|
Vafa–Witten Theorem
In theoretical physics, the Vafa–Witten theorem, named after Cumrun Vafa and Edward Witten, is a theorem that shows that vector-like global symmetries (those that transform as expected under reflections) such as isospin and baryon number in vector-like gauge theories like quantum chromodynamics cannot be spontaneously broken as long as the theta angle is zero. This theorem can be proved by showing the exponential fall off of the propagator of fermions. See also *F-theory In theoretical physics, F-theory is a branch of string theory developed by Iranian-American physicist Cumrun Vafa. The new vacua described by F-theory were discovered by Vafa and allowed string theorists to construct new realistic vacua — in ... References * * Gauge theories Theorems in quantum mechanics {{quantum-stub ... [...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] |
Cumrun Vafa
Cumrun Vafa (, ; born 1 August 1960) is an Iranian-American theoretical physicist and the Hollis Professor of Mathematicks and Natural Philosophy at Harvard University. Early life and education Cumrun Vafa was born in Tehran, Iran on 1 August 1960. He became interested in physics as a young child, specifically how the moon was not falling from the sky, and he later grew his interests in math by high school and was fascinated by how mathematics could predict the movement of objects. He graduated from Alborz High School in Tehran and moved to the United States in 1977 to study at university. He received a B.S. in mathematics and physics from the Massachusetts Institute of Technology (MIT) in 1981. He received his Ph.D. in physics from Princeton University in 1985 after completing a doctoral dissertation, titled "Symmetries, inequalities and index theorems", under the supervision of Edward Witten. Academia After his PhD degree, Vafa became a junior fellow via the Harvard Soc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edward Witten
Edward Witten (born August 26, 1951) is an American theoretical physics, theoretical physicist known for his contributions to string theory, topological quantum field theory, and various areas of mathematics. He is a professor emeritus in the school of natural sciences at the Institute for Advanced Study in Princeton, New Jersey, Princeton. Witten is a researcher in string theory, quantum gravity, supersymmetry, supersymmetric quantum field theories, and other areas of mathematical physics. Witten's work has also significantly impacted pure mathematics. In 1990, he became the first physicist to be awarded a Fields Medal by the International Mathematical Union, for his mathematical insights in physics, such as his 1981 proof of the positive energy theorem in general relativity, and his interpretation of the Vaughan Jones, Jones invariants of knots as Feynman integrals. He is considered the practical founder of M-theory.Duff 1998, p. 65 Early life and education Witten was born on A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theorem
In mathematics and formal logic, a theorem is a statement (logic), statement that has been Mathematical proof, proven, or can be proven. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In mainstream mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice (ZFC), or of a less powerful theory, such as Peano arithmetic. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems. Moreover, many authors qualify as ''theorems'' only the most important results, and use the terms ''lemma'', ''proposition'' and ''corollary'' for less important theorems. In mathematical logic, the concepts of theorems and proofs have been formal system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Global Symmetry
The symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation. A family of particular transformations may be ''continuous'' (such as rotation of a circle) or ''discrete'' (e.g., reflection of a bilaterally symmetric figure, or rotation of a regular polygon). Continuous and discrete transformations give rise to corresponding types of symmetries. Continuous symmetries can be described by Lie groups while discrete symmetries are described by finite groups (see ''Symmetry group''). These two concepts, Lie and finite groups, are the foundation for the fundamental theories of modern physics. Symmetries are frequently amenable to mathematical formulations such as group representations and can, in addition, be exploited to simplify many problems. Arguably the most important example of a symmetry in physics is that the speed of light has the same value in all frames of re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isospin
In nuclear physics and particle physics, isospin (''I'') is a quantum number related to the up- and down quark content of the particle. Isospin is also known as isobaric spin or isotopic spin. Isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions of baryons and mesons. The name of the concept contains the term ''spin'' because its quantum mechanical description is mathematically similar to that of angular momentum (in particular, in the way it couples; for example, a proton–neutron pair can be coupled either in a state of total isospin 1 or in one of 0). But unlike angular momentum, it is a dimensionless quantity and is not actually any type of spin. Before the concept of quarks was introduced, particles that are affected equally by the strong force but had different charges (e.g. protons and neutrons) were considered different states of the same particle, but having isospin values related to the number of charge states. A close exami ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baryon Number
