International Journal of Modern Physics A

A supersymmetric nonlinear σ-model provides us a tool for studying the dynamics of superstrings on a compactified space. If the compactified space is a Ricci-flat Kähler manifold, the nonlinear σ-model has extended superconformal symmetry and the partition function of the model is expressed in terms of characters of the superconformal algebra. The partition function must be modular invariant and this condition gives strong constraints on the spectrum of the model. These constraints are intimately related to geometry of the compactified space. Their implications to particle spectra of the compactified heterotic string theory are also discussed.

C. Y. Chao's contribution to physicists' acceptance of QED in 1933–1934 through his experiments of 1930 is analyzed. It is pointed out that Blackett and Occhialini's key suggestion of 1933 about hole theory was based on identifying Chao's "additional scattered rays" (1930) as due to pair annihilation.

The one-loop effective action (EA) for arbitrary supersymmetric theory with broken supersymmetry on the background R_b × T_d−n, where R_n, T_d are n-dimensional curved space-time and d-dimensional torus, is obtained. Vilcovisky-De Witt EA in d = 5 (super)gravity on the background R₄ × T₁ at nonzero temperature is calculated with accuracy to linear curvature terms. Vacuum energy for open and closed superstrings with broken supersymmetry on the background M₄ × T₆, where M₄ is Minkowski space, is also obtained. The question of the possibility of spontaneous compactification in models under consideration is analyzed.

Quantum consistency of open string theories is considered at the one-loop level, using a unified and consistent regularization of all divergences. Finiteness of all amplitudes with open string states is shown to be possible for any SO(n) or USp(n) gauge group. Two consequences of the nonunitarity of tachyonic theories are discussed; the presence of unphysical cuts in amplitudes and the nondecoupling of null states. If not for contributions of the open string tachyon, decoupling of all null open bosonic string states would be obtained for SO(2^D/2) independently of the regularization, corresponding to vanishing tadpoles of unphysical closed string states.

The geometrical structure of the noncompact, nonhomogeneous Kähler sigma models arising from supersymmetric gauge theories is described. Topics discussed include the choice of target manifold for the sigma model, the supersymmetric vacuum alignment problem and the nature of chiral symmetry breaking, the role of isometry anomalies, the construction of the Kähler potential and metric, and the embedding of the conventional compact coset space sigma model in the supersymmetric Kähler model.

The instanton sum in the partition function for D bosons on a Riemann surface of genus g, with values in a general D-dimensional torus, T^D = R^D/Λ_D is given explicitly. When the rational metric Q of the lattice, Λ_D, is the identity we get the bosonization formula of Alvarez-Gaumé et al. for SO(2D). If Q is orthogonal, in the bosonization formula, we get the theta function associated with the quadratic form Q, if Q is generic we get rational Conformal Field Theory. Also we look for conditions on a twisted spin bundle L_E, which may ensure that our partition functions arise from some generalized bosonization formulas.

It is shown here that the holomorphic quantum mechanics in a complexified Minkowski space-time helps us to study the geometrical feature of the internal space of a particle and its relevance with conformal geometry. It is noted that the conformal reflection can be depicted in the formalism of an internal helicity which takes the value and for the particle and antiparticle state. This again can be described in the framework of holomorphic quantum mechanics in terms of the half-orbital angular momentum of a constituent in an anisotropic space in the sense of Minkowski space-time with a fixed l_z value for the particle and antiparticle configuration when a composite system is considered. A massive or massless spinor moving with such characteristic in the configuration of a composite system can be depicted as a Cartan semispinor and behaves as a twistor. The doublet of such spinors with opposite helicities represent an eight-component conformal spinor. The internal symmetry group SU(3) for a composite system of hadrons can then be realized from the reflection group. This formalism reveals the microlocal region of a complexified Minkowski space-time as a twistor space.

The global operator formalism proposed recently by Krichever and Novikov using meromorphic tensor fields on general Riemann surfaces of arbitrary genus is applied to the bosonic string. The well-known Green's function of the scalar boson fields is obtained in a simple manner from the spectral representation. Proof of Wick's theorem is also given.

