|
Primary Field
In theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in contrast to experimental p ..., a primary field, also called a primary operator, or simply a primary, is a local operator in a conformal field theory which is annihilated by the part of the conformal algebra consisting of the lowering generators. From the representation theory point of view, a primary is the lowest dimension operator in a given representation of the conformal algebra. All other operators in a representation are called ''descendants''; they can be obtained by acting on the primary with the raising generators. History of the concept Primary fields in a ''D''-dimensional conformal field theory were introduced in 1969 by Mack and Salam where they were called ''interpolating fields''. They were then studied by Ferrara, Ga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Theoretical Physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena. The advancement of science generally depends on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations.There is some debate as to whether or not theoretical physics uses mathematics to build intuition and illustrativeness to extract physical insight (especially when normal experience fails), rather than as a tool in formalizing theories. This links to the question of it using mathematics in a less formally rigorous, and more intuitive or heuristic way than, say, mathematical physics. For example, while developing special relativity, Albert E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Conformal Field Theory
A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified. Conformal field theory has important applications to condensed matter physics, statistical mechanics, quantum statistical mechanics, and string theory. Statistical and condensed matter systems are indeed often conformally invariant at their thermodynamic or quantum critical points. Scale invariance vs conformal invariance In quantum field theory, scale invariance is a common and natural symmetry, because any fixed point of the renormalization group is by definition scale invariant. Conformal symmetry is stronger than scale invariance, and one needs additional assumptions to argue that it should appear in nature. The basic idea behind its plausibility is that ''local'' scale invariant theories have t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Conformal Algebra
Conformal symmetry is a property of spacetime that ensures angles remain unchanged even when distances are altered. If you stretch, compress, or otherwise distort spacetime, the local angular relationships between lines or curves stay the same. This idea extends the familiar Poincaré group —which accounts for rotations, translations, and boosts—into the more comprehensive conformal group. Conformal symmetry encompasses special conformal transformations and dilations. In three spatial plus one time dimensions, conformal symmetry has 15 degrees of freedom: ten for the Poincaré group, four for special conformal transformations, and one for a dilation. Harry Bateman and Ebenezer Cunningham were the first to study the conformal symmetry of Maxwell's equations. They called a generic expression of conformal symmetry a spherical wave transformation. General relativity in two spacetime dimensions also enjoys conformal symmetry. Generators The Lie algebra of the conformal group h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
