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THE THEORY OF QUANTIZED FIELDS. II

Description: The arguments leading to the formulation of the Action Principle for a general field are presented. In association with the complete reduction of all numerical matrices into symmetrical and anti-symmetrical parts, the general field is decomposed into two sets, which are identified with Bose-Einstein and Fermi-Dirac fields. The spin restriction on the two kinds of fields is inferred from the time reflection invariance requirement. The consistency of the theory is verified in terms of a criterion involving the various generators of infinitesimal transformations. Following a discussion of charged fields, the electromagnetic field is introduced to satisfy the postulate of general gauge invariance. As an aspect of the latter, it is recognized that the electromagnetic field and charged fields are not kinematically independent. After a discussion of the field-strength commutation relations, the independent dynamical variables of the electromagnetic field are exhibited in terms of a special gauge.
Date: January 1, 1951
Creator: Schwinger, J.
Partner: UNT Libraries Government Documents Department

THE THEORY OF QUANTIZED FIELDS. PART 3

Description: In this paper we discuss the electromagnetic field, as perturbed by a prescribed current. All quantities of physical interest in various situations, eigenvalues, eigenfunctions, and transition probabilities, are derived from a general transformation function which is expressed in a non-Hermitian representation. The problems treated are: the determination of the energy-momentum eigenvalues and eigenfunctions for the isolated electromagnetic field, and the energy eigenvalues and eigenfunctions for the field perturbed by a time-independent current; the evaluation of transition probabilities and photon number expectation values for a time-dependent current that departs from zero only within a finite time interval, and for a time-dependent current that assumes non-vanishing time-independent values initially and finally. The results are applied in a discussion of the infra-red catastrophe and of the adiabatic theorem. It is shown how the latter can be exploited to give a uniform formulation for all problems requiring the evaluation of transition probabilities or eigenvalue displacements.
Date: May 1, 1953
Creator: Schwinger, J.
Partner: UNT Libraries Government Documents Department

A PULSED EDDY CURRENT TECHNIQUE FOR MEASURING CLAD THICKNESS. Metallurgy Program 12.1.2

Description: A pulsed eddy current technique for measuring the cladding thicknesses of reactor fuel elements is described. Special emphasis has been put on the measurement of zirconium cladding. In this technique an electromagnetic field is applied at the surface of the clad fuel element by means of a probe coil. Whenever the waves enco nter a sudden discontinuity, such as an interface,''echoes'' are produced. The same probe coil is used for sending the electromagnetic radiation and receiving the echces. The echo received from the front surface of the specimen is balanced out by means of a bridge circuit. The echo from the clad core interface contains formation concerning the thickness of the clad. The echo has a positive peak followed by a small negative peak. The ''crossing point'' between the positive and negative peak or the amplitude of the echo can be used to determine clad thickness. One of the difficult problems with this technique is the extreme sensitivity to variations in probe-to-metal spacing. Methods for eliminating or minimizing this effect have been tried, with some success. (auth)
Date: May 1, 1955
Creator: Waidelich, D.L.; DeShong, J.A. & McGonnagle, W.J.
Partner: UNT Libraries Government Documents Department

FURTHER ASPECTS OF THE THEORY OF THE MASER. Special Technical Report on RESEARCH INVESTIGATION DIRECTED TOWARD EXTENDING THE USEFUL RANGE OF THE ELECTROMAGNETIC SPECTRUM

