Weak neutral currents in atomic physics

Possible ways of detecting weak neutral currents in atomic physics through parity-violating effects in heavy atoms are analysed from a theoretical point of view.     

Weyl transformation in Fermi systems

In the path integral representation, the Hamiltonian in a quantum system is associated with the Hamiltonian in a classical system through the Weyl transformation. From this, it is possible to describe the time evolution in a quantum system by the Hamiltonian in a classical system. In a Bose system, the Weyl transformation is defined by the eigenstates of the canonical operators, since the Hamiltonian is given by a function of the canonical operators. On the other hand, in a Fermi system, the Hamiltonian is usually described by a function of the creation and annihilation operators, and hence the Weyl transformation is defined by the coherent states which are the eigenstate of an annihilation operator. Here, we formulate the Weyl transformation in Fermi systems in terms of the eigenstates of the canonical operators so as to clarify the correspondence between both systems. Using this, we can derive the path integral representation in Fermi systems.     

Weak neutral currents in elastic muon-nucleon scattering

Elastic polarized muon scattering is considered as an independent source of information on weak neutral currents involving muons. At low energies and high intensities cross section asymmetries are measurable which are sensitive to the right-handed weak muon charge, involve new combinations of coupling constants and depend remarkably on the details of weak nucleon form factors.     

Collective coordinates in Fermi systems

The problem of developing a consistent perturbation theory for a Fermi system in the case in which the unperturbed system exhibits dynamical symmetry breaking is discussed, by using collective coordinate methods. By adapting to this problem the methods used in the quantization of gauge theories, it is shown how to deal with composite zero-frequency excitations in such a way that the resulting perturbation theory is free of infrared divergencies. Explicit calculations are carried out in the case of a simple quantum mechanical model representing a superfluid Fermi system.     

Weak neutral currents in deep inelastic bremsstrahlung

We consider the role of weak neutral currents in the processesl ^± + Nl ^± + + X. In the quark-parton model, with regard to hadronic radiation as well as leptonic, we obtain the differential cross-section of the processes, and investigate various P-odd effects that allow us to distinguish the weak current contribution.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 25–29, December, 1987.     

Weak neutral currents and neutrino transport

Transport coefficients are evaluated for a mixture of neutrinos and complex nuclei with neutral current weak interaction as proposed by Freedman. The transport properties of this system are particularly relevant to the neutrino transport supernova model.     

Weak mesonic currents of second class

A weak current operator of second class which is constructed of mesons only been suggested by Lipkin. If this current is extended to full SU₃ it contributes a second class part to tthe axial vector form factor of ΣΛ decay. This is calculated, using a standard Feynman cut-off to circumvent the logarithmic divergence. Present experiments restrict the coupling of such a current to the leptonic current to about one order of magnitude below the weak four fermi coupling.     

Gamma radiation in non-Markovian Fermi systems

The gamma-quanta emission is considered within the framework of the non-Markovian kinetic theory. It is shown that the memory effects have a strong influence on the spectral distribution of gamma quanta in the case of long-time relaxation regime. It is shown that the gamma radiation can be used as a probe for both the time-reversible hindrance force and the dissipative friction caused by the memory integral.     

Weak neutral currents and neutrino electromagnetic properties

The phenomenological Hamiltonian for weak lepton interaction that contains, along with a charged current V-A interaction, a neutral current V-A interation and the dispersion method are used to study the effect of lepton and nucleon currents on the electromagnetic properties of the neutrino. Expressions are obtained for the neutrino formfactor F(q²) when it satisfies the dispersion relations without subtraction and with one subtraction.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 43–48, May, 1977.     

