Derivation of transport equations for anharmonic lattices

Non-equilibrium properties of dielectric crystals are described using a Green function approach which represents transport phenomena by correlation functions of the equilibrium system. The equation which is equivalent to a Boltzmann equation for phonons is the integral equation for the vertex part corrections. Including all irreducible diagrams quadratic in the cubic and linear in the quartic anharmonicities the vertex part equation is reduced to a form which could be used as a starting point for numerical studies of microscopic models. The vertex part is also used to express the space and time variation of the phonon density and the frequency change of the phonons in response to an external displacement field. We also relate the integral equation for the vertex part to a form of the transport equation which is used in Landau's theory of quantum liquids.     

QCD sum rules and pion wave functions

We consider light cone sum rules for a vertex function involving a pion state. These incorporate radiative corrections, continuum effects and power corrections; the latter depend on the non-asymptotic form of a higher twist component of the pion wave function. We derive restrictions on this component from sum rules for two-point functions and propose a model wave function for it. Finally we analyse our vertex sum rules in the light of this information and find results for the lowest twist component in good agreement with those already obtained from two-point function sum rules with derivative currents.     

Nuclear partition functions in the random phase approximation and the temperature dependence of collective states

Green functions techniques at finite temperature are used to calculate nuclear partition functions in the random phase approximation. The theory is shown to yield corrections to the results of functional methods neglecting exchange terms. We discuss the special case of a schematic model for which the level density and the temperature dependence of collective states can be worked out explicitly.     

Spurious Effects in Perturbative Calculations

We show spurious effects in perturbativecalculations due to different orderings of inhomogeneousterms while computing corrections to Green functions fortwo different metrics. These effects are not carried over to physically measurable quantities likethe renormalized value of the vacuum expectation valueof the stress-energy tensor.     

Effective integral equation and vertex operator of the green function

A simple and rigorous formulation of effective integral equations for the Green functions is presented and a general formula for the effective vertex operator (or function) has been derived. As an illustration, this formalism has been applied to obtain (i) the effective Dyson equation and effective mass operator for the single-particle Green function, and (ii) the effective integral equation and effective interaction operator for the two-particle Green function as well as those for the particle-hole Green function.     

Ultraviolet asymptotics of the Green and vertex functions in supergauge invariant field theory

Ultraviolet asymptotics of the Green and vertex functions in supergauge invariant field theory for the SU(N) group is established. Renormalization of the gauge field coupling constant is calculated and the condition for asymtotic freedom is found.     

Vertex functions for the three-particle interaction of the Higgs bosons <Emphasis Type="Italic">h</Emphasis><Superscript>0</Superscript> and <Emphasis Type="Italic">H</Emphasis><Superscript>0</Superscript> in the minimal supersymmetric standard model: One-loop analysis

Within the minimal supersymmetric standard model, two vertex functions for the three-particle interaction of the neutral Higgs bosons h⁰ and H⁰ are analyzed in the one-loop approximation with allowance for a complete set of one-loop diagrams. The analysis is performed in the c.m. frame under the assumption that one of the Higgs bosons is virtual. The results obtained in this way are compared with those that involve only leading corrections in the low-energy approximation. The vertex functions in question are presented graphically versus the mixing angle β and the energy \(\sqrt s\). It is shown that corrections to these vertex functions may be significant in some domain of the model-parameter space, so that they must be taken into account in performing a detailed analysis of experimental data and theoretical predictions. The possibility of experimentally observing the dependences under study is explored.     

Semiclassical and quantum Liouville theory on the sphere

We solve the Riemann–Hilbert problem on the sphere topology for three singularities of finite strength and a fourth one infinitesimal, by determining perturbatively the Poincaré accessory parameters. In this way we compute the semiclassical four point vertex function with three finite charges and a fourth infinitesimal. Some of the results are extended to the case of n finite charges and m infinitesimal. With the same technique we compute the exact Green function on the sphere with three finite singularities. Turning to the full quantum problem we address the calculation of the quantum determinant on the background of three finite charges and the further perturbative corrections. The zeta function technique provides a theory which is not invariant under local conformal transformations. Instead by employing a regularization suggested in the case of the pseudosphere by Zamolodchikov and Zamolodchikov we obtain the correct quantum conformal dimensions from the one loop calculation and we show explicitly that the two loop corrections do not change such dimensions. We expect such a result to hold to all order perturbation theory.     

Antiparticle Contribution in the Cross Ladder Diagram for Bethe-Salpeter Equation in the Light-Front

We construct the homogeneous integral equation for the vertex of the bound state in the light front with the kernel approximated to order g ⁴. We will truncate the hierarchical equations from Green functions to construct dynamical equations for the two boson bound state exchanging interacting intermediate σ bosons and including pair creation process contributing to the crossed ladder diagram.     

Nonfactorizable B→xcoK Decay and QCD Factorization

We study the unexpectedly large rate for the factorization-forbidden decay B→χ_c0K within the QCD factorization approach. We use a non-zero gluon mass to regularize the infrared divergences in vertex corrections. The end-point singularities arising from spectator corrections are regularized and carefully estimated by the off-shellness of quarks. We find that the contributions arising from the vertex and leading-twist spectator corrections are numerically small, and the twist-3 spectator contribution with chiral enhancement and linear end-point singularity becomes dominant. With reasonable choices for the parameters, the branching ratio for B→χ_c0K decay is estimated to be in the range (2～4)×10^-4, which is compatible with the Belle and BaBar data.     

