abstract

We present a new method of deriving under some mild assumptions the most general options for the B.R.S.T. transformation, without having recourse either to Lagrange or Feynman’s integral-over-all-paths formalisms. It turns out that these different variants can be reduced eventually to two cases, from which one encompasses the conventional B.R.S.T. transformation.

abstract

We review the path integral formulation for relativistic spinning particles and show how the spin factor appears as a geometrical phase. We also explain how the three dimensional spin factor can be expressed as a Wilson loop in a Chern–Simons gauge theory.

abstract

Anomalies related to an external global symmetry of the gauge-fixed action may well possess relevance in physical observables. Their gauge-(in-)dependence is most suitably controlled by a combination of the BRS-technique which includes a BRS-transformation of the gauge-parameters, with the external symmetry coupled to an external gauge field. For an external symmetry which commutes with BRS, anomalies are shown to be essentially gauge-independent (to one loop order). A nontrivial example is the ghost number anomaly of the bosonic string. However, e.g. the anomalies of superconformal transformations do not fall into this category.

abstract

The \(N\) \(\theta \)-sector of the Lee model is studied in the framework of a relativistic theory, in which also the recoil of the \(N\)- and \(V\)-particle are taken into account. For several values of the mass ratios the \(s\)-wave phase shift and total cross section are calculated as functions of the energy. The Riemann surface of the scattering amplitude as a function of the complex Mandelstam variable \(s\) is investigated. It is found to have an infinite number of sheets. The poles of the \(S\)-matrix on the first (physical), second and third sheet are calculated and found to describe orbits of a peculiar form when the coupling constant is varied. In order to compare these results with nonrelativistic potential scattering the same quantities were first calculated for the \(\delta \)-shell potential. It is concluded that even this simple relativistic field theory and the nonrelativistic field theory have very different characteristics.

abstract

The gauge hierarchy problem is reviewed and a class of effective field theories obtained from superstrings is described. These are characterized by a classical symmetry, related to the space-time duality of string theory, that is responsible for the suppression of observable supersymmetry breaking effects. At the quantum level, the symmetry is broken by anomalies that provide the seed of observable supersymmetry breaking, and an acceptably large gauge hierarchy may be generated.

abstract

In this lecture recent results obtained from radiative corrections to the Drell–Yan process and heavy flavour production are presented. The \(K\)-factors in both processes are large and in the case of heavy flavour production depend very heavily on the choice of the renormalisation and factorisation scale. The contribution of the gluon–gluon subprocess to both reactions will be discussed.

abstract

Two regularizations of the Nambu–Jona–Lasinio model with vector mesons are compared: the proper-time method which preserves the gauge invariance of the quark loop term and a 4-momentum cutoff method which breaks gauge invariance. When meson masses are substituted for the coupling constants, the action has only a logarithmic dependence on the cutoff, and the two methods yield similar results. The binding of \(\bar q q\) excitations is discussed as well as the importance of calculating on-shell meson masses rather than using a gradient expansion of the action. The vector mesons are expected to reduce significantly the modification of a nucleon in nuclear matter. A consistent way to compare the model predictions with experiment is proposed.

abstract

Some results on the effective action of a Dime field in the background of a chiral mass term are presented. They concern the convergence of the gradient expansion and a new numerical method for evaluating the zero point energy in a nonperturbative way.

abstract

In the framework of chiral colour theory, it is shown how the choice of gauge couplings is constrained by low energy phenomenology. The requirement that there be a massless gluon yields a relationship between the two coupling constants. Their allowed values as the mass of the axigluon are further constrained by present \(e^+e^-\) data.

abstract

On the basis of the \(\sigma \)-model, it is argued that there may exist a new phase of matter at densities of the order of a few nuclear densities, and temperatures below \(\sim \) 100 MeV. The phase consists of a gas of quarks with constituent-like masses, submerged in a periodic chiral field — a “pion condensate”. The appearance of this phase is a general feature of the \(\sigma \)-model and other models based on the chiral dynamics (e.g. the NJL model), and it occurs for a broad range of model parameters. Phenomenological consequences on the physics of dense matter are discussed, in particular we describe interesting magnetic properties of the phase.

abstract

The problem of temperature dependence of nucleon mass is addressed by considering a retarded correlator of two currents with quantum numbers of a nucleon at finite temperature \(T \ll F_{\pi }\) in the chiral limit. It is shown that at Euclidean momenta the leading one-loop corrections arise from direct interaction of thermal pious with the currents. A dispersive representation for the correlator shows that this interaction smears the nucleon pole over frequency interval with width \(\sim T\). This interaction does not change the exponential fall-off of the correlator in Euclidean space but gives an \(O(T^2/F^2_{\pi })\) contribution to the pre-exponential factor.

abstract

A systematic theory of quarks in the instanton medium is developed beyond the framework of the zero-mode approximation. At large number of colours a closed equation for the quark propagator is derived. The chiral symmetry is shown to be spontaneously broken. The effective quark mass and the quark condensate are calculated.

abstract

Modifications of meson and baryon properties due to the presence of an external hot baryon medium are investigated in the Nambu–Jona–Lasinio model. The corresponding meson sector is solved for a quark continuum at finite density and temperature. We use two regularization schemes with 3-dimensional sharp, Pauli–Villars and proper time cutoff types. Due to the medium the constituent quark mass and the pion and sigma masses are modified. We find a first-order chiral phase transition at relatively low temperatures less than 100 MeV which changes to second order at higher temperatures. The corresponding temperature-density phase diagram is non-monotonic.

abstract

We discuss recent developments in the study of multiplicity fluctuations where scaling properties are searched for and partly established in full phase space (“KNO scaling”) and limited domains of phase space (“Intermittency”). Such scaling properties are expected in parton cascade models based on QCD which are well established in \(e^+e^-\)-annihilation with timelike parton evolution. In the other collision processes, in particular soft processes, similar phenomena are observed but no common theoretical description is available yet.

abstract

We discuss the role of the renormalization group improved YFS theory in \(Z^0\) physics at SLC and LEP. The general theory is reviewed. Some results of this application recently at SLC and LEP are presented. Future directions for the theory’s further development and application are outlined.

abstract

Results of the ALEPH and other LEP experiments are presented. Very good agreement with the Standard Model has been found within experimental accuracy of about 1%.