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Field of a particle in uniform motion and uniform acceleration
474
ABSTBACTS
OF
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TO
APPEAR
IN
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the validity of approximate calculations and to indicate what must, be done to improve t.he result,s. The response function is calculated for :I Fermi gas by using a combined diagrammatic perturhation theory and (ireen’s function technique. Expressing the response function in terms of the irreducible particle-hole propagator, it, is shown that a many fermion system w-ith repulsive interactions between particles can be expected to respond strongly at cert,ain frequencies at least for disturbances of very small wave number. This enhanced response can he associated lvith t,he excitation of a plaarnon or second sound. It is also shown that the approximations usually made in treat.ing the elect.ron gas lead to a response function which violates a priori conditions. The corrections needed t,o rcmcdy this defect are indicat,ed. Chid
SyV/U/MtrieS.
s.
COLEMAN
AriD
H. L.
C;LASIIOW.
A systematic study of chiral symmetries (symmet.ries involving yh) is presented. Two important varieties of chiral symmetry are examined in det,ail~bound chiral symmetry and free chiral symmetry. All the possible free chiral symmetries are constructed, rind representative examples of bound chiral symmetries are discussed. Recently proposed theories of Gell-Mann and of Gtirsey are treated as special cases.
THEIMER .4x11 R. GENTRY. A new method for calculating the partition funct,ion of real gases is dcvelopcd and applied to a system of point charges without repulsive core, e.g., a fully ionized hydrogen gas. The electrostatic energy (7 of the t,ot,al system is represented as a function of t,he Fourier coefiGents, d, , of the particle density, and the contigurat.ion integral is evaluated by direct int,egration in the function space which is generated by t,he -4, To this purpose, the 11, are treated as stochastic variab!es charact,erized by a mult,iv:triate probability density whose determination represents a major part of this paper. The potential of mean force, W(r) is found equal to the average IIebye~Hiickel potential, (Z2e2/rj esp (- r/h), (Ze = ionic charge, h = lIebye shielding length The radial distribution function q(r) is determined as q(r) = exp-W’(r)/&], and the part of cJ which is proportional to the total particle number K is found to he equal to the IIebye~Hiickel energy. 0.
It is shown that the usual formulas for diffusion of charged an external magnetic field can be derived as a Brownian motion the fluctuating electric fields of the plasma.
particles across ant1 along of particles arising from
On thr
Theory oj’ Nwleur Reactions. 11. LIPPERHEIUE. A system of equations for the description of nuclear reactions is derived in which rigorous account is taken of the effects of the recoil of t,he target nucleus, the presence of hard cores in the txo-body int,eractions, and the Pauli exclusion principle. The elastic and inelastic scattering processes are described in terms of “equivalent potentials.” The relat,ion bet,ween the equivalent potential in the elastic channel and t,he opt,ical model potential is estab lished. A self-consistent scheme for the approximate calculat.ion of t,he phenomenological optical model pot,ential is proposed. Field of a l’urticle in TTnij”orm Motion and Ikijorm Llcceleration. EATHAN ROSEN. The line element in the neighborhood of a charged particle, according to general reht,ivit,v theory, is put into the isotropic form. By means of a Lorent,z transformation the gravitational and electromagnetic fields of a particle in uniform motion are obtained. By transforming to a uniformly accelerat,ed syst,em one obtains the fields of a particle accelerated in a uniform gravitational field. From the form of the solution it can be concluded that a charged particle in a uniform gravitational field does not radiate.
ABSTBACTS
OF
PAPEHS
TO
APPEAR
IN
FUTURE
ISSUES
the validity of approximate calculations and to indicate what must, be done to improve t.he result,s. The response function is calculated for :I Fermi gas by using a combined diagrammatic perturhation theory and (ireen’s function technique. Expressing the response function in terms of the irreducible particle-hole propagator, it, is shown that a many fermion system w-ith repulsive interactions between particles can be expected to respond strongly at cert,ain frequencies at least for disturbances of very small wave number. This enhanced response can he associated lvith t,he excitation of a plaarnon or second sound. It is also shown that the approximations usually made in treat.ing the elect.ron gas lead to a response function which violates a priori conditions. The corrections needed t,o rcmcdy this defect are indicat,ed. Chid
SyV/U/MtrieS.
s.
COLEMAN
AriD
H. L.
C;LASIIOW.
A systematic study of chiral symmetries (symmet.ries involving yh) is presented. Two important varieties of chiral symmetry are examined in det,ail~bound chiral symmetry and free chiral symmetry. All the possible free chiral symmetries are constructed, rind representative examples of bound chiral symmetries are discussed. Recently proposed theories of Gell-Mann and of Gtirsey are treated as special cases.
THEIMER .4x11 R. GENTRY. A new method for calculating the partition funct,ion of real gases is dcvelopcd and applied to a system of point charges without repulsive core, e.g., a fully ionized hydrogen gas. The electrostatic energy (7 of the t,ot,al system is represented as a function of t,he Fourier coefiGents, d, , of the particle density, and the contigurat.ion integral is evaluated by direct int,egration in the function space which is generated by t,he -4, To this purpose, the 11, are treated as stochastic variab!es charact,erized by a mult,iv:triate probability density whose determination represents a major part of this paper. The potential of mean force, W(r) is found equal to the average IIebye~Hiickel potential, (Z2e2/rj esp (- r/h), (Ze = ionic charge, h = lIebye shielding length The radial distribution function q(r) is determined as q(r) = exp-W’(r)/&], and the part of cJ which is proportional to the total particle number K is found to he equal to the IIebye~Hiickel energy. 0.
It is shown that the usual formulas for diffusion of charged an external magnetic field can be derived as a Brownian motion the fluctuating electric fields of the plasma.
particles across ant1 along of particles arising from
On thr
Theory oj’ Nwleur Reactions. 11. LIPPERHEIUE. A system of equations for the description of nuclear reactions is derived in which rigorous account is taken of the effects of the recoil of t,he target nucleus, the presence of hard cores in the txo-body int,eractions, and the Pauli exclusion principle. The elastic and inelastic scattering processes are described in terms of “equivalent potentials.” The relat,ion bet,ween the equivalent potential in the elastic channel and t,he opt,ical model potential is estab lished. A self-consistent scheme for the approximate calculat.ion of t,he phenomenological optical model pot,ential is proposed. Field of a l’urticle in TTnij”orm Motion and Ikijorm Llcceleration. EATHAN ROSEN. The line element in the neighborhood of a charged particle, according to general reht,ivit,v theory, is put into the isotropic form. By means of a Lorent,z transformation the gravitational and electromagnetic fields of a particle in uniform motion are obtained. By transforming to a uniformly accelerat,ed syst,em one obtains the fields of a particle accelerated in a uniform gravitational field. From the form of the solution it can be concluded that a charged particle in a uniform gravitational field does not radiate.