Three of the six plenary talks were dedicated to subjects of current interest in the area: Electroweak Symmetry Breaking R. There were six, out of eleven, parallel talks that dealt with QFT. Helayel , and Covariant Formalism for the Superstring N.

- Gauge Field Theories.
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Besides, there were 47 oral communications, and posters on [1]:. The list above shows that the meeting covered practically all topics of present interest in QFT. Several of the presentations were the fruit of scientific collaborations, many among them involving graduate students.

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There were many discussions during the various sessions, held in a very pleasant and lively atmosphere, which has become a trademark of the Particles and Fields area. From what was presented in the meeting, one may hope that its extensions may lead to unification, as well as to its widespread use in several other areas of Physics and beyond. Developments in this subject have hit the newspaper headlines more than once in recent years, and yet there is no direct experimental evidence that string theory is the fundamental theory of nature.

To appreciate what string theory aims to achieve and how it attempts to fulfill these aims, it is necessary to recollect the present formulation of the physics of elementary particles and fields. After reviewing the basic principles of particle physics, we will turn to a description of the fundamentals of string theory in non-technical terms.

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## Quantum Field Theory III: Gauge Theory

Elementary Particles and Fields. Consider the familiar force of electromagnetism. At the simplest level applicable to many phenomena at everyday scales of distance it is described by a "classical field". In this picture, a magnet exerts a force on another magnet because each one is a source of an electromagnetic field, pervading all of space but becoming weak with distance away from the source. The field needs no medium to support it, and can be thought of as a perturbation of the vacuum. Postulating the existence of such a field, subject to "wave equations", explains, in a unified way, all phenomena associated to electricity and magnetism up to a point.

- Unified field theory.
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The classical field theory of electromagnetism breaks down at very short distances, or in the presence of very strong fields. It becomes necessary to assume that this field is not just a number at every point of space and time, but a "quantum operator", having definite but somewhat complicated mathematical properties.

## Unified field theory - Wikipedia

The quantum field reduces to the classical one under familiar circumstances, but differs sharply from it in some regimes of distance or energy. In quantum theory, a field is not just something associated with waves, but is also related to particles by virtue of the well-known wave-particle duality. The first chapter is an introduction to solitons and instantons, as well as the topological quantum numbers, subjects that arose from the study of the non-linear field equations in gauge theories.

The succeeding chapters deal with the concept of gravitational field, electrodynamical systems, the Yang-mills gauge fields, and the Higgs mechanism. The remaining chapters highlight the speculations on possible lepton and quark structured. These chapters present the SU 5 model of grand unification.

## Unified field theory

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