Interaction versus dimerization in one-dimensional Fermi systems

In order to study the effect of interaction and lattice distortion on quantum coherence in one-dimensional Fermi systems, we calculate the ground state energy and the phase sensitivity of a ring of interacting spinless fermions on a dimerized lattice. Our numerical DMRG studies, in which we keep up to 1000 states for systems of about 100 sites, are supplemented by analytical considerations using bosonization techniques. We find a delocalized phase for an attractive interaction, which differs from that obtained for random lattice distortions. The extension of this delocalized phase depends strongly on the dimerization induced modification of the interaction. Taking into account the harmonic lattice energy, we find a dimerized ground state for a repulsive interaction only. The dimerization is suppressed at half filling, when the correlation gap becomes large. Received: 11 February 1998 / Revised: 1st April 1998 / Accepted: 30 April 1998     

Weak nucleon currents in beta decay and muon capture

We made extensive investigations on the weak charged nucleon currents and structure of complex nuclei in weak nuclear processes. Using our new formalism, which has almost no approximation as far as the lepton part is concerned, we have studied the beta-ray spectra and beta-ray angular distributions in the¹²B and¹²N beta decays. The weak magnetism predicted by CVC is in excellent agreement with the experimental data on beta-ray spectra given by the Columbia and Heidelberg groups. It is noticed here that the difference _– – ₊ of the coefficients in the beta-ray angular distributions in aligned¹²B and¹²N is free from ambiguity of the nuclear model. We found practically no second-class induced tensor current with the data given by the Osaka, Louvain and Zürich groups. On the other hand, the sum _– + ₊ of the coefficients represents the time component of the main axial vector current, and it is free from weak form factors. With this sum we studied the exchange-current and core-polarization effects. These two effects are large, and they are almost cancelled out by each other in this case. We also found the strength of the induced pseudoscalar form factor which is generally consistent with PCAC, from nuclear polarizations of¹²B in muon capture of¹²C performed by the Zürich and Tokyo groups. These nuclear polarizations are insensitive to the nuclear model, if the exchange-current and corepolarization effects are properly taken into account.This paper was partially delivered at the Annual Meeting of the Korean Physical Society, Seoul, 1983; the Asia Pacific Physics Conference, Singapore, 1983; and the International Symposium on Nuclear Spectroscopy and Nuclear Interactions, Osaka, 1984.The present paper is based on our recent theoretical investigations, which have been performed by the theory group, Department of Physics, Osaka Unicersity. The author would like to express his sincere thanks to Professors H. Ohtsubo, Y. Yokoo, Drs. T. Sato, K. Koshigiri, M. Nishimura, M. Kobayashi, and Mr. M. Fukui for their collaboration, to Professors C.W. Kim, Y.K. Lee and K. Kubodera for their stimulating discussions during his 1983 summer visit to Johns Hopkins University, to Professors K. Sugimoto, T. Minamisono, V.L. Telegdi, L. Grenacs, T. Yamazaki and K. Nagamine for sending him their experimental results before publication. Numerical calculations were performed with the aid of NEAC ACOS 1000, Computor Center, Osaka University. This work is partly supported by Grant-in-Aid for Scientific Research, The Ministry of Education, Science, and Culture.This paper is dedicated to Professor K. Sugimoto in commemoration of his sixtieth birthday.     

Collective modes in asymmetric ultracold Fermi systems

We derive the long wavelength effective action for the collective modes in systems of fermions interacting via a short-range s-wave attraction, featuring unequal chemical potentials for the two fermionic species (asymmetric systems). As a consequence of the attractive interaction, fermions form a condensate that spontaneously breaks the U(1) symmetry associated with total number conservation. Therefore at sufficiently small temperatures and asymmetries, the system is a superfluid. We reproduce previous results for the stability conditions of the system as a function of the four-fermion coupling and asymmetry. We obtain these results analyzing the coefficients of the low energy effective Lagrangian of the modes describing fluctuations in the magnitude (Higgs mode) and in the phase (Nambu-Goldstone, or Anderson-Bogoliubov, mode) of the difermion condensate. We find that for certain values of parameters, the mass of the Higgs mode decreases with increasing mismatch between the chemical potentials of the two populations, if we keep the scattering length and the gap parameter constant. Furthermore, we find that the energy cost for creating a position dependent fluctuation of the condensate is constant in the gapped region and increases in the gapless region. These two features may lead to experimentally detectable effects. As an example, we argue that if the superfluid is put in rotation, the square of the radius of the outer core of a vortex should sharply increase on increasing the asymmetry, when we pass through the relevant region in the gapless superfluid phase. Finally, by gauging the global U(1) symmetry, we relate the coefficients of the effective Lagrangian of the Nambu-Goldstone mode with the screening masses of the gauge field.     