A study is made of a class of four-dimensional heterotic string models with complex fermionic degrees of freedom to discover whether there are any examples with 3 or 4 generations of quarks and leptons and SU_C(3) × SU_L(2) × U^p(1) low energy gauge group.

It is argued that the usual statement of the Fradkin-Vilkovisky theorem, which determines the dependence of the path-integral for gauge-invariant systems on their gauge-fixing, cannot be correct. A more precise statement is given, by considering the structure of the modular space of gauge orbits. The discussion is illustrated in the case of the scalar particle with specific examples.

The relation between multiplicity and transverse energy in high energy h-h and A-A collisions is investigated using a Monte Carlo generator of nondiffractive processes. The width of multiplicity fluctuation D/<n> for fixed E_⊥ is found to be small and approximately constant for a wide range of E_⊥.

We review the occurrence of exceptional groups in string theory: their dual role as gauge symmetry and as a symmetry unifying space-time, superconformal ghost and internal degrees of freedom. In both cases the relation to the extended world-sheet supersymmetries is discussed in detail. This is used to construct the supermultiplet structure of the massless sectors of all supergravity theories possible in string theory, in even space-time dimensions between four and ten.

Using the path integral formulation of QED in the Schrödinger picture, we explicitly show the completeness of photon and electron states at equal (discrete) time. We then formulate an approximation of the bound state wave function, based on its maximal Fock state content, by restricting the intermediate states at all times in the bound state propagator. The approximation becomes (formally) exact as the restriction on the intermediate states is lifted. Hence the Fock expansion provides an alternative to bound state calculations based on the Bethe-Salpeter equation.

As an example, we study the bound states formed by a fermion f is an external potential, and by a fermion-antifermion pair . At the valence level of the Fock expansion, where the wave function is at all times restricted to f (or ), we show that only instantaneous Coulomb exchange occurs between the fermions. The resulting bound state equation is similar to the Salpeter equation, but has only positive energy projectors.

We discuss and contrast search limits for and properties of new Z′ gauge bosons which can be probed at high energy e⁺e⁻ colliders within the context of several E₆ superstring-inspired models. In particular, we discuss the probability of distinguishing these various models from one another and determining the Z′ coupling parameters uniquely. Using the deviations from the standard model predictions for asymmetries and cross sections for various final state fermions, we set discovery limits for new Z′ bosons at and 1 TeV e⁺e⁻ colliders. We find quite generally that cross section deviations provide the strongest limits on the existence of new Z′ bosons below threshold even when 100% beam polarization is available. The possibility of using Z′ pair production as a sensitive probe of the e⁺e⁻Z′ coupling is also examined.

Two-dimensional gauge models with chiral anomalies — "left-handed" QED and the chiral Schwinger model are consistently quantized in the frames of the minimal quantization method. The choice of the cone time as a physical time for the system of quantization is motivated. The well-known mass spectrum is found but with a fixed value of the regularization parameter a = 2. Such a unique solution is obtained due to the strong requirement of self-consistency of the minimal quantization method that is reflected in the physically motivated choice of the time axis.

Supplementing the Gauss law operator of an anomalous gauge theory with a certain set of functionals of the gauge potentials, one obtains a closed algebra. The algebras obtained in this way are Abelian extensions of the Lie algebra of the group of gauge transformations, and are natural generalizations of Kac-Moody algebras, both in two and four dimensions.

On the physical states, two-dimensional quantum chromodynamics (QCD₂) is shown to reduce to the theory of fermions in a chiral background.

In order to investigate the weak coupling limit of lattice gauge theories, it has been suggested recently to apply the semiclassical approximation to the Schrödinger equation in the Hamiltonian formalism. This method is used to study pure SU(2) gauge theory on a cube with sides of length one lattice constant and with antiperiodic boundary conditions. We show the existence of caustics, i.e. envelopes of families of classical trajectories where the ground state wave function peaks, and describe their shape.

The formal representation-independence of topological effects in quantum field theory like those associated with monopole line bundles on the configuration space or vacuum angles is established within the framework of geometric quantization by studying simple finite-dimensional examples. Some deficiencies of the ordinary momentum representation are pointed out and an alternative generalization of the momentum representation to homogeneous spaces is suggested.