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Super Virasoro Algebra
In mathematical physics, a super Virasoro algebra is an extension of the Virasoro algebra (named after Miguel Ángel Virasoro) to a Lie superalgebra. There are two extensions with particular importance in superstring theory: the Ramond algebra (named after Pierre Ramond) and the Neveu–Schwarz algebra (named after André Neveu and John Henry Schwarz). Both algebras have ''N'' = 1 supersymmetry and an even part given by the Virasoro algebra. They describe the symmetries of a superstring in two different sectors, called the Ramond sector and the Neveu–Schwarz sector. The ''N'' = 1 super Virasoro algebras There are two minimal extensions of the Virasoro algebra with ''N'' = 1 supersymmetry: the Ramond algebra and the Neveu–Schwarz algebra. They are both Lie superalgebras whose even part is the Virasoro algebra: this Lie algebra has a basis consisting of a central element ''C'' and generators ''L''''m'' (for integer ''m'') satisfying L_m , L_n = ( m - n ) L_ + \frac m ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Physics
Mathematical physics refers to the development of mathematical methods for application to problems in physics. The '' Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics (also known as physical mathematics). Scope There are several distinct branches of mathematical physics, and these roughly correspond to particular historical periods. Classical mechanics The rigorous, abstract and advanced reformulation of Newtonian mechanics adopting the Lagrangian mechanics and the Hamiltonian mechanics even in the presence of constraints. Both formulations are embodied in analytical mechanics and lead to understanding the deep interplay of the notions of symmetry and conserved quantities during the dynamical evoluti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stephen Shenker
Stephen Hart Shenker (born 1953) is an American theoretical physicist who works on string theory. He is a professor at Stanford University and former director of the Stanford Institute for Theoretical Physics. His brother Scott Shenker is a computer scientist. Work Shenker's contributions to physics include: * Basic results on the phase structure of gauge theories (with Eduardo Fradkin) * Basic results on two dimensional conformal field theory and its relation to string theory (with Daniel Friedan, Emil Martinec, Zongan Qiu, and others) * The nonperturbative formulation of matrix models of low-dimensional string theory, the first nonperturbative definitions of string theory (with Michael R. Douglas) * The discovery of distinctively stringy nonperturbative effects in string theory, later understood to be caused by D-branes. These effects play a major role in string dynamics * The discovery of Matrix Theory, the first nonperturbative definition of String/M theory in a physica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Worldsheet
In string theory, a worldsheet is a two-dimensional manifold which describes the embedding of a string in spacetime. The term was coined by Leonard Susskind as a direct generalization of the world line concept for a point particle in special and general relativity. The type of string, the geometry of the spacetime in which it propagates, and the presence of long-range background fields (such as gauge fields) are encoded in a two-dimensional conformal field theory defined on the worldsheet. For example, the bosonic string in 26 dimensions has a worldsheet conformal field theory consisting of 26 free scalar bosons. Meanwhile, a superstring worldsheet theory in 10 dimensions consists of 10 free scalar fields and their fermionic superpartners. Mathematical formulation Bosonic string We begin with the classical formulation of the bosonic string. First fix a d-dimensional flat spacetime (d-dimensional Minkowski space), M, which serves as the ambient space for the strin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boundary Value Problem
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. A large class of important boundary value problems are the Sturm–Liouville problems. The analysis of these problems involves the eigenfunctions of a differential operator. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differentia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closed String
In physics, a string is a physical entity postulated in string theory and related subjects. Unlike elementary particles, which are zero-dimensional or point-like by definition, strings are one-dimensional extended entities. Researchers often have an interest in string theories because theories in which the fundamental entities are strings rather than point particles automatically have many properties that some physicists expect to hold in a fundamental theory of physics. Most notably, a theory of strings that evolve and interact according to the rules of quantum mechanics will automatically describe quantum gravity. Overview In string theory, the strings may be open (forming a segment with two endpoints) or closed (forming a loop like a circle) and may have other special properties. Prior to 1995, there were five known versions of string theory incorporating the idea of supersymmetry, which differed in the type of strings and in other aspects. Today these different string th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermionic Field
In quantum field theory, a fermionic field is a quantum field whose quanta are fermions; that is, they obey Fermi–Dirac statistics. Fermionic fields obey canonical anticommutation relations rather than the canonical commutation relations of bosonic fields. The most prominent example of a fermionic field is the Dirac field, which describes fermions with spin-1/2: electrons, protons, quarks, etc. The Dirac field can be described as either a 4-component spinor or as a pair of 2-component Weyl spinors. Spin-1/2 Majorana fermions, such as the hypothetical neutralino, can be described as either a dependent 4-component Majorana spinor or a single 2-component Weyl spinor. It is not known whether the neutrino is a Majorana fermion or a Dirac fermion; observing neutrinoless double-beta decay experimentally would settle this question. Basic properties Free (non-interacting) fermionic fields obey canonical anticommutation relations; i.e., involve the anticommutators = ''ab'' + ''ba'', r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neveu-Schwarz Boundary Conditions
