Author: Andrei Linde

Published in: Stanford University, Stanford

ISBN: 0-0000-0000-0

File Type: pdf

File Size:  2 MB

Language: English


With the invention and development of unified gauge theories of weak and electromagnetic interactions, a genuine revolution has taken place in elementary Particle Physics in the last 15 years. One of the basic underlying ideas of these theories is that of spontaneous symmetry breaking between different types of interactions due to the appearance of constant classical scalar fields φ over all space (the so-called Higgs fields). Prior to the appearance of these fields, there is no fundamental difference between strong, weak, and electromagnetic interactions. Their spontaneous appearance over all space essentially signifies a restructuring of the vacuum, with certain vector (gauge) fields acquiring high mass as a result. The interactions mediated by these vector fields then become shortrange, and this leads to symmetry breaking between the various interactions described by the unified theories.

The first consistent description of strong and weak interactions was obtained within the scope of gauge theories with spontaneous symmetry breaking. For the first time, it became possible to investigate strong and weak interaction processes using high-order perturbation theory. A remarkable property of these theories — asymptotic freedom — also made it possible in principle to describe interactions of elementary particles up to center-of-mass energies E ∼ MP ∼ 1019 GeV, that is, up to the Planck energy, where quantum gravity effects become important.

Here we will recount only the main stages in the development of gauge theories, rather than discussing their properties in detail. In the 1960s, Glashow, Weinberg, and Salam proposed a unified theory of the weak and electromagnetic interactions [1], and real progress was made in this area in 1971–1973 after the theories were shown to be renormalizable [2]. It was proved in 1973 that many such theories, with quantum chromodynamics in particular serving as a description of strong interactions, possess the property of asymptotic freedom (a decrease in the coupling constant with increasing energy [3]). The first unified gauge theories of strong, weak, and electromagnetic interactions with a simple symmetry group, the so-called grand unified theories [4], were proposed in 1974. The first theories to unify all of the fundamental interactions, including gravitation, were proposed in 1976 within the context of supergravity theory. This was followed by the development of Kaluza–Klein theories, which maintain that our four-dimensional space-time results from the spontaneous compactification of a higher-dimensional space [6]. Finally, our most recent hopes for a unified theory of all interactions have been invested in super string theory [7]. Modern theories of elementary particles are covered in a number of excellent reviews and monographs (see [8–17], for example).

The rapid development of elementary particle theory has not only led to great advances in our understanding of particle interactions at superhigh energies, but also (as a consequence) to significant progress in the theory of superdense matter. Only fifteen years ago, in fact, the term superdense matter meant matter with a density somewhat higher than nuclear values, ρ ∼ 1014–1015 g · cm−3 and it was virtually impossible to conceive of how one might describe matter with ρ ≫ 1015 g · cm−3. The main problems involved strong-interaction theory, whose typical coupling constants at ρ >∼ 1015 g · cm−3 were large, making standard perturbation-theory predictions of the properties of such matter unreliable. Because of asymptotic freedom in quantum chromodynamics, however, the corresponding coupling constants decrease with increasing temperature (and density). This enables one to describe the behavior of matter at temperatures approaching T ∼ MP ∼ 1019 GeV, which corresponds to a density ρP ∼ M4 P ∼ 1094 g · cm−3 Present-day elementary particle theories thus make it possible, in principle, to describe the properties of matter more than 80 orders of magnitude denser than nuclear matter! The study of the properties of superdense matter described by unified gauge theories began in 1972 with the work of Kirzhnits [18], who showed that the classical scalar field φ responsible for symmetry breaking should disappear at a high enough temperature T. This means that a phase transition (or a series of phase transitions) occurs at a sufficiently high temperature T > Tc, after which symmetry is restored between various types of interactions. When this happens, elementary particle properties and the laws governing their interaction change significantly.
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