Dimensionally Renormalized Green's functions for theories with massless particles. I

In the framework of dimensional renormalization the existence of Green's functions to all orders of perturbation theory is proved for theories of massless particles without super-renormalizable couplings. For those Green's functions Schwinger's Action Principle holds as in the massive case.     

Green's functions in an exterior gauge field

We consider the problem of evaluating the fermion Green's functions in an exterior Abelian-like gauge field. It is shown that in the field considered, the fermion Green's functions are expressed in terms of spinor particle Green's functions in some exterior electromagnetic field. The Green's functions are found in a combination of a constant homogeneous field and a plane wave field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 67–70, September, 1987.In conclusion the authors wish to express thanks to V. G. Bagrov and D. M. Gitman for helpful discussions of the problems touched upon in the article.     

Green's functions in an external electromagnetic field

The possibility is discussed of using eigenfunctions to find different propagators in quantum electrodynamics (QED) with an external electromagnetic field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 59–64, May, 1989.The authors are grateful to B. L. Voronov and I. V. Tyutin for useful discussion of the questions examined here.     

Dimensionally renormalized Green's functions for theories with massless particles. II

In the framework of dimensional renormalization the existence of Green's functions to all orders of perturbation theory is proved for theories with massless particles, provided all terms in the interaction Lagrangian have infrared degree 4. If the vanishing of masses is enforced by some symmetry and this symmetry is respected by dimensional regularization, Schwinger's action principle holds for these Green's functions as in the massive case.On leave of absence from Max-Planck-Institut für Physik und Astrophysik, D-8000 München, Federal Republic of GermanySupported in part by the National Science Foundation Grant # MPS-74-13208 A01Supported in part by the National Science Foundation Grant # GU 3186     

Conformal field theories and modular invariant partition functions for parafermion field theories

Parafermion conformal field theories with D_2N discrete symmetry are examined in detail. The structure of field space of parafermion field theories is studied with the help of a projection operator G. Characters of the representations of the twist sector of parafermion algebra and projected characters are given. A new class of modular invariant partition functions, therefore conformal field theories, for parafermion theories are found. We argue that the principal theories correspond to the generic critical SOS models of Andrew, Baxter and Forrest.     

One-point functions in perturbed boundary conformal field theories

We consider the one-point functions of bulk and boundary fields in the scaling Lee–Yang model for various combinations of bulk and boundary perturbations. The one-point functions of the bulk fields are analysed using the truncated conformal space approach and the form-factor expansion. Good agreement is found between the results of the two methods, though we find that the expression for the general boundary state given by Ghoshal and Zamolodchikov has to be corrected slightly. For the boundary fields we use thermodynamic Bethe ansatz equations to find exact expressions for the strip and semi-infinite cylinder geometries. We also find a novel off-critical identity between the cylinder partition functions of models with differing boundary conditions, and use this to investigate the regions of boundary-induced instability exhibited by the model on a finite strip.     

Hyperfunction quantum field theory II. Euclidean Green's functions

The axioms for Euclidean Green's functions are extended to hyperfunction fields without being supplemented by any condition like the linear growth condition of Osterwalder and Schrader.     

Non-abelian gauge couplings in thermal gauge field theories

Properties of the effective gauge couplings renormalized at finite temperature and density in thermal non-abelian gauge field theories are studied within one-loop approximations. Strong and severe vertex dependence is shown to come out both in the temperature and chemical potential dependences. Difficulties appearing in the perturbative calculation of physical quantities, indicated by the above disaster, are discussed. Also discussed is what insight might be gained from the present analysis into the “magnetic” screening of effective charge.     

Internal consistency of the method of two-time thermal Green's functions

The problem of calculating the correlation functions of a system in terms of its Green's functions and possible ways of solving this problem are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 80–83, July, 1980.I am very grateful to D. N. Zubarev and N. M. Plakide for reading the draft and drawing my attention to a number of new papers that I had originally missed, including [6].     

Axioms for Euclidean Green's functions

We establish necessary and sufficient conditions for Euclidean Green's functions to define a unique Wightman field theory.Supported by the National Science Foundation under grant GP 31239X.Supported in part by the Air Force Office of Scientific Research, contract AF 44620-70-C-0030.     

电磁学中的格林函数

文章回顾了电磁学中的格林函数理论与格林函数方法。首先,引入标量波动方程对应的格林函数,并与信号系统中的冲击响应函数作类比。其次,引入矢量波动方程对应的并矢格林函数,包括均匀和非均匀介质中的格林函数,并探讨其与电磁理论中的互易定理、等效原理之间的联系。最后,介绍了考虑介质的运动效应和电磁场的量子效应下的格林函数理论。此外,文章也探讨了电磁格林函数在无线通信、电磁兼容等工程领域的应用。     

Kinetic Green's functions

It is shown that the theory of kinetic Green's functions coincides completely with the theory of vacuum Green's functions after the choice of the operatorO ^?1 in its overall part. An expression for the energy of the system is obtained directly in terms of the mass operators. An equation is given that is a generalization of the Boltzmann equation and has the same mathematical structure.     

Modular invariant partition functions for N = 2 superconformal field theories

We find the characters of all the unitary degenerate highest weight representations of the N = 2 superconformal algebras with c<3. The constraints of modular invariance on the field contents of the two-dimensional N = 2 superconformal field theories are explored. The constraints take the form of sum rules on the number of superconformal highest weight representations. Models which satisfy these constraints are classified. We also discuss the condition of unbroken supersymmetry in these models.