Showing papers in "Progress of Theoretical Physics in 1978"

Theory of Early Stage Spinodal Decomposition in Fluids near the Critical Point. II

Abstract: In Figs. 3, 4, 5 and 6 the experimental points and the dashed lines of LBM have been taken from Ref. 1). Recently Professor Goldburg and Dr. Schwartz communicated to us that in Ref. 1) an error of factor 2 in time scale occurred in plotting the LBM results corresponding to 2-r=!"LBM· This is also true in our work provided that L=L (or r=1), and the lines of LBM should be shifted to the left accordingly. On the other hand, if L~L" as in our case, we have 2r-r=rLBM and the factor 2r is 1 r=1/2 as in our work. Then this error dissappears. In our work we have regarded the LBM results to be applicable to the model in which L=L" (that is, the renormalization contribution to L comes from fluctuations with k>A=tr:) and long-range hydrodynamic interactions are absent. On the other hand, in drawing the LBM curve in Fig. 5 and the LBM curve with c=1/ v3 ( _,_) in Fig. 10 we have chosen r=L Thus, in order to be consistent with the above-mentioned interpretation of the LBM results, these curves ought to be moved appropriately to the right.

Gravity and Electromagnetism as Collective Phenomena of Fermion-Antifermion Pairs

Abstract: A generally covariant formulation is made for the previously proposed unified model of the Nambu-Jona-Lasinio type for gravity and electromagnetism. The gravitational and electro-magnetic fields are generated as collective excitations of fermion-antifermion pairs. The modl is shown to be effectively equivalent to the Einstein-Weyl theory of general relativity. The G-α relation, the relation between the fine structure constant and the Newtonian gravitational constant is re-derived.

CP Violation and Off-Diagonal Neutral Currents

Abstract: We discuss the CP violation based on the SU(2) ×U(1) ×SU_F(2) gauge model, where the new gauge bosons S_µ^i are introduced in association with the extra subgroup SU_F(2). The effective coupling constant G_S for the interaction mediated by the S_µ^i is found to be G_S/G_F > 5 ×10^-6. In this model the gauge bosons S_µ^i are coupled to off-diagonal neutral currents. The ratio R = [ Γ(K^± →π^± e µ) + Γ(K^± →π^± µe ] / Γ(K^- →π^0 µν_µ) is predicted to be R > 2 ×10^-9.

Indefinite-Metric Quantum Field Theory of General Relativity

Abstract: Quantum field theory of Einstein's general relativity is formulated in the indefinite­ metric Hilbert space in such a way that asymptotic fields are manifestly Lorentz covariant and the physical S-matrix is unitary. The general coordinate transformation is transcribed into a q-number transformation, called the BRS transformation. Its abstract definition is presented on the basis of the BRS transformation for the Yang-Mills theory. The BRS transformation for general relativity is then explicitly constructed. The gauge-fixing Lagrangian density and the Faddeev-Popov one are introduced in such a way that their sum behaves like a scalar density under the BRS transformation. One can then proceed in the same way as in the Kugo-Ojima formalism of the Yang-l\1ills theory to estnblish thL> unitarity of the physical S-matrix.

Orthogonality Catastrophe for a System of Interacting Electrons. III

Abstract: The Anderson orthogonality theorem is derived for a general non· separable local potential. It is shown that the overlap integral is given for this general case by exp [ - 2(2~i)' Tr(!nS(It»'log N], where S(It) is the scattering S·matrix at the Fermi energy. This form of the overlap integral is also shown to hold for interacting conduction electrons if local potential V in the final state is replaced by the self· energy difference ;E*(It) due to the local potential.

Giant Resonances--A Comparison between TDHF and Fluid Dynamics in Small Amplitude Vibrations of Spherical Nuclei

Abstract: Small amplitude vibrations of spherical nuclei are considered in microscopic (RPA) and fluid-dynamical description. Assuming the concentration of transition strength into one collective state, the microscopic result can be brought into close analogy to constrained fluid­ dynamical motion. The decisive difference occurs in the contribution of the microscopic kinetic energy to the collective potential energy. It is shown that extension of fluid dyna­ mics to include dynamical distortions of the local Fermi surface is sufficient to reproduce the microscopic results. Numerical examples are given for L=O and L=2 isoscalar modes for a Skyrme-type nucleon-nucleon force.

On a Superfield Theoretical Treatment of the Higgs-Kibble Mechanism

Abstract: The superfield theoretical aspect of the Riggs-Kibble mechanism is discussed by realiz­ ing the supersymmetry of Becchi, Rouet and Stora (BRS) as translation and dilatation operations on the real elements of the Grassmann algebra. The Slavnov-Taylor identity becomes a statement on each connected Green's function separately in this formulation, and some of the pathological cases discussed in the literature can be avoided by imposing the manifest BRS covariance in terms of the superfields. This is applied to the discussion of non-linear (quadratic) gauge conditions. The manifestly BRS covariant treatment of non­ linear gauge conditions requires a quartic self-coupling of Faddeev-Popov fields to ensure the multiplicative renormalization, although the physical S-matrix is independent of this ghost coupling. The proof of unitarity (i.e., the ghost cancellation) follows the same mechanism as the divergence cancellation in the ordinary superfield theory. The gauge independence is proved by a simple classification of operators according to their BRS trans­ formation properties. We also briefly comment on the canonical treatment of superfields. The renormalization of the Yang-Mills fieldsn and the Riggs-Kibble mecha­ nism2> has been extensively discussed in the literature.s>.•> The Faddeev-Popov Lagrangian 5> provides a starting point for these discussions of the renormalizability and unitarity. In connection with the Faddeev-Popov Lagrangian, Becchi, Rcuet and Stora (BRS) a> introduced a supersymmetry pseudo-algebra which gives rise to a very neat way to derive the Slavnov-Taylor identityn (i.e., the Ward-Takahashi identity associated with the BRS symmetry). It was also recognized that a detailed study of the BRS symmetry is sufficient to investigate the unitarity of the S-matrix elements. 8> Recently, Kugo and Ojima9> further clarified the contents of the BRS symmetry and the structure of the physical Hilbert space. They made the following important observations: (i) The auxiliary Lagrangian multiplier field makes the BRS symmetry manifest, and (ii) the ghost number of the Faddeev-Popov fields should be properly associated with the scale transformation of the ghost fields. Although the latter point is not crucial in the perturbative treatmeneo> of the Yang-Mills fields, the structure of the physical space is much simplified by this interpretation. It is also nicer to keep the Lagrangian manifestly Hermitian at all the stages of the calculation. In this paper, we discuss the superfield theoryll)~J•> associated with the BRS symmetry. Some of the initial attempts 15> toward this direction have been made,

Thomas-Fermi Theory for Atoms in a Strong Magnetic Field

Abstract: Along the general scheme of Sondheimer and Wilson, the kinetic energy density o£ an electron gas under constant magnetic field is expressed as a functional o£ the electron density at absolute zero of temperature. On this basis, the statistical theory for atoms in a magnetic field is formulated, which includes the theory developed by Banerjee et al. as an extreme of high magnetic field. Some numerical results on the atomic radius, the total energy etc. are also shown for free neutral Ne atom.