In particle physics, the baryon number (B) is an additive quantum number of a system. It is defined as B = \frac(n_\text - n_), where is the number of quarks, and is the number of antiquarks. Baryons (three quarks) have B = +1, mesons (one quark, one antiquark) have B = 0, and antibaryons (three antiquarks) have B = −1. Exotic hadrons like pentaquarks (four quarks, one antiquark) and tetraquarks (two quarks, two antiquarks) are also classified as baryons and mesons depending on their baryon number. In the standard model B conservation is an accidental symmetry which means that it appears in the standard model but is often violated when going beyond it. Physics beyond the Standard Model theories that contain baryon number violation are, for example, Standard Model with extra dimensions, Supersymmetry, Grand Unified Theory and String theory. Baryon number vs. quark number Quarks carry not only electric charge, but also charges such as color charge and weak iso ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Chromodynamics
In theoretical physics, quantum chromodynamics (QCD) is the study of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group special unitary group, SU(3). The QCD analog of electric charge is a property called ''color''. Gluons are the force carriers of the theory, just as photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of particle physics. A large body of Quantum chromodynamics#Experimental tests, experimental evidence for QCD has been gathered over the years. QCD exhibits three salient properties: * Color confinement. Due to the force between two color charges remaining constant as they are separated, the energy grows until a quark–antiquark pair is mass–energy equivalence, spontaneously produced, turning ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spontaneous Symmetry Breaking
Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state spontaneously ends up in an asymmetric state. In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry. Overview The spontaneous symmetry breaking cannot happen in quantum mechanics that describes finite dimensional systems, due to Stone-von Neumann theorem (that states the uniqueness of Heisenberg commutation relations in finite dimensions). So spontaneous symmetry breaking can be observed only in infinite dimensional theories, as quantum field theories. By definition, spontaneous symmetry breaking requires the existence of physical laws which are invariant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theta Vacuum
In quantum field theory, the theta vacuum is the semi-classical vacuum state of non- abelian Yang–Mills theories specified by the vacuum angle ''θ'' that arises when the state is written as a superposition of an infinite set of topologically distinct vacuum states. The dynamical effects of the vacuum are captured in the Lagrangian formalism through the presence of a ''θ''-term which in quantum chromodynamics leads to the fine tuning problem known as the strong CP problem. It was discovered in 1976 by Curtis Callan, Roger Dashen, and David Gross, and independently by Roman Jackiw and Claudio Rebbi. Yang–Mills vacuum Topological vacua The semi-classical vacuum structure of non-abelian Yang–Mills theories is often investigated in Euclidean spacetime in some fixed gauge such as the temporal gauge A_0 = 0. Classical ground states of this theory have a vanishing field strength tensor which corresponds to pure gauge configurations A_i = i\Omega \nabla_i \Omega^, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
F-theory
In theoretical physics, F-theory is a branch of string theory developed by Iranian-American physicist Cumrun Vafa. The new vacua described by F-theory were discovered by Vafa and allowed string theorists to construct new realistic vacua — in the form of F-theory compactified on elliptically fibered Calabi–Yau four-folds. The letter "F" supposedly stands for "Father" in relation to "Mother"-theory. Compactifications F-theory is formally a 12-dimensional theory, but the only way to obtain an acceptable background is to compactify this theory on a two-torus. By doing so, one obtains type IIB superstring theory in 10 dimensions. The SL(2,Z) S-duality symmetry of the resulting type IIB string theory is manifest because it arises as the group of large diffeomorphisms of the two-dimensional torus. More generally, one can compactify F-theory on an elliptically fibered manifold ( elliptic fibration), i.e. a fiber bundle whose fiber is a two-dimensional torus (also calle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauge Theories
In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local transformations according to certain smooth families of operations (Lie groups). Formally, the Lagrangian is invariant under these transformations. The term "gauge" refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian of a physical system. The transformations between possible gauges, called gauge transformations, form a Lie group—referred to as the ''symmetry group'' or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field (usually a vector field) called the gauge field. Gauge fields are included in the Lagrangian to ensure its invariance under the local group transformations (called gauge invariance). When such a theory is quantized, the quanta of the g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
