Titlebook: Riemann, Topology, and Physics; Michael Monastyrsky,R. O. Wells Book 19871st edition Springer Science+Business Media New York 1987 crystal

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Fortuitous

https://doi.org/10.1007/978-1-4899-3514-4crystal; manifold; topology

痛打

断断续续

Systems with Spontaneous Symmetry-Breakingmethods. This possibility, which unifies such physically different systems as liquid crystals, magnetism and superfluid helium, is called spontaneous symmetry-breaking. It underlies many contemporary concepts in the theories of elementary particles and phase transitions, and a series of problems of cosmology.

我邪恶

Topological Particlesitional scalar fields (the fields of Goldstone-Higgs).. These solutions had one topological charge which was interpreted as a “magnetic charge.” G. ’t Hooft suggested calling them magnetic monopoles. The name was to symbolize the deep commonality of the newly discovered “particle” with another mysterious object—the magnetic monopole of Dirac.

匍匐

昏暗

IntroductionTopology is probably the youngest of the classical branches of mathematics. In contrast to algebra, geometry, and number theory, whose genealogies date to classical times, topology (or, as it was earlier called, “analysis situs,” i.e., analysis of position) appeared only in the seventeenth century.

Resign

Topology and Liquid CrystalsLiquid crystals are structures found in an intermediate state between the liquid and solid phases—a duality expressed in their very name. True liquid crystals have both some crystalline properties (orderly structure) and the properties of a liquid (fluidity).

Choreography

The Theory of Gauge FieldsUnderlying all contemporary theories of elementary particles is the concept of the field. For each elementary particle, there is a corresponding quantum field, and the interaction of these particles is defined by the interaction of their fields.

会议

What Next?In the preceding chapters, I have tried to give the reader an idea about several areas of physics in which topological methods have proved useful. I have tried to show that topological ideas are exceptionally close to contemporary (and less contemporary) ideas in physics.