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CCR algebra

In quantum field theory, if V is a real vector space equipped with a nonsingular real antisymmetric bilinear form (,) (i.e. a symplectic vector space), the unital
- -algebra generated by elements of V subject to the relations :

fg-gf=i(f,g)

:f
- =f for any f, g in V is called the canonical commutation relations (CCR) algebra. The uniqueness of the representations of this algebra when V is finite dimensional is discussed in the Stone-von Neumann theorem. There is also a corresponding unital C
- -algebra, often referred to as the Weyl form of the algebra, generated by e^if subject to :

e^e^=e^

e^e^=e^e^e^

:(e^if)
- =e^-if for real numbers c₁, c₂. If V is equipped with a nonsingular real symmetric bilinear form (,) instead, the unital
- -algebra generated by the elements of V subject to the relations :

fg+gf=(f,g)

:f
- =f for any f, g in V is called the canonical anticommutation relations (CAR) algebra. If V is a real Z₂-graded vector space equipped with a nonsingular antisymmetric bilinear superform (,) (i.e. (g,f)=-(-1)^|f||g|(g,f) ) such that (f,g) is real if either f or g is an even element and imaginary if both of them are odd, the unital
- -algebra generated by the elements of V subject to the relations :

fg-(-1)^gf=i(f,g)

:f
- =f, g
- =g for any two pure elements f, g in V is the obvious super generalization which unifies CCRs with CARs.

Motî:cråne (robinet)
cråne 2 [f.n.] 1. sôre di crombe taessale, avou ene broke k' on distoûne pu rserer, po prinde ene pitite cwantité d' likide d' on tonea. L' efant, rivnant del cåve, tot sbaré: - "Man, man, gn a... gn a..." Li mame, dismontêye: - "Tchante lu si t' nel sais dire !" L' efant, tot tchantant podbon: - "Gn a l' cråne (do tonea d' bire) k' a låtchî !" (ramexhné pa L. Mahin). Ny. kraan. 2. robinet (d' keuve) d'

Motî:cråne (addj.)
cråne 3 [addj.] 1. bon, bon ådla. Vola do cråne peket. F. excellent, fameux. >> cråne tins: bon tins. Cråne tins, dowai, enute ? F. propice, favorable. >> cråne idêye: boune idêye. Cråne idêye, la, di xhufler des årguedinnes, tot codant ås fenès ceréjhes (A. Laloux). Franwal: ahåyant po "génial".

Motî:Coûtchant
Coûtchant [o.n.] pont cardinål, metou a hintche so ene mape, wice ki l' solea s' coûtche u k' i boute foû (solea boutant), pa opôzucion å solea picant u levant (al pikete do djoû). On dit eto: Ouwess, Ombrant, Boutant, Solea-djus. Disfondowes:

Motî:coulot
coulot [o.n.] 1. plaece a costé do feu, el måjhone. Li londmwin, el coujhene, come ene ki n' a måy fwait k' çoula, elle arindjive tos les mets å coulot do feu, tot gruzinant si tchanson favorite (A. Lebrun). rl a: recouloter. F. coin de l'âtre. 2. boket d' on viyaedje, d' ene veye. Ele ni dmeure nén e nosse coulot. Nos avans aprin ki, di ç' tins la, gn aveut ene peclêye di ptits mestîs dins c' coulot la.

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CCR algebra

See also