By K Moriyasu
Gauge thought is now famous as probably the most innovative discoveries in physics because the improvement of quantum mechanics. This primer explains how and why gauge concept has dramatically replaced our view of the basic forces of nature. The textual content is designed for the non-specialist. a brand new, intuitive technique is used to make the guidelines of gauge thought available to either scientists and scholars with just a historical past in quantum mechanics. Emphasis is put on the physics instead of the formalism.
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Extra info for An Elementary Primer For Gauge Theory
This diversity of interest in gauge theory indicates that it is in fact a very general area of study and not exclusively limited to elementary particles. In this primer for gauge theory, our purpose is to present an elementary introduction which will provide an adequate background for appreciating both the new theoretical developments and the experimental investigations into gauge theory. We have therefore adopted a very general pedagogical approach which should be useful for very different areas of physics.
In mathematical jargon, the new space formed by the union of 4-dimensional space-time with an internal space is called a “fiber bundle” space. The reason for this name is that the internal spaces or “fibers” at each space-time point can all be viewed as the same space because they can be transformed into each other by a gauge transformation. Hence, to a mathematician the total space is a collection or “bundle” of fibers. Given that Yang and Mills developed their theory using the same terminology as electrodynamics, it is relevant to ask if there is any good reason to describe gauge theory in geometrical terms, other than to establish a historical link with relativity.
Generalizing the concept that all physical measurements are relative, Weyl proposed that the absolute magnitude or norm of a physical vector also should not be an absolute quantity but should depend on its location in space-time. A new connection would then be necessary in order to relate the lengths of vectors at different positions. This idea became known as scale or “gauge” invariance. It is important to note here that the true significance of Weyl’s proposal lies in the local property of gauge symmetry and not in the particular choice of the norm or “gauge” as a physical variable.
An Elementary Primer For Gauge Theory by K Moriyasu