A generalized field theory. II. Linearized field equations

A thorough examination of the generalized field theory, formulated by the same authors in a previous paper, is being carried out in the absence of feedback effects. The results obtained are found to be in complete agreement with those of linear field theories of gravity and electromagnetism. Strict functions, which serve as indicators of the strength of the two fields, are being identified. This study reveals also two interesting results: the first is the classification of tetrad vector fields used, the second is the definite appearance of a mutual interaction between gravitational and electromagnetic fields.     

Conformal field theory and the symmetries of string field theory

The two-dimensional conformal field theory representation of Witten's bosonic string field theory is discussed. The basic overlap equations, K_n symmetry and BRST invariance are proved directly, without the usual expansion in oscillators. The conformal field theory approach naturally provides local overlap identities which (when integrated over half the string) can be used to verify properties of the cubic action. In particular, a recently proposed diffeomorphism invariance is shown to be free of anomalies. Finally, a new class of symmetries, including generalizations of the K_n symmetries which are local in spacetime, are presented.     

Zero-dimensional field theory

A study of zero-dimensional theories, based on exact results, is presented. First, relying on a simple diagrammatic representation of the theory, equations involving the generating function of all connected Green's functions are constructed. Second, exact solutions of these equations are obtained for several theories. Finally, renormalization is carried out. Based on the anticipated knowledge of the exact solutions the full dependence on the renormalized coupling constant is studied. Received: 1 February 2001 / Published online: 23 March 2001     

Ising-like field theory

A field theory model onR ² in which the basic fields are Ising spins instead of Gaussian spins is examined. Using statistical mechanics techniques we discuss the ultraviolet and the infrared problems. In particular we discuss a technique yielding the asymptotic expansion in of the ground state energy, as 0, without using the cluster expansion.Supported in part by Consiglio Nazionale delle Ricerche.     

Euclidean field theory

The extension of the Schwinger functions to various positive linear functionals on the Borchers algebra is discussed. In one case, we construct a measure onL and give criteria for uniqueness as well as for the homogeneous chaos to lead to an ?₂-space.     

Nuclear field theory

By using path integral techniques nuclear field theory (NFT) is developed for Fermi systems interacting via a general two-body force. The NFT Lagrangian is strictly derived. As a by-product, the corresponding graphical rules are obtained. The relation between the NFT and the conventional Feynman diagrammatic many-body perturbation theory is established for processes connecting initial and final states, too.     

More about superconformal field theory. Hamiltonian formalism

The Hamiltonian formalism for theN=1,d=4 superconformal system is given. The first-order formalism is found by starting from the canonical covariant one. As the conformal supergravity is a higher-derivative theory, to analyze the second-order Hamiltonian formalism the Ostrogradski transformation is introduced to define canonical momenta.     

Massive gauge field in source theory. II

In an earlier source theory investigation it was shown that the vacuum polarization of a massive gauge field is finite, provided that the conservation of current is imposed everywhere, including the interior of the sources. It is shown in the present paper that radiative corrections to a vertex function (two-particle production by an external source) are also finite if the same requirement about current conservation is imposed. In other words one-loop corrections turn out to be finite in both calculations. The cancellations leading to convergence may be understood in terms of Ward identities. The three form factors that appear are not only shown to be finite but are also explicity found.     

Nuclear field theory

The nuclear spectrum is described in terms of elementary modes of excitation comprising pairing and surface vibrations and single-particle degrees of freedom. A unified theory of the mutual interweaving of these excitations which makes use of many-body field theoretical concepts is reviewed. The theory is illustrated through the study of the nuclear structure of ²⁰⁹ Bi.     

Massive gauge field in source theory. I

The vacuum polarization is calculated for a massive gauge field according to the methods of source theory. The spectral integral turns out to be convergent and the numerical coefficient, which is (1/3)(e²/4π²) in spinor electrodynamics, is here (3f/16)(g²/4π²) where f depends on the group and f = 1 for SU(2).     

Conformal field theory representation and background-independent action for superstring field theory

The two-dimensional conformal field theory representation of Witten's open superstring field theory is discussed. We argue that the previously suggested cubic action for the superstring is actually dependent on the spacetime background, and suggest a modification which formally removes this dependence. The transformation from the new version of the superstring cubic action to Witten's action for open string states is discussed. A class of linearized solutions to the equations of motion of the open superstring cubic action are exhibited. These solutions are in one-to-one correspondence with the physical excitations (both massless and massive) of the open and closed type I superstrings.     

Particle creation,classicality and related issues in quantum field theory: II. Examples from field theory

We adopt the general formalism, which was developed in Paper I to analyze the evolution of a quantized time-dependent oscillator, to address several questions in the context of quantum field theory in time dependent external backgrounds. In particular, we study the question of emergence of classicality in terms of the phase space evolution and its relation to particle production, and clarify some conceptual issues. We consider a quantized scalar field evolving in a constant electric field and in FRW spacetimes which illustrate the two extreme cases of late time adiabatic and highly non-adiabatic evolution. Using the time-dependent generalizations of various quantities like particle number density, effective Lagrangian etc. introduced in Paper I, we contrast the evolution in these two limits bringing out key differences between the Schwinger effect and evolution in the de Sitter background. Further, our examples suggest that the notion of classicality is multifaceted and any one single criterion may not have universal applicability. For example, the peaking of the phase space Wigner distribution on the classical trajectory alone does not imply transition to classical behavior. An analysis of the behavior of the classicality parameter, which was introduced in Paper I, leads to the conclusion that strong particle production is necessary for the quantum state to become highly correlated in phase space at late times.     

Effective field theory in background field gauge

It is shown how to construct effective lagrangians to the two-loop level for non-abelian gauge theories, quantized in background field gauge. This construction is no more difficult than the analogous computation in abelian gauge theories when minimal subtraction is employed. It is argued that for three or more loops, one can no longer separate heavy or mixed light-heavy graphs in an intermediate renormalization, and the more general algorithm presented by us in an earlier work must be employed even in background field gauge.     

Self-consistent field theory of collisions I. Scattering channels

The conventional Hartree and Hartree-Fock approaches for treating many-electron bound systems have been extended recently to positive energy scattering problems, in which both the bound and continuum orbitals are determined by the requirement of full self-consistency. Serious consequences of such a theory are that the target orbitals become energy dependent and the asymptotic boundary conditions are satisfied only approximately, in lowest order. It is important therefore to test the theory for its convergence under configuration mixing. This self-consistent field (SCF) theory for scattering has been tested here for scattering from hydrogenic target as a model where the target function is determined dynamically. Penetration of the projectile inside the bound target orbital is manifest through the SCF for the bound state. Our results show that the theory converges to the correct amplitudes and to the exact boundary conditions as more configurations are added. The use of the amputated functions and the weak asymptotic condition (WAC) upon which the SCF theory is based, is justified as the WAC converges to the correct limit. It is then applied to the positron-helium and electron-helium scattering systems where the helium function is calculated simultaneously together with the scattering function. The resulting phase shifts and the SCF target functions are compared with those obtained with the pre-determined target functions in the conventional approaches. Received 22 September 1999     

Quenched string field theory

We construct a toy model of Witten's open string field theory by truncating the Virasoro group to its SU(1,1) subgroup. The string field is given in terms of finite-dimensional matrices, which satisfy a non-trivial BRST cohomology. The string gauge group is found to be SO(3). Finally, we perform the gauge fixing of the action, finding an explicit formula for calculating the partition function.