Fermi surface reconstruction in strongly correlated Fermi systems as a first-order phase transition

A quantum phase transition in strongly correlated Fermi systems beyond the topological quantum critical point has been studied using the Fermi liquid approach. The transition takes place between topologically equivalent states with three Fermi surface sheets, but one of them is characterized by a quasiparticle halo in the quasiparticle momentum distribution n(p), and the other one is characterized by a hole pocket. It has been found that the transition between these states is a first-order phase transition for the interaction constant g and temperature T. The phase diagram in the vicinity of this transition has been constructed.     

Low-temperature collapse of the Fermi surface and phase transitions in correlated Fermi systems

A topological crossover, associated with the collapse of the Fermi surface in strongly correlated Fermi systems, is examined. It is demonstrated that in these systems, the temperature domain where standard Ferrai liquid results hold dramatically narrows, because the Landau regime is replaced by a classical one. The impact of the collapse of the Fermi surface on pairing correlations is analyzed. In the domain of the Lifshitz phase diagram where the Fermi surface collapses, splitting of the BCS superconducting phase transition into two different ones of the same symmetry is shown to occur.     

Weyl-Wigner-Moyal formalism for Fermi classical systems

The Weyl-Wigner-Moyal formalism of fermionic classical systems with a finite number of degrees of freedom is considered. The Weyl correspondence is studied by computing the relevant Stratonovich-Weyl quantizer. The Moyal -product, Wigner functions and normal ordering are obtained for generic fermionic systems. Finally, this formalism is used to perform the deformation quantization of the Fermi oscillator and the supersymmetric quantum mechanics.     

Fermi systems with strong forward scattering

We review the theory of interacting Fermi systems whose low-energy physics is dominated by forward scattering, that is scattering processes generated by effective interactions with small momentum transfers. These systems include Fermi liquids as well as several important non-Fermi-liquid phases: one-dimensional Luttinger liquids, systems with long-range interactions, and fermions coupled to a gauge field. We report results for the critical dimensions separating different 'universality classes' and discuss the behaviour of physical quantities such as the momentum distribution function, the single-particle propagator and low-energy response functions in each class. The renormalization group for Fermi systems will be reviewed and applied as a link between microscopic models and effective lowenergy theories. Particular attention is paid to conservation laws, which constrain any effective low-energy theory of interacting Fermi systems. In scattering processes with small momentum transfers the velocity of each scattering particle is (almost) conserved. This asymptotic conservation law leads to non-trivial cancellations of Feynman diagrams and other simplifications, making thus possible a non-perturbative treatment of forward scattering via Ward identities or bosonization techniques.     

Surface properties of semi-infinite Fermi systems

A functional relation between the kinetic-energy density and the total density is used to analyze the surface properties of semi-infinite Fermi systems. We find an explicit expression for the surface thickness in which the role of the infinite matter compressibility, binding energy and non-locality effects is clearly shown. The method, which holds both for nuclear and electronic systems (liquid metals), yields a very simple relation between the surface thickness and the surface energy.     

The physical states of Fermi systems

A classification of all translationally invariant states over the algebra of anticommutation relations which satisfy criteria of finite mean density, finite mean kinetic energy, and finite mean entropy is given. It is demonstrated that these concepts can be discussed in terms of affine, semi-continuous, functionals which respect the barycentric decompositions of invariant states. Many other pertinent results, both local and global, are derived.