|
Global Anomaly
Primary Examples In theoretical physics, a global anomaly is a type of anomaly: in this particular case, it is a quantum effect that invalidates a large gauge transformation that would otherwise be preserved in the classical theory. This leads to an inconsistency in the theory because the space of configurations which is being integrated over in the functional integral involves both a configuration and the same configuration after a large gauge transformation has acted upon it and the sum of all such contributions is zero and the space of configurations cannot be split into connected components for which the integral is nonzero. Alternatively, the existence of a global anomaly implies that the measure of Feynman's functional integral cannot be defined globally. The adjective "global" refers to the properties of a group that are detectable via large gauge or diffeomorphism transformations, but are not detectable locally via infinitesimal transformations. For example, all f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
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 string. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dark Matter
In astronomy, dark matter is an invisible and hypothetical form of matter that does not interact with light or other electromagnetic radiation. Dark matter is implied by gravity, gravitational effects that cannot be explained by general relativity unless more matter is present than can be observed. Such effects occur in the context of Galaxy formation and evolution, formation and evolution of galaxies, gravitational lensing, the observable universe's current structure, mass position in galactic collisions, the motion of galaxies within galaxy clusters, and cosmic microwave background Anisotropy, anisotropies. Dark matter is thought to serve as gravitational scaffolding for cosmic structures. After the Big Bang, dark matter clumped into blobs along narrow filaments with superclusters of galaxies forming a cosmic web at scales on which entire galaxies appear like tiny particles. In the standard Lambda-CDM model of cosmology, the mass–energy equivalence, mass–energy content o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Unparticle Physics
In theoretical physics, unparticle physics is a speculative theory that conjectures a form of matter that cannot be explained in terms of particles using the Standard Model of particle physics, because its components are scale invariant. Howard Georgi proposed this theory in two 2007 papers, "Unparticle Physics" and "Another Odd Thing About Unparticle Physics". His papers were followed by further work by other researchers into the properties and phenomenology of unparticle physics and its potential impact on particle physics, astrophysics, cosmology, CP violation, lepton flavour violation, muon decay, neutrino oscillations, and supersymmetry. Background All particles exist in states that may be characterized by a certain energy, momentum and mass. In most of the Standard Model of particle physics, particles of the same type cannot exist in another state with all these properties scaled up or down by a common factor – electrons, for example, always have the same mass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Quantum Field Theories
In gauge theory and mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory that computes topological invariants. While TQFTs were invented by physicists, they are also of mathematical interest, being related to, among other things, knot theory and the theory of four-manifolds in algebraic topology, and to the theory of moduli spaces in algebraic geometry. Donaldson, Jones, Witten, and Kontsevich have all won Fields Medals for mathematical work related to topological field theory. In condensed matter physics, topological quantum field theories are the low-energy effective theories of topologically ordered states, such as fractional quantum Hall states, string-net condensed states, and other strongly correlated quantum liquid states. Overview In a topological field theory, correlation functions do not depend on the metric of spacetime. This means that the theory is not sensitive to changes in the shape ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Higgs Mechanism
In the Standard Model of particle physics, the Higgs mechanism is essential to explain the Mass generation, generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles, the other being fermions) would be considered Massless particle, massless, but measurements show that the W boson, W+, W−, and Z boson, Z0 bosons actually have relatively large masses of around . The Higgs field resolves this conundrum. The simplest description of the mechanism adds to the Standard Model a quantum field (the Higgs boson, Higgs field), which permeates all of space. Below some extremely high temperature, the field causes spontaneous symmetry breaking during interactions. The breaking of symmetry triggers the Higgs mechanism, causing the bosons with which it interacts to have mass. In the Standard Model, the phrase "Higgs mechanism" refers specifically to the generation of masses for the W and Z bosons, W±, and Z Weak for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weak Hypercharge
In the Standard Model (mathematical formulation), Standard Model of electroweak interactions of particle physics, the weak hypercharge is a quantum number relating the electric charge and the third component of weak isospin. It is frequently denoted Y_\mathsf and corresponds to the gauge symmetry U(1). It is Conservation law (physics), conserved (only terms that are overall weak-hypercharge neutral are allowed in the Lagrangian). However, one of the interactions is with the Higgs field. Since the Higgs field vacuum expectation value is nonzero, particles interact with this field all the time even in vacuum. This changes their weak hypercharge (and weak isospin ). Only a specific combination of them, \ Q = T_3 + \tfrac\, Y_\mathsf\ (electric charge), is conserved. Mathematically, weak hypercharge appears similar to the Gell-Mann–Nishijima formula for the hypercharge of strong interactions (which is not conserved in weak interactions and is zero for leptons). In the electroweak ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
B − L
In particle physics, ''B'' − ''L'' (pronounced "bee minus ell") is a quantum number which is the difference between the baryon number () and the lepton number () of a quantum system. Details This quantum number is the charge of a global/ gauge U(1) symmetry in some Grand Unified Theory models, called . Unlike baryon number alone or lepton number alone, this hypothetical symmetry would not be broken by chiral anomalies or gravitational anomalies, as long as this symmetry is global, which is why this symmetry is often invoked. If exists as a symmetry, then for the seesaw mechanism to work has to be spontaneously broken to give the neutrinos a nonzero mass. The anomalies that would break baryon number conservation and lepton number conservation individually cancel in such a way that is always conserved. One hypothetical example is proton decay where a proton () would decay into a pion () and positron (). The weak hypercharge is related to via X + 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baryon
In particle physics, a baryon is a type of composite particle, composite subatomic particle that contains an odd number of valence quarks, conventionally three. proton, Protons and neutron, neutrons are examples of baryons; because baryons are composed of quarks, they belong to the hadron list of particles, family of particles. Baryons are also classified as fermions because they have half-integer Spin (physics), spin. The name "baryon", introduced by Abraham Pais, comes from the Ancient Greek, Greek word for "heavy" (βαρύς, ''barýs''), because, at the time of their naming, most known elementary particles had lower masses than the baryons. Each baryon has a corresponding antiparticle (antibaryon) where their corresponding antiquarks replace quarks. For example, a proton is made of two up quarks and one down quark; and its corresponding antiparticle, the antiproton, is made of two up antiquarks and one down antiquark. Baryons participate in the residual strong force, which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cobordism
In mathematics, cobordism is a fundamental equivalence relation on the class of compact space, compact manifolds of the same dimension, set up using the concept of the boundary (topology), boundary (French ''wikt:bord#French, bord'', giving ''cobordism'') of a manifold. Two manifolds of the same dimension are ''cobordant'' if their disjoint union is the ''boundary'' of a compact manifold one dimension higher. The boundary of an (n+1)-dimensional manifold W is an n-dimensional manifold \partial W that is closed, i.e., with empty boundary. In general, a closed manifold need not be a boundary: cobordism theory is the study of the difference between all closed manifolds and those that are boundaries. The theory was originally developed by René Thom for smooth manifolds (i.e., differentiable), but there are now also versions for Piecewise linear manifold, piecewise linear and topological manifolds. A ''cobordism'' between manifolds M and N is a compact manifold W whose boundary is th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