In mathematical physics, a super Virasoro algebra is an extension of the Virasoro algebra (named after Miguel Ángel Virasoro) to a Lie superalgebra. There are two extensions with particular importance in superstring theory: the Ramond algebra (named after Pierre Ramond) and the Neveu–Schwarz algebra (named after André Neveu and John Henry Schwarz). Both algebras have ''N'' = 1 supersymmetry and an even part given by the Virasoro algebra. They describe the symmetries of a superstring in two different sectors, called the Ramond sector and the Neveu–Schwarz sector. The ''N'' = 1 super Virasoro algebras There are two minimal extensions of the Virasoro algebra with ''N'' = 1 supersymmetry: the Ramond algebra and the Neveu–Schwarz algebra. They are both Lie superalgebras whose even part is the Virasoro algebra: this Lie algebra has a basis consisting of a central element ''C'' and generators ''L''''m'' (for integer ''m'') satisfying L_m , L_n = ( m - n ) L_ + \frac m ( m^2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neveu-Schwarz Boundary Condition
In mathematical physics, a super Virasoro algebra is an extension of the Virasoro algebra (named after Miguel Ángel Virasoro) to a Lie superalgebra. There are two extensions with particular importance in superstring theory: the Ramond algebra (named after Pierre Ramond) and the Neveu–Schwarz algebra (named after André Neveu and John Henry Schwarz). Both algebras have ''N'' = 1 supersymmetry and an even part given by the Virasoro algebra. They describe the symmetries of a superstring in two different sectors, called the Ramond sector and the Neveu–Schwarz sector. The ''N'' = 1 super Virasoro algebras There are two minimal extensions of the Virasoro algebra with ''N'' = 1 supersymmetry: the Ramond algebra and the Neveu–Schwarz algebra. They are both Lie superalgebras whose even part is the Virasoro algebra: this Lie algebra has a basis consisting of a central element ''C'' and generators ''L''''m'' (for integer ''m'') satisfying L_m , L_n = ( m - n ) L_ + \frac m ( m^2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neveu–Schwarz Boundary Conditions
In mathematical physics, a super Virasoro algebra is an extension of the Virasoro algebra (named after Miguel Ángel Virasoro) to a Lie superalgebra. There are two extensions with particular importance in superstring theory: the Ramond algebra (named after Pierre Ramond) and the Neveu–Schwarz algebra (named after André Neveu and John Henry Schwarz). Both algebras have ''N'' = 1 supersymmetry and an even part given by the Virasoro algebra. They describe the symmetries of a superstring in two different sectors, called the Ramond sector and the Neveu–Schwarz sector. The ''N'' = 1 super Virasoro algebras There are two minimal extensions of the Virasoro algebra with ''N'' = 1 supersymmetry: the Ramond algebra and the Neveu–Schwarz algebra. They are both Lie superalgebras whose even part is the Virasoro algebra: this Lie algebra has a basis consisting of a central element ''C'' and generators ''L''''m'' (for integer ''m'') satisfying L_m , L_n = ( m - n ) L_ + \frac m ( m^2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neveu–Schwarz Boundary Condition
In mathematical physics, a super Virasoro algebra is an extension of the Virasoro algebra (named after Miguel Ángel Virasoro) to a Lie superalgebra. There are two extensions with particular importance in superstring theory: the Ramond algebra (named after Pierre Ramond) and the Neveu–Schwarz algebra (named after André Neveu and John Henry Schwarz). Both algebras have ''N'' = 1 supersymmetry and an even part given by the Virasoro algebra. They describe the symmetries of a superstring in two different sectors, called the Ramond sector and the Neveu–Schwarz sector. The ''N'' = 1 super Virasoro algebras There are two minimal extensions of the Virasoro algebra with ''N'' = 1 supersymmetry: the Ramond algebra and the Neveu–Schwarz algebra. They are both Lie superalgebras whose even part is the Virasoro algebra: this Lie algebra has a basis consisting of a central element ''C'' and generators ''L''''m'' (for integer ''m'') satisfying L_m , L_n = ( m - n ) L_ + \frac m ( m^2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ramond Boundary Conditions
In mathematical physics, a super Virasoro algebra is an extension of the Virasoro algebra (named after Miguel Ángel Virasoro) to a Lie superalgebra. There are two extensions with particular importance in superstring theory: the Ramond algebra (named after Pierre Ramond) and the Neveu–Schwarz algebra (named after André Neveu and John Henry Schwarz). Both algebras have ''N'' = 1 supersymmetry and an even part given by the Virasoro algebra. They describe the symmetries of a superstring in two different sectors, called the Ramond sector and the Neveu–Schwarz sector. The ''N'' = 1 super Virasoro algebras There are two minimal extensions of the Virasoro algebra with ''N'' = 1 supersymmetry: the Ramond algebra and the Neveu–Schwarz algebra. They are both Lie superalgebras whose even part is the Virasoro algebra: this Lie algebra has a basis consisting of a central element ''C'' and generators ''L''''m'' (for integer ''m'') satisfying L_m , L_n = ( m - n ) L_ + \frac m ( m^2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ramond Boundary Condition
In mathematical physics, a super Virasoro algebra is an extension of the Virasoro algebra (named after Miguel Ángel Virasoro) to a Lie superalgebra. There are two extensions with particular importance in superstring theory: the Ramond algebra (named after Pierre Ramond) and the Neveu–Schwarz algebra (named after André Neveu and John Henry Schwarz). Both algebras have ''N'' = 1 supersymmetry and an even part given by the Virasoro algebra. They describe the symmetries of a superstring in two different sectors, called the Ramond sector and the Neveu–Schwarz sector. The ''N'' = 1 super Virasoro algebras There are two minimal extensions of the Virasoro algebra with ''N'' = 1 supersymmetry: the Ramond algebra and the Neveu–Schwarz algebra. They are both Lie superalgebras whose even part is the Virasoro algebra: this Lie algebra has a basis consisting of a central element ''C'' and generators ''L''''m'' (for integer ''m'') satisfying L_m , L_n = ( m - n ) L_ + \frac m ( m^2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