Description: The theory of the molecular transitions which are induced by the microwave field in a maser and the effects of various design parameters are examined in detail. It is shown that the theoretical minimum detectable beam intensity when the maser is used as a spectrometer for the 3-3 line of ammonia is about 10{sup 9} molecules/sec under typical experimental conditions. Various systematic frequency shifts and random fequency fluctuations of the maser oscillator are discussed and evaluated. The most prominent of the former are the"frequency-pulling" effect which arises from detuning of the cavity and the Doppler shift due to the asymmetrical coupling of the beam with the two travelling wave components of the standing waves which are set up in the cavity. These two effects may produce fractional shifts as large as one part in 10{sup 9}. If adequate precautions are taken, however, they can be reduced to one part in 10{sup 10} or possibly less. The random fluctuations are shown to be of the order of one part in 10{sup 13} under typical operating conditions. For molecular beams in which the electric-dipole transition is used the TM{sub 010} mode is usually the most suitable for the maser while in atomic beams in which magnetic transitions are utilized, the TE{sub 011} mode is to be preferred.
Date: March 1, 1956
Creator: Shimoda, K.; Wang, T.C. & Townes, C.H.
Partner: UNT Libraries Government Documents Department

BEVATRON OPERATION AND DEVELOPMENT. XVI. Period Covered November, December 1957, January 1958

Description: The study of interactions and decay of K mesons continued, using the 10- inch liquid hydrogen bubble chamber and emulsions. Four emulsion stacks were exposed for two internal groups and twenty-three stacks were exposed for seventeen groups from outside the Laboratory. Interactions of pi /sup -/ mesons were observed with a 30-inch propane bubble chamber and with emulsions. Ten emulsion stacks were exposed to neutral-particle beams and one stack to the internal 6.2-Bev proton beam. The 30-inch propane bubble chamber and emulsions were used to study the interactions of antiprotons. Eighteen target bombardments in the internal proton beam were made for the chemistry group. Successful tests were completed of two static-electromagnetic velocity spectrometers for the separation of highenergy particles. One was of coaxial construction, the other of parallel-plate construction. (For preceding period see UCRL-6114.) (auth)
Date: May 26, 1958
Creator: Hartsough, W.D. & Salsig, W.W.
Partner: UNT Libraries Government Documents Department

450-Mev/C K$sup -$ and /Anti p/ Beams at the Northwest Target Area of the Bevatron Separated by the Coaxial Velocity Spectrometer

Description: Enriched beams of 450 Mev/c K/sup -/ mesons and antiprotons have been produced by separation with the coaxial static electromagnetic velocity spectrometer. Characteristics of the final separated beams as observed in the 15- inch hydrogen bubble chamber are given together with a detailed description of the beam optics and apparatas. (auth)
Date: June 1, 1958
Creator: Horwitz, N.; Murray, J.J.; Ross, R.R. & Tripp, R.D.
Partner: UNT Libraries Government Documents Department

Alpha-Decay Studies in the Heavy-Element Region

Description: Using primarily a 75-cm radius of curvature 60 deg symmetrical electromagnetic analyzer, a study of the complexity of the following alpha spectra was made: Es/sup 253/, Cf/sup 246/, Cm/sup 244/, Am/sup 243/, Pu/sup 236,242/, Pa/sup 231/ , Th/sup 227,230/, Ac/sup 225/, At/sup 209/ and Po/sup 206/. An investigation of the gamma rays associated with the following isotopes was also madei /sup 236/, and Pa/sup 231/. Decay schemes have been suggested for most of the isotopes included in this study. Those for the even-even isotopes were found to conform well with the previously existing systematics for that group of nuclides. Many of the decay features of the odd-mass isotopes seemed to conform well with presently expanding theories. (auth)
Date: July 1, 1956
Creator: Hummel, J. P.
Partner: UNT Libraries Government Documents Department

Progress Report No. 50 for the Period June 1, 1957 Through August 31, 1957

Description: Progress is reported in fission elements chemistry, organic and inorganic nuclear chemistry, cosmic ray research, high-energy accelerator experimentation and physics, bubble chamber experimentation, and theoretical physics. Considerable attention was given to the ionization of mineral acids and hydrogen haloraetallates in inorganic solvents and to anion exchnnge behavior in metal complexes. Studies of various chemical reaction mechanisms were continued. The self-energy of a Dirac particle coupled through its charge with the electromagnetic field was investigated without perturbation theory. (For preceding period see AECU-3580.) (D.E.B.)
Date: August 31, 1957
Partner: UNT Libraries Government Documents Department