Download Geometric Quantization-Fundamentals of Classical and Relativistic Mechanics-Lecture Handout and more Exercises Classical and Relativistic Mechanics in PDF only on Docsity! A June 20857
A Tasle of Geomebere Qrotizehin
Th, Sebvsdmgen's eppraeds be QM, ye bbe He cory, Space
A of 2 cloecicad cy shen. gk ih 2 Riserannion mebre
& he. Bren a Hilbe-E spare UG, vel) phase. ual ve clas
se skates SN He corresponding questem system whee val
Ps He eesure Coming vo KR Riemann metre. qT
gentle grocbtekn, te the d cmsbeach He INbet pre
Fo Ue phese space xX, vlioh BR 2 sympleckic ron ibold
De. Broglie & fren Bebe a Sarne-beld vabiced e guotitohen
condita rihich picked oul He allowed “Gue-tom orbits”
~~
Brrdno the clessic al mes ts Sey , He heron ie osct th» or
habe. apn, .
It H. obit BR ome loop YX: S'->X, itt, en Alaved orbit
if Ue phese
ih X/k = ~~
docsity.com
109
where 0 is te commigd [-b. o X Ce X= TO
~ ad Ki Pls coset © fae). Hee te
se ten em He ecb GO Ae ph Plo XR &
Ha extended plese spce, 2 @/5 7, ulel appears & He
wore apport by Ci — Ke “eiorsk apprximtiw velelns
porlivle s by owes | So we ‘re demand Hel we get
Complete Consbrcbve ple lence _ UA on pobreles
Taoerenetn Comes beck om phase. whe (Le pele gees ~ Y,
Whe, X= T*Q we Lave
fa > fe 2 \
whee D may dat ilk aD=y.
Te Q = & )
D ~ we =dprd
A Pr UL
% Se Sou = ee ot p.
The Bob -Smmefebt quankeeln edie segs
e ‘Jou |
J, a= aenk =k
wha fa A mosh agrees wil, Be modem Cprmule (ne dVb |
docsity.com |
(2
3 June 2005
“The phese space i 2 sphery post pelicle of biol angele woe hn
je lo? rs
X, > TeR s ythe i$,
a sphere with, Poisson shrctuve sd.
Inyiee tyes =x fe, x3 my
Que cm check Het tha Comes far a sympleche ghructwe as
on X, :
2693 = as (dq , AF)
tr G& e@ multple of he sree 2-farm on ue sphere, Xx.
a)
novralited $e Hot ~~
{ Uo = Yay Coshe : not dnj* /)
x
Wher fs a mbegeal 7 Thee'’s @ bese. tht says cled
Dforn Sox cme vanileld Kis legeal fh be ny 2
§ w € Z.
s
Here we real, went
| # eZ (=!)
x i
j ~~
4
docsity.com
BB. Lag) = eZ
~ . i 3g 1 2j az
)
ie.
= a 2
jt Or2, Gi,
— te usued quetizala, comdibin GH ogele- pomedtum | When His
codibio bis, Hore exists 2 UCI) bedle P—?X; with e
connec FE vabsse curvebre F € XO, AA PS = OG mi)
=UOG, iR) is yn [aco
We the bald He ibe space H. ol shes of a gaocten
~~ a po Hicle asing P as Cows. We brn on Associated
Vera bundle
t= Px €
sig We Gd - give echo of acy ~ Cc. Toes sort of
bundle , wily € as Fibers | is Called 2 comple x _fme bundle
oe aseall a me b.-dle.
~
t Whe 2 comple x farchtan on the
A sechon, uy at a looks locelly
R docsity.com
4
phese spece* The (4, Ibe spre H; wf casigt of cerka
Sechons y of ©, We sholdad se Al L? cecliens, srce
we beak H. by be Finibe dimersicnah | To set He right
Basher we pank of x; 2s He Remenn spree cP’
= Cu fot. This Fe us de complex arelysis on x; ;
art delre holemonphie seclas of C. The~ we let
H; be te spece of bese halomaphic Sechnms . The. .
dim He = (2340
as deswed, We wee H, mle a Hallet Dpece OS
Bllass : Ua) ache am C in @ ~y ot prerves A
pane pradsck on C, Sp pha fibere Ly of b get
an Maer poducl | jks lek us dolme
(,@> = J <¥00,¢4> ur
VWhek's gong ex gonerel 2 One phese space K stack
at as an ble vol synpleche ponifold, whid then aires a
lime bendle LX. Te delne bralomen phic sec bien 5
of Lo ue need fo equip X wih extra structure —
namely 2 Kelle Skrackure *
docsity.com