引力子三顶点与引力自能的曲率激发

基于微扰展开,计算了联络场三点Green函数及单圈引力子自能对量子Wilson圈的贡献.结果表明,引力子三顶点及引力自能将使Einstein引力获得定域曲率的激发.     

Ward identity and effective medium approximation for conductivity of liquid metals

The self-energy to define the ensemble average of a one-electron Green function for a disordered system is related to the vertex correction for the average of the product of two Green functions by the generalized optical theorem or by the so-called Ward identity. Using this relationship, we evaluate the conductivity of liquid metals both by the Ishida-Yomezawa approximation and by the effective medium approximation from the self-energy forms corresponding to respective approximations. The conductivity formulations thus obtained are shown to be identical with those derived from the diagram method.     

Green functions in a super self-dual Yang-Mills background

In euclidean supersymmetric theories of chiral superfields and vector superfields coupled to a super-self-dual Yang-Mills background, we define Green functions for the Laplace-type differential operators which are obtained from the quadratic part of the action. These Green functions are expressed in terms of the Green function on the space of right chiral superfields, and an explicit expression for the right chiral Green function in the fundamental representation of an SU(n) gauge group is presented using the supersymmetric version of the ADHM formalism. The superfield kernels associated with the Laplace-type operators are used to obtain the one-loop quantum corrections to the super-self-dual Yang-Mills action, and also to provide a superfield version of the super-index theorems for the components of chiral superfields in a self-dual background.     

Various Full Green Functions in QED

We are interested in deriving various full Green functions through general Ward–Takahashi identities (WTIs) for quantized field theories. With the help of a postulate of gauge group parameter, the general local gauge transformation laws preserving the gauge-invariance of the generating functional itself of QED model have been established successfully. By using path-integral technique, the various WTIs with resulting anomaly terms are derived under the gauge transformations. The arising of Jacobian factor from the integration measure gives a viable possibility to express full Green function. As a consequence, the complete expressions of the full vector, the full axial-vector, the full tensor vertex functions and so on are presented respectively by solving the complete set of the WTIs in the momentum space without considering the constraint imposing any Ansatz. In addition, anomaly function also provides an effective means to judge the divergence of variant coupling currents on fields.     

Equation of state for neutron matter in the presence of a pion condensate

The energy density for neutron matter including a pion condensed phase is studied, with particular emphasis on the role of Δ-isobars. Relativistic corrections to vertex functions involving isobars are considered and turn out to be important in the high density region. We arrive at a simple schematic model in which the inclusion of isobars leads to an effective enhancement of the axial vector coupling constant, which competes with an effective reduction due to the Lorentz-Lorenz correction. In the equation of state, inclusion of a pion condensed phase can lead to an appreciable reduction of total pressure.     

Quantum perturbation theory of solitons

We develop a systematic perturbation theory for amplitudes involving a single soliton (extended finite energy solution of a classical field theory). These methods allow one in principle to compute to any desired order quantum corrections to soliton masses, form factors and Green functions. The major technical problem encountered is an infrared divergence of the naive perturbation theory rules. This divergence is dominated by a modification of the usual functional methods so as to properly define the soliton as a momentum eigenstate. The extension of these methods to soliton-soliton scattering is discussed.     

The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement

The infrared behavior of the quark-gluon vertex of quenched Landau gauge QCD is studied by analyzing its Dyson-Schwinger equation. Building on previously obtained results for Green functions in the Yang-Mills sector, we analytically derive the existence of power-law infrared singularities for this vertex. We establish that dynamical chiral symmetry breaking leads to the self-consistent generation of components of the quark-gluon vertex forbidden when chiral symmetry is forced to stay in the Wigner-Weyl mode. In the latter case the running strong coupling assumes an infrared fixed point. If chiral symmetry is broken, either dynamically or explicitly, the running coupling is infrared divergent. Based on a truncation for the quark-gluon vertex Dyson-Schwinger equation which respects the analytically determined infrared behavior, numerical results for the coupled system of the quark propagator and vertex Dyson-Schwinger equation are presented. The resulting quark mass function as well as the vertex function show only a very weak dependence on the current quark mass in the deep infrared. From this we infer by an analysis of the quark-quark scattering kernel a linearly rising quark potential with an almost mass independent string tension in the case of broken chiral symmetry. Enforcing chiral symmetry does lead to a Coulomb type potential. Therefore, we conclude that chiral symmetry breaking and confinement are closely related. Furthermore, we discuss aspects of confinement as the absence of long-range van der Waals forces and Casimir scaling. An examination of experimental data for quarkonia provides further evidence for the viability of the presented mechanism for quark confinement in the Landau gauge.     

(Quasi)elastic electron-muon large-angle scattering within the two-loop approximation: Vertex contributions

We consider quasielastic large-angle electron-muon scattering at high energies with radiative corrections up to the two-loop level. The lowest order radiative corrections arising from the one-loop virtual photon emission and a real soft emission are presented within a power accuracy. Two-loop corrections are supposed to be of three gauge-invariant classes. One of them, the so-called vertex contribution, is given in the logarithmic approximation. The relation to the renormalization group approach is discussed.     

Peratization of the vertex in the theory of weak interactions with the W-meson

The integral equation for the vertex with crossed boson lines is solved by the known peratization technique. In the zero energy approach some numerical corrections to the simple vertex are obtained and it is shown that higher order corrections cannot be neglected. The influence of these corrections on the cross-section for the neutrino production of the W-meson in the nuclear field and on the W-mass is investigated.This work is a part of a thesis written in 1965 at the Faculty of Technical and Nuclear Physics of The Czech Technical University in Prague.