Information about Critical Dimension
In the renormalization group analysis of phase transitions in physics, a critical dimension is the dimensionality of space at which the character of the phase transition changes. Below the lower critical dimension there is no phase transition. Above the upper critical dimension the critical exponents of the theory become the same as that in mean field theory.
Since the renormalization group sets up a relation between a phase transition and a quantum field theory, this also has implications for the latter. Above the upper critical dimension, the quantum field theory which belongs to the model of the phase transition is a free field theory. Below the lower critical dimension, there is no field theory corresponding to the model.
In the context of string theory, the phrase critical dimension has a more restricted meaning. It indicates the dimension at which string theory is consistent assuming a constant dilaton background. The precise number may be determined by the required cancellation of conformal anomaly on the worldsheet and it equals 26 for the bosonic string theory and 10 for superstring theory.
Since the renormalization group sets up a relation between a phase transition and a quantum field theory, this also has implications for the latter. Above the upper critical dimension, the quantum field theory which belongs to the model of the phase transition is a free field theory. Below the lower critical dimension, there is no field theory corresponding to the model.
In the context of string theory, the phrase critical dimension has a more restricted meaning. It indicates the dimension at which string theory is consistent assuming a constant dilaton background. The precise number may be determined by the required cancellation of conformal anomaly on the worldsheet and it equals 26 for the bosonic string theory and 10 for superstring theory.
In theoretical physics, renormalization group (RG) refers to a mathematical apparatus that allows one to investigate the changes of a physical system as one views it at different distance scales.
..... Click the link for more information.
..... Click the link for more information.
phase transition or phase change is the transformation of a thermodynamic system from one phase to another. The distinguishing characteristic of a phase transition is an abrupt change in one or more physical properties, in particular the heat capacity, with a small change in
..... Click the link for more information.
..... Click the link for more information.
Physics is the science of matter[1] and its motion[2][3], as well as space and time[4][5] —the science that deals with concepts such as force, energy, mass, and charge.
..... Click the link for more information.
..... Click the link for more information.
dimension (Latin, "measured out") is a parameter or measurement required to define the characteristics of an object—i.e., length, width, and height or size and shape.
..... Click the link for more information.
..... Click the link for more information.
Critical exponents describe the behaviour of physical quantities near continuous phase transitions. Remarkable about them is that they are universal, i.e. do not depend on details of the physical system, but only on
..... Click the link for more information.
- the dimension of the system,
..... Click the link for more information.
mean field theory (MFT, also known as self-consistent field theory) is to resolve these combinatorial problems.
The main idea of MFT is to replace all interactions to any one body with an average or effective interaction.
..... Click the link for more information.
The main idea of MFT is to replace all interactions to any one body with an average or effective interaction.
..... Click the link for more information.
Quantum field theory (QFT) is a theoretical framework for constructing quantum mechanical models of field-like systems, or, equivalently, of many-body systems. It is widely used in particle physics and condensed matter physics.
..... Click the link for more information.
..... Click the link for more information.
insufficient context for those unfamiliar with the subject matter.
Please help [ improve the introduction] to meet Wikipedia's layout standards. You can discuss the issue on the talk page.
..... Click the link for more information.
Please help [ improve the introduction] to meet Wikipedia's layout standards. You can discuss the issue on the talk page.
..... Click the link for more information.
String theory is a model of fundamental physics, whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point particles that form the basis for the standard model of particle physics.
..... Click the link for more information.
..... Click the link for more information.
String theory is a model of fundamental physics, whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point particles that form the basis for the standard model of particle physics.
..... Click the link for more information.
..... Click the link for more information.
In theoretical physics, dilaton originally referred to a theoretical scalar field; as photon refers in one sense to the electromagnetic field. For the dilaton, also known as the radion or graviscalar, it is the scalar field which appears in Kaluza-Klein theory—as the
..... Click the link for more information.
..... Click the link for more information.
Conformal anomaly is an anomaly i.e. a quantum phenomenon that breaks the conformal symmetry of the classical theory.
In string theory, conformal symmetry on the worldsheet is a local Weyl symmetry and must therefore cancel if the theory is to be consistent.
..... Click the link for more information.
In string theory, conformal symmetry on the worldsheet is a local Weyl symmetry and must therefore cancel if the theory is to be consistent.
..... Click the link for more information.
In string theory, the worldsheet is a two-dimensional manifold which describes the embedding of the string in spacetime. It is a direct generalization of the familiar worldline of a particle in special and general relativity.
..... Click the link for more information.
..... Click the link for more information.
Bosonic string theory is the original version of string theory, developed in the late 1960s. Although it has many attractive features, it has a pair of features that render it unattractive as a physical model.
..... Click the link for more information.
..... Click the link for more information.
Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings. It is considered one of the most promising candidate theories of quantum gravity.
..... Click the link for more information.
..... Click the link for more information.
This article is copied from an article on Wikipedia.org - the free encyclopedia created and edited by online user community. The text was not checked or edited by anyone on our staff. Although the vast majority of the wikipedia encyclopedia articles provide accurate and timely information please do not assume the accuracy of any particular article. This article is distributed under the terms of GNU Free Documentation License.
Herod_Archelaus
