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Topic: Glossary of field theory


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  Field theory (mathematics) - Wikipedia, the free encyclopedia
Field theory is a branch of mathematics which studies the properties of fields.
Galois, who did not have the term "field" in mind, is honored to be the first mathematician linking group theory and field theory.
For instance, the field of algebraic numbers is the algebraic closure of the field of rational numbers and the field of complex numbers is the algebraic closure of the field of real numbers.
en.wikipedia.org /wiki/Field_theory_(mathematics)   (331 words)

  
 Glossary
A theory of thunderstorm charge separation based upon the suggested occurrence of the Lenard effect in thunderclouds, that is, the separation of electric charge due to the breakup of water drops.
An avalanche cannot possibly begin until the local electric field strength is high enough to accelerate a free electron to the minimum ionizing speed in the space and time interval corresponding to one mean free path of the electron, for upon collision, the electron usually loss its forward motion in the direction of the field.
According to this theory, the lower negative charge of a thundercloud is generated by the accumulation there of raindrops which have captured predominantly negative ions in their descent through the cloud.
www.met.tamu.edu /personnel/faculty/orville/Glossary.htm   (11057 words)

  
 Field (mathematics)   (Site not responding. Last check: 2007-11-05)
In abstract algebra, a field is an algebraic structure in which the operations of addition, subtraction, multiplication, and division (except division by zero) may be performed and the associative, commutative, and distributive rules hold, which are familiar from the arithmetic of ordinary numbers.
Fields are important objects of study in algebra since they provide the proper generalization of number domains, such as the sets of rational numbers, real numbers, or complex numbers.
An algebraic extension of a field F is the smallest field containing F and a root of a irreducible polynomial p(x) in F[x].
usapedia.com /f/field-mathematics-.html   (1262 words)

  
 Field (mathematics) - Wikipedia, the free encyclopedia   (Site not responding. Last check: 2007-11-05)
The concept of a field is of use, for example, in defining vectors and matrices, two structures in linear algebra whose components can be elements of an arbitrary field.
For a given field F, the set F(X) of rational functions in the variable X with coefficients in F is a field; this is defined as the set of quotients of polynomials with coefficients in F.
The polynomial field F(x) is the field of fractions of polynomials in x with coefficients in F.
xahlee.org /_p/wiki/Field_(mathematics).html   (1204 words)

  
 [No title]
A field is a commutative ring (F, +, *) such that 0 does not equal 1 and all elements of F except 0 have a multiplicative inverse.
The surreal numbers form a Field containing the reals, and would be a field except for the fact that they are a proper class, not a set.
An algebraic extension of a field F is the smallest field containing F and a root of an irreducible polynomial p(x) in F[x].
en-cyclopedia.com /wiki/Field_(mathematics)   (1146 words)

  
 Glossary of field theory -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-11-05)
Subfield : A subfield of a field F is a (A set whose members are members of another set; a set contained within another set) subset of F which is closed under the field operation + and * of F and which, with these operations, forms itself a field.
Field homomorphism : A field homomorphism between two fields E and F is a (A mathematical relation such that each element of one set is associated with at least one element of another set) functionf : E → F
Fields, together with these homomorphisms, form a (A general concept that marks divisions or coordinations in a conceptual scheme) category.
www.absoluteastronomy.com /encyclopedia/g/gl/glossary_of_field_theory.htm   (1294 words)

  
 Glossary of field theory - Wikipedia, the free encyclopedia
Field theory is the branch of mathematics in which fields are studied.
The characteristic of the field F is the smallest positive integer n such that n·1 = 0; here n·1 stands for n summands 1 + 1 + 1 +...
The subject in which symmetry groups of differential equations are studied along the lines traditional in Galois theory.
en.wikipedia.org /wiki/Glossary_of_field_theory   (723 words)

  
 Wave-Guide: Glossary Containing EMF/EMR Terminology
Fields that are nonuniform over volumes comparable to the human body may occur due to highly directional sources, standing-waves, re-radiating sources or in the near field.
For FCC purposes, applies to human exposure to RF fields when the general public is exposed or in which persons who are exposed as a consequence of their employment may not be made fully aware of the potential for exposure or cannot exercise control over their exposure.
A field vector that is equal to the magnetic flux density divided by the permeability of the medium.
www.wave-guide.org /library/glossary.html   (7522 words)

  
 Glossary
Field line preservation--a property of fluids which are perfect conductors of electricity (including "ideal plasmas"), by which two particles which initially share the same field line, continue to do so into the future.
Mercury has a weak magnetic field, Mars and the Moon are magnetized in patches (probably on their surfaces) and Venus, although non-magnetic, has its own interaction with the solar wind, by means of its thick ionosphere.
The magnetic field observed at any point in space is a vector; other examples are velocity, acceleration, force and the electric field, which maps the electric force acting on ions and electrons.
www-spof.gsfc.nasa.gov /Education/gloss.html   (5877 words)

