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E8 Theory
"An Exceptionally Simple Theory of Everything" is a physics preprint proposing a basis for a unified field theory, often referred to as "E8 Theory", which attempts to describe all known fundamental interactions in physics and to stand as a possible theory of everything. The paper was posted to the physics arXiv by Antony Garrett Lisi on November 6, 2007, and was not submitted to a peer-reviewed scientific journal. The title is a pun on the algebra used, the Lie algebra of the largest "simple", " exceptional" Lie group, E8. The paper's goal is to describe how the combined structure and dynamics of all gravitational and Standard Model particle fields are part of the E8 Lie algebra. The theory is presented as an extension of the grand unified theory program, incorporating gravity and fermions. The theory received a flurry of media coverage, but also met with widespread skepticism. ''Scientific American'' reported in March 2008 that the theory was being "largely but not entirely igno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Model
The Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide, with the current formulation being finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then, proof of the top quark (1995), the tau neutrino (2000), and the Higgs boson (2012) have added further credence to the Standard Model. In addition, the Standard Model has predicted various properties of weak neutral currents and the W and Z bosons with great accuracy. Although the Standard Model is believed to be theoretically self-consistent and has demonstrated huge successes in providing experimental predictions, it leaves some physics beyond the standard m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SU(5)
In mathematics, the special unitary group of degree , denoted , is the Lie group of unitary matrices with determinant 1. The more general unitary matrices may have complex determinants with absolute value 1, rather than real 1 in the special case. The group operation is matrix multiplication. The special unitary group is a normal subgroup of the unitary group , consisting of all unitary matrices. As a compact classical group, is the group that preserves the standard inner product on \mathbb^n. It is itself a subgroup of the general linear group, \operatorname(n) \subset \operatorname(n) \subset \operatorname(n, \mathbb ). The groups find wide application in the Standard Model of particle physics, especially in the electroweak interaction and in quantum chromodynamics. The groups are important in quantum computing, as they represent the possible quantum logic gate operations in a quantum circuit with n qubits and thus 2^n basis states. (Alternatively, the more general ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grand Unified Theories
A Grand Unified Theory (GUT) is a model in particle physics in which, at high energies, the three gauge interactions of the Standard Model comprising the electromagnetic, weak, and strong forces are merged into a single force. Although this unified force has not been directly observed, many GUT models theorize its existence. If unification of these three interactions is possible, it raises the possibility that there was a grand unification epoch in the very early universe in which these three fundamental interactions were not yet distinct. Experiments have confirmed that at high energy the electromagnetic interaction and weak interaction unify into a single electroweak interaction. GUT models predict that at even higher energy, the strong interaction and the electroweak interaction will unify into a single electronuclear interaction. This interaction is characterized by one larger gauge symmetry and thus several force carriers, but one unified coupling constant. Unifying ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charge (physics)
In physics, a charge is any of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. Charges correspond to the time-invariant generators of a symmetry group, and specifically, to the generators that commute with the Hamiltonian. Charges are often denoted by the letter ''Q'', and so the invariance of the charge corresponds to the vanishing commutator ,H0, where H is the Hamiltonian. Thus, charges are associated with conserved quantum numbers; these are the eigenvalues ''q'' of the generator ''Q''. Abstract definition Abstractly, a charge is any generator of a continuous symmetry of the physical system under study. When a physical system has a symmetry of some sort, Noether's theorem implies the existence of a conserved current. The thing that "flows" in the current is the "charge", the charge is the generator of the (local) symmetry group. This charge is sometimes called the Noether charge. Thus, for exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lie Algebra Representation
In the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms of a vector space) in such a way that the Lie bracket is given by the commutator. In the language of physics, one looks for a vector space V together with a collection of operators on V satisfying some fixed set of commutation relations, such as the relations satisfied by the angular momentum operators. The notion is closely related to that of a representation of a Lie group. Roughly speaking, the representations of Lie algebras are the differentiated form of representations of Lie groups, while the representations of the universal cover of a Lie group are the integrated form of the representations of its Lie algebra. In the study of representations of a Lie algebra, a particular ring, called the universal enveloping algebra, associated with the Lie algebra plays an important role. The universa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weight (representation Theory)
