[permalink] [id link]

Every quantum field theory satisfying certain technical assumptions about its S-matrix that has non-trivial interactions can only have a symmetry Lie algebra which is always a direct product of the Poincaré group and an internal group if there is a mass gap: no mixing between these two is possible.

from
Wikipedia

## Some Related Sentences

Every and quantum

__Every__isolated unstable black hole decays rapidly to

**a**stable black hole ;

**and**( modulo

__quantum__fluctuations ) stable black holes

**can**be completely described ( in

**a**Cartesian coordinate system ) at any moment in time by

**these**eleven numbers

**:**

__Every__

__quantum__mechanical observable corresponds to

**a**unique function or distribution on phase space,

**and**vice versa, as specified by Hermann Weyl ( 1927 )

**and**supplemented by John von Neumann ( 1931 ); Eugene Wigner ( 1932 );

**and**, in

**a**grand synthesis, by H J Groenewold ( 1946 ).

__Every__computer must be compatible with

**the**principles

**of**information

**theory**, statistical thermodynamics,

**and**

__quantum__mechanics

**.**

Every and field

__Every__

__field__

**has**

**an**algebraic extension

**which**

**is**algebraically closed ( called

**its**algebraic closure ), but proving this in general requires some form

**of**

**the**axiom

**of**choice

**.**

__Every__time

**an**MTA receives

**an**email message, it adds

**a**< tt > Received </ tt > trace header

__field__to

**the**top

**of**

**the**header

**of**

**the**message, thereby building

**a**sequential record

**of**MTAs handling

**the**message

**.**

__Every__ordered

__field__

**is**

**a**formally real

__field__, i

**.**e., 0 cannot be written as

**a**sum

**of**nonzero squares

**.**

__Every__instruction consists

**of**

**a**9-bit opcode,

**a**4-bit register code,

**and**

**a**23-bit effective address

__field__,

**which**consists in turn

**of**

**a**1-bit indirect bit,

**a**4-bit register code,

**and**

**an**18-bit offset

**.**

__Every__

__field__

**theory**

**of**particle physics

**is**based on

**certain**symmetries

**of**nature whose existence

**is**deduced from observations

**.**

__Every__planetary body ( including

**the**Earth )

**is**surrounded by

**its**own gravitational

__field__,

**which**exerts

**an**attractive force on all objects

**.**

__Every__prime ideal P in

**a**Boolean ring R

**is**maximal

**:**

**the**quotient ring R / P

**is**

**an**integral domain

**and**also

**a**Boolean ring, so it

**is**isomorphic to

**the**

__field__F < sub > 2 </ sub >,

**which**shows

**the**maximality

**of**P

**.**Since maximal ideals are

**always**prime, prime ideals

**and**maximal ideals coincide in Boolean rings

**.**

__Every__year,

**the**British Political Studies Association awards

**the**Walter Bagehot Prize for

**the**best dissertation in

**the**

__field__

**of**government

**and**public administration

**.**

__Every__polynomial in

**can**be factorized into polynomials

**that**are irreducible over F

**.**This factorization

**is**unique up to permutation

**of**

**the**factors

**and**

**the**multiplication

**of**

**the**factors by nonzero constants from F ( because

**the**ring

**of**polynomials over

**a**

__field__

**is**

**a**unique factorization domain whose units are

**the**nonzero constant polynomials ).

__Every__quadratic form q in n variables over

**a**

__field__

**of**characteristic not equal to 2

**is**equivalent to

**a**diagonal form

__Every__kind

**of**material

**has**unique magnetic properties, even those

**that**we do not think

**of**as being “ magnetic .” Different materials below

**the**ground

**can**cause local disturbances in

**the**Earth ’ s magnetic

__field__

**that**are detectable with sensitive magnetometers

**.**

Every and theory

* Duality

**:**__Every__statement, theorem, or definition in category__theory__**has****a**dual**which****is**essentially obtained by " reversing all**the**arrows ".
While also refining Galen's erroneous

__theory__**of****the**pulse, Avicenna provided**the**first correct explanation**of**pulsation**:**"__Every__beat**of****the**pulse comprises**two**movements**and****two**pauses**.**__Every__epimorphism in this algebraic sense

**is**

**an**epimorphism in

**the**sense

**of**category

__theory__, but

**the**converse

**is**not true in all categories

**.**

__Every__one

**of**

**the**features encompassed by

**the**

__theory__still requires

**a**reason for it to be maintained after hominids left

**the**aquatic environment

**.**

" Some also hold to

**the**__theory__**that**Kidd conspired with Henry__Every__**and**Oak Island was used as**a**pseudo community bank**between****the****two****.****:**

__Every__countable

__theory__

**which**

**is**satisfiable in

**a**model M,

**is**satisfiable in

**a**countable substructure

**of**M

**.**

Iwasawa worked with so-called-extensions

**:**infinite extensions**of****a**number**field**with Galois**group**isomorphic to**the**additive**group****of**p-adic integers for some prime p**.**__Every__closed subgroup**of****is****of****the**form, so by Galois__theory__, a-extension**is****the**same thing as**a**tower**of**fields such**that****.**
Is fundamental for

**the**many-body__theory__**that**__Every__operator**can**be expressed in terms**of**annihilation**and**creation operators**.**__Every__Skolem

__theory__

**is**model complete, i

**.**e

**.**every substructure

**of**

**a**model

**is**

**an**elementary substructure

**.**

__Every__issue

**of**

**the**magazine opens with

**a**description

**of**The Skeptics Society

**and**

**its**mission statement,

**which**

**is**to explore subjects such as creationism, pyramid power, Bigfoot, pseudohistorical claims ( as in

**the**examples

**of**Holocaust denial

**and**extreme Afrocentrism ),

**the**use or misuse

**of**

__theory__

**and**statistics, conspiracy theories, urban myths, witch-hunts,

**mass**hysterias, genius

**and**intelligence,

**and**cultural influences on science, as well as controversies involving protosciences at

**the**leading edge

**of**established science,

**and**even fads like cryonics

**and**low-carb diets

**.**

__Every__proper subgroup

**of**G

**can**be assumed

**a**solvable

**group**, meaning

**that**much

__theory__

**of**such subgroups could be applied

**.**

__Every__major Korean neo-Confucianist shared Toegye's preoccupation with single-mindedness,

**which**signalled new stress on praxis in

**the**development

**of**Korean neo-Confucianism

**:**

**the**fusion

**of**

**the**metaphysical

**and**

**the**physical

**is**better brought

**about**through action than speculation, important as

__theory__might be

**.**

__Every__

__theory__

**which**refuses to ascribe to God

**an**attribute

**which**

**is**essential to

**a**worthy conception

**of**His character

**is**anti-theistic

**.**

0.909 seconds.