  
 NTU Info Centre: Field theory (mathematics)   (Site not responding. Last check: 2007-11-05)
The concept of fields was used implicitly by Niels Henrik Abel and Evariste Galois on the solvability of equations.
However it was Emil Artin who first developed the relationship of groups and fields in great details during 1928-1942.
The central concept of Galois theory is the algebraic extension of an underlying field.
www.nowtryus.com /article:Field_theory_(mathematics)   (305 words)

  
 Rupert Sheldrake Online
Darwin's theory of evolution by natural selection enabled this process to be thought of as blind and purposeless, and this interpretation is central to neo-Darwinism (q.v.), the dominant orthodoxy in modern biology.
Morphic fields are shaped and stabilized by morphic resonance from previous similar morphic units, which were under the influence of fields of the same kind.
It differs from Darwin's theory in that it denies the possibility of Lamarckian inheritance (q.v.); heredity is explained in terms of genes passed on by Mendelian inheritance (q.v.).
www.sheldrake.org /glossary   (3464 words)

  
 FIELD (MATHEMATICS) WEALTHY AND WISE FACT FINDER   (Site not responding. Last check: 2007-11-05)
In abstract_algebra, a field is an algebraic_structure in which the operations of addition, subtraction, multiplication and division (except division by zero) may be performed, and the same rules hold which are familiar from the arithmetic of ordinary numbers.
Fields are important objects of study in algebra since they provide a useful generalization of many number systems, such as the rational numbers, real numbers, and complex_numbers.
An algebraic_number_field is a finite field extension of the rational_numbers Q, that is, a field containing Q which has finite dimension as a vector_space over Q.
www.boostmoney.com /field_(mathematics)   (1494 words)

  
 natural theology > synopsis > 21 quantum field theory   (Site not responding. Last check: 2007-11-05)
The essential content of the special theory of relativity is that the laws of physics are the same in all inertial frames of reference.
Quantum field theory describes this process of the creation and annihilation of particles, telling us how frequently it will happen and what can be created from the annihilation of what.
Topics are incl;uded that are not usually found in books on quantum field theory, such as the Batalin-Vilkovsky formalism and its application to renomralisation and anomalies in gauge theories; the background field method; the effective field theory approach to symmetry breaking; critical phenomena; and superconductivity.
www.naturaltheology.net /Synopsis/s21Field.html   (1466 words)

  
 Number Theory Glossary
A field F2 is called an extension of another field F if F is contained in F2 as a subfield.
Fields with a finite number of elements are called Galois fields.
A Galois Field is a field with finite number of elements.
www.math.umbc.edu /~campbell/NumbThy/Class/Glossary.html   (827 words)

  
 Glossary
Field The region in which a particular type of force can be observed; depending on the force, one can thus speak of a gravity field, magnetic field, electric field (or when the two are linked by fast oscillations, electromagnetic field) and nuclear field.
Field line preservation A property of an ideal plasma, well approximated in real plasmas, characterizing the way the flow of plasma may deform the magnetic field in which it is embedded.
Milankovich theory -- Theory by which ice ages were caused by slow changes of the motion of the Earth in space, including the coupling between the 26 000 year cycle of the precession of the equinoxes and the annual variation of the Earth-Sun distance.
www-spof.gsfc.nasa.gov /stargaze/Sgloss.htm   (11162 words)

  
 Nonlinear Dynamics and Complex Systems Theory (Glossary)   (Site not responding. Last check: 2007-11-05)
The mean field theories are qualitatively quite successful in that they predict the existence of critical points and power law dependence of the various thermodynamic quantities near the critical point.
A theory introduced in 1972 to account for what the fossil record appears to suggest are a series of irregularly spaced periods of chaotic and rapid evolutionary change in what are otherwise long periods of evolutionary stasis.
It is also a universal theory in that it predicts that the global properties of complex systems are independent of the microscopic details of their structure, and is therefore consistent with the "the whole is greater than the sum of its parts" approach to complex systems.
www.cna.org /isaac/Glossb.htm   (8566 words)

  
 SUPERSTRINGS! Glossary
A special kind supersymmetric of point particle quantum field theory, in which the graviton is in a supermultiplet.
When both theories are at weak coupling they may look very different, however when one is at strong coupling and the other at weak coupling they describe exactly the same physics.
Therefore when one of the theories is on a very small circle the other theory is on a very large circle.
www.sukidog.com /jpierre/strings/glossary.htm   (930 words)

  
 ipedia.com: Glossary of field theory Article   (Site not responding. Last check: 2007-11-05)
; Subfield : A subfield of a field F is a subset of F which is closed under the field operation + and * of F and which, with these operations, forms itself a field.
; Algebraically closed field : A maximal algebraic extension field of F is its algebraic closure.
;Differential Galois theory: The subject in which symmetry groups of differential equations are studied along the lines traditional in Galois theory.
www.ipedia.com /glossary_of_field_theory.html   (843 words)

