Spacetime symmetries
Main article: Spacetime symmetries
Fields are often classified by their behaviour under transformations of spacetime. The terms used in this classification are —
- scalar fields (such as temperature) whose values are given by a single variable at each point of space. This value does not change under transformations of space.
- vector fields (such as the magnitude and direction of the force at each point in a magnetic field) which are specified by attaching a vector to each point of space. The components of this vector transform between themselves as usual under rotations in space.
- tensor fields, (such as the stress tensor of a crystal) specified by a tensor at each point of space. The components of the tensor transform between themselves as usual under rotations in space.
- spinor fields are useful in quantum field theory.
[edit]Internal symmetries
Main article: Gauge symmetry
Fields may have internal symmetries in addition to spacetime symmetries. For example, in many situations one needs fields which are a list of space-time scalars: (φ1,φ2...φN). For example, in weather prediction these may be temperature, pressure, humidity, etc. In particle physics, the colorsymmetry of the interaction of quarks is an example of an internal symmetry of the strong interaction, as is the isospin or flavour symmetry.
If there is a symmetry of the problem, not involving spacetime, under which these components transform into each other, then this set of symmetries is called an internal symmetry. One may also make a classification of the charges of the fields under internal symmetries.
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2012/5/25 王雄 <wangxiong8686@gmail.com>
External symmetry in general relativity
Ion I. Cotaescu (The West University of Timişoara, Romania)(Submitted on 31 May 2000)We propose a generalization of the isometry transformations to the geometric context of the field theories with spin where the local frames are explicitly involved. We define the external symmetry transformations as isometries combined with suitable tetrad gauge transformations and we show that these form a group which is locally isomorphic with the isometry one. We point out that the symmetry transformations that leave invariant the equations of the fields with spin have generators with specific spin terms which represent new physical observables. The examples we present are the generators of the central symmetry and those of the maximal symmetries of the de Sitter and anti-de Sitter spacetimes derived in different tetrad gauge fixings.
Pacs: 04.20.Cv, 04.62.+v, 11.30.-j
Comments: 25 pages, Latex Subjects: General Relativity and Quantum Cosmology (gr-qc) Journal reference: J.Phys.A33:9177-9192,2000 DOI: 10.1088/0305-4470/33/50/304 Cite as: arXiv:gr-qc/0005135v1
Groupoids: Unifying Internal and External Symmetry
作者：A Weinstein - 1996 - 被引用次数：170 - 相关文章
Groupoids: Unifying Internal and External. Symmetry. A Tour through Some Examples. Alan Weinstein. 744. NOTICES OF THE AMS. VOLUME 43, NUMBER 7 ...[PDF]INTERNAL, EXTERNAL AND GENERALIZED SYMMETRIES
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作者：IM Anderson - 1990 - 被引用次数：54 - 相关文章
ones which do not come from classical "external" symmetries. ... external symmetry of a system of differential equations gives rise to an internal symmetry ...About the Origin of the Division between Internal and External Symmetries in Quantum Field Theory
(Submitted on 17 Oct 2009)It is made the attempt to explain why there exists a division between internal symmetries referring to quantum numbers and external symmetries referring to space-time within the description of relativistic quantum field theories. It is hold the attitude that the symmetries of quantum theory are the origin of both sorts of symmetries in nature. Since all quantum states can be represented as a tensor product of two dimensional quantum objects, called ur objects, which can be interpreted as quantum bits of information, described by spinors reflecting already the symmetry properties of space-time, it seems to be possible to justify such an attitude. According to this, space-time symmetries can be considered as a consequence of a representation of quantum states by quantum bits. Internal symmetries are assumed to refer to relations of such fundamental objects, which are contained within the state of one single particle, with respect to each other. In this sense the existence of space-time symmetries, the existence of internal symmetries and their division could obtain a derivation from quantum theory interpreted as a theory of information.
Comments: 5 pages Subjects: General Physics (physics.gen-ph) Cite as: arXiv:0910.3303v1 [physics.gen-ph]
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