In the mathematical field of representation theory, a weight of an algebra ''A'' over a field F is an algebra homomorphism from ''A'' to F, or equivalently, a one-dimensional representation of ''A'' over F. It is the algebra analogue of a multiplicative character of a group. The importance of the concept, however, stems from its application to representations of Lie algebras and hence also to representations of algebraic and Lie groups. In this context, a weight of a representation is a generalization of the notion of an eigenvalue, and the corresponding eigenspace is called a weight space. Motivation and general concept Given a set ''S'' of n\times n matrices over the same field, each of which is diagonalizable, and any two of which commute, it is always possible to simultaneously diagonalize all of the elements of ''S''.In fact, given a set of commuting matrices over an algebraically closed field, they are simultaneously triangularizable, without needing to assume that they are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Root System
In mathematics, a root system is a configuration of vectors in a Euclidean space satisfying certain geometrical properties. The concept is fundamental in the theory of Lie groups and Lie algebras, especially the classification and representation theory of semisimple Lie algebras. Since Lie groups (and some analogues such as algebraic groups) and Lie algebras have become important in many parts of mathematics during the twentieth century, the apparently special nature of root systems belies the number of areas in which they are applied. Further, the classification scheme for root systems, by Dynkin diagrams, occurs in parts of mathematics with no overt connection to Lie theory (such as singularity theory). Finally, root systems are important for their own sake, as in spectral graph theory. Definitions and examples As a first example, consider the six vectors in 2-dimensional Euclidean space, R2, as shown in the image at the right; call them roots. These vectors Linear span, s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eigenvalues
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by \lambda, is the factor by which the eigenvector is scaled. Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated. Formal definition If is a linear transformation from a vector space over a field into itself and is a nonzero vector in , then is an eigenvector of if is a scalar multiple of . This can be written as T(\mathbf) = \lambda \mathbf, where is a scalar in , known as the eigenvalue, characteristic value, or characteristic root ass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to an open subset of n-dimensional Euclidean space. One-dimensional manifolds include lines and circles, but not lemniscates. Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, and also the Klein bottle and real projective plane. The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows complicated structures to be described in terms of well-understood topological properties of simpler spaces. Manifolds naturally arise as solution sets of systems of equations and as graphs of functions. The concept has applications in computer-graphics given the need to associate pictures with coordinates (e.g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermion
In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks and leptons and all composite particles made of an odd number of these, such as all baryons and many atoms and nuclei. Fermions differ from bosons, which obey Bose–Einstein statistics. Some fermions are elementary particles (such as electrons), and some are composite particles (such as protons). For example, according to the spin-statistics theorem in relativistic quantum field theory, particles with integer spin are bosons. In contrast, particles with half-integer spin are fermions. In addition to the spin characteristic, fermions have another specific property: they possess conserved baryon or lepton quantum numbers. Therefore, what is usually referred to as the spin-statistics relation is, in fact, a spin statistics-quantum numb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Communications In Mathematical Physics
''Communications in Mathematical Physics'' is a peer-reviewed academic journal published by Springer. The journal publishes papers in all fields of mathematical physics, but focuses particularly in analysis related to condensed matter physics, statistical mechanics and quantum field theory, and in operator algebras, quantum information and relativity. History Rudolf Haag conceived this journal with Res Jost, and Haag became the Founding Chief Editor. The first issue of ''Communications in Mathematical Physics'' appeared in 1965. Haag guided the journal for the next eight years. Then Klaus Hepp succeeded him for three years, followed by James Glimm, for another three years. Arthur Jaffe began as chief editor in 1979 and served for 21 years. Michael Aizenman became the fifth chief editor in the year 2000 and served in this role until 2012. The current editor-in-chief is Horng-Tzer Yau. Archives Articles from 1965 to 1997 are available in electronic form free of charge, via Pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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