  
 A Glossary of Gifted Education   (Site not responding. Last check: 2007-11-05)
Interactionism - A social-psychological theory that the self is formed by interacting with others and that social life depends on the ability to imagine ourselves in other social roles.
Labeling theory - The proposition that labels placed on a person may lead him/her to act the role associated with the label whether or not it was initially accurate.
You may reprint all or part of the Glossary as long as the author and copyright holder is attributed and no content is altered.
members.aol.com /svennord/ed/GiftedGlossary.htm   (5589 words)

  
 Energy Science Made Simple...theory, applications, physics, chemistry, biology, wavicle, field, substratum, ...
Theories about how mass and energy behaved as they traveled through the universe were being developed long before Einstein stated his famous theories.
In 1986 the string theory and a little later the superstring theory [27], Membrane theory, and around 1998 the M-theory [29] were proposed which claimed that all matter and force particles are the result of different nodes of vibrating strings or membranes.
These fields are considered to be the product of matter, so the argument given is that there would be no fields and so no type of structure in the universe without matter.
www.benwiens.com /energy1.html   (20710 words)

  
 GLOSSARY OF FIELD THEORY   (Site not responding. Last check: 2007-11-05)
Field theory is the branch of mathematics in which fieldss are studied.
; Extension field : If F is a subfield of E then E is an extension field of F.
The two fields are then identical for all practical purposes.
www.websters-online-dictionary.org /definition/GLOSSARY+OF+FIELD+THEORY   (494 words)

  
 Synthetic Theory of Evolution: Glossary of Terms
the field of geology that studies the fossil record of ancient life forms.
Since no other fertilizer is usually applied, fields are abandoned after a few years, when crop yields go down, and clearing occurs elsewhere.
This is essentially a combination of Darwin's concept of natural selection, Mendel's basic genetics, along with the facts and theories of population genetics and molecular biology.
anthro.palomar.edu /synthetic/glossary.htm   (3918 words)

  
 unified field theory - a Whatis.com definition   (Site not responding. Last check: 2007-11-05)
Unified field theory is sometimes called the Theory of Everything (TOE, for short): the long-sought means of tying together all known phenomena to explain the nature and behavior of all matter and energy in existence.
The theory of relativity explains the nature and behavior of all phenomena on the macroscopic level (things that are visible to the naked eye); quantum theory explains the nature and behavior of all phenomena on the microscopic (atomic and subatomic) level.
The current quest for a unified field theory (sometimes called the holy grail of physicists) is largely focused on superstring theory and, in particular, on an adaptation known as M-theory.
searchsmb.techtarget.com /gDefinition/0,,sid44_gci554508,00.html   (435 words)

  
 [No title]   (Site not responding. Last check: 2007-11-05)
It is an introduction to the theory of Elliptic Curve Cryptography.
The field elements are given in hexadecimal, the curve's order in decimal form as h * n, where h (the "cofactor") is small and n is a large prime number.
For these fields the elliptic curve E(a, b) is defined to be the set of solutions of the equation y^2 = x^3 + ax + b plus the point at infinity 'o'.
www.phrack.org /phrack/63/p63-0x03_Linenoise.txt   (8698 words)

  
 Glossary: SLAC Virtual Visitor Center
The electric field E has both a magnitude and a direction at each point in space, and the magnitude and direction of the resulting force on a charge q at that point is given by F= qE.
String theory is a possible framework for constructing unified theories which include both the microscopic forces and gravity.
A unified field theory is one that attempts to combine any two or more of the known interaction types (strong, electromagnetic, weak and gravitational) in a single theory so that the two distinct types of interaction are seen as two different aspects of a single mathematical structure.
www2.slac.stanford.edu /vvc/glossary.html   (5563 words)

  
 Holocaust Glossary
In Nazi racial theory, a person of pure German "blood." The term "non-Aryan" was used to designate Jews, part-Jews and others of supposedly inferior racial stock.
Today, a field of trees planted in their honor at the Yad Vashem Holocaust Memorial in Jerusalem, Israel, commemorates their courage and compassion.
Socialism: A theory or system of social organization that advocates the ownership and control of land, capital, industry, etc. by the community as a whole.
fcit.coedu.usf.edu /holocaust/resource/glossary.htm   (4877 words)

  
 Theory: SLAC Virtual Visitor Center
The name given to the theory that best incorporates all observations to date in the particle realm is "the Standard Model".
Gravitational interactions have yet to be successfully incorporated into the quantum field theory and are a tiny effect in high energy particle collisions, so are ignored in the Standard Model.
Particle physics theories are written in mathematical language called relativistic quantum field theory.
www2.slac.stanford.edu /vvc/theory.html   (210 words)

  
 Ali-Baba.com » Science » Math » Algebra » Field Theory
Field Arithmetic Archive - This archive stores electronic preprints on the arithmetic of fields, Galois theory, model theory of fields, and related topics.
Field Theory and Polynomials - Section 12 of the Mathematical Atlas by Dave Rusin.
Galois Field Package - Allows the use of many Mathematica functions over finite fields without any modification; e.g solving linear equations, inverses, determinants, derivations, resultants.
www.bergersallemands.com /Science/Math/Algebra/Field_Theory   (298 words)

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