabilities during high-current and multi-bunch beam operations at the Duke free electron laser (FEL) and high intensity gamma-ray source (HIgammaS) facilities, we have been developing a new generation digital bunch-by-bunch longitudinal feedback (LFB) system which is based on an Integrated gigasample processor (iGp-64F). In this paper, we describe the new generation digital longitudinal feedback system for the Duke FEL and HIgammaS facilities.
120264896
Status of the Pohang light source project
Abstract The Pohang Light Source is a third-generation synchrotron radiation facility currently under construction in Pohang, Korea. It consists of a 2 GeV full energy injection linac, a storage ring, and three initial beamlines. Construction of the conventional facility is now nearly completed and the machine integration of the linac and the storage ring is well under way. The commissioning is scheduled to take place toward the fall of 1994, and it will be opened to national as well as international users by mid-1995. The facility will eventually furnish high-brightness sources of radiation utilizing 22 bending magnets and 10 insertion devices. Characteristics of the design and beamlines under construction will be described.
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.
14653529
Vector susceptibility and chiral phase transition in AdS/QCD Models
We calculated the vector susceptibilitiy in holographic QCD models to study QCD chiral/deconfinemnt phase transition. We found that the vector susceptibility obtained in this work agrees with the results from various model calculations and lattice QCD. Just above Tc χV from QCD calculations [12, 17, 18] saturate to the value of the free-quark gas faster than what we obtain in this work. We also discuss the chiral phase transitions in AdS/QCD models.
16257249
The fast tracker architecture for the LHC baseline luminosity
A. Annovi,a M. Beretta,a, E. Bossini,b A. Boveia,c E. Brubaker,c F. Canelli,c V. Cavasinni,b F. Crescioli,b H. DeBerg,d M. Dell’Orso,b M. Dunford,c M. Franklin,e P. Giannetti,b A. Kapliy,c Y. K. Kim,c P. Laurelli,a A. McCarn,d C. Melachrinos,c C. Mills,e M. Neubauer,d J. Proudfoot, f , M. Piendibene,b G. Punzi,b F. Sarri,b L. Sartori,bh M. Shochet,c L. Tripiccione,i J. Tuggle,c I. Vivarelli,b G. Volpi∗,b K. Yorita,c J. Zhang. f aINFN Frascati, bUniv. and INFN of Pisa, cUniv. of Chicago, dUniv. of Illinois at Urbana-Champain, eHarvard Univ, f Argonne National Lab, hMarie Curie Fellowship, iUniv. and INFN Ferrara