Table of contents for The geometry of Heisenberg groups : with applications in signal theory, optics, quantization, and field quantization / Ernst Binz, Sonja Pods ; with an appendix by Serge Preston.


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Counter
aptcr 1    'Fhe Sikew Field of Quaternions
I. 1.  m lion Af [hte Field of Quat,n ion>  i   nnd Ett,ni -t Forrmdai
12. F mbednings of C into the QuiterniCns and Naurat  niary Groups  7
f:n-7lintear Structures. Syrnplectaic Structures tani O(rintation.
Pauli Arenemens
I. LIter    itom orphimns of                                     12
.5. Th (Orienited Foutation \ngle of the hintner Aut 111r1>ism wih
R spe-C to tht N ;tural \finkowski Netrit 1r
I6i. Link hbet-ten Space-iiie Gouietry aid ELclhian (  immtrv ion to h
(2atr -ion-s                                               20
(haptp r 2. E   nts of the A(atwmr:n   of Von--f Bust thops aIml Spin
Represe ntiictins                                     25
1.  1(e--P  ameter        'trCc2ps of Ci (> ) and S ()          5
2.2. Pairallels f U titudell  and Meridianis on SY3              27
"2.  )rOnIe--Parameer Sublroups of S10(21 and h[opf GuiCi  le:s  2
"L. 1  Spin Rep -ese itaton
2.5.  ThI Inf i zitsml Spii -Rleprseortation
Chaptter 3  tlriil Variab h,s of Sing(dl tir y Frie e  itor Fielt , in A i E a icide;
3.1.  Th(h (' oiinplex  I,inc  Blunille Fa
"3. 2. Sinph icti: and Hcr mitiCi   Striit cures> il 
13. I cra1 nat I   clitis
3-. C (LVa[( FCCIe IF 07 o11nS e I tJV   S, iu s 1
\3n.Vwaw FOi ik I NOW? by T"4I
AT     wi (  a imi e rii c Pt Imip;d  i   idle   ii
31. thdamonl atul Periokic IANt Wt n  ; 'Amys                    69
( hpter L InspUTonWns ( C-t 0t fiernt C1s  af iornotlops (.'lsss of
Sn  iulait>  Frt.e \ci-,or FIdi.tF1-s i0 3 Spac e      71
1. laniinaVplakhiniC (Chnsses i(I Cliractr-istic PrFiltipal funnihlcu )i- Vector
I2   f'  St i-il nc ulii  of I onl rphisn ' lIass,m'             TT
i.L. NOtll   [    , UPI Fiat (Arnli-e Rharn (lana,
I S.  H,dt-;-  h[,r  iv  D+,c< n+[ >osi ri on              t
1TjwA                   Inw11  1. 11ch  -  ,r (r 1  AluS w "
J.ord1  Alebra and SL(, 2                              I
5.1. Nmatlurl Symplectic Strunto   o" a Pll ie n  1-S]a>          f)7
.2. '1 hi Noi on of a Heislnherg A]gebr                           12
1.3. leisekeilg (rou> 11d its lie Al Aera                        115
5.. 1.   as a Semi-direct Produc                                  11
-3.k.   Heisenberg Algebra Siruci,ur o1 sopff)                   121
VG.   Ih Spin Group and the SkWoN FiUd of Quatninhont am1 Gov )   1wd
by ()nly On)t[ HGis-nle  Croulp                            121
5..  Scala; Prodlct an31d ilinkowNsi Meirics oiln t  HOw -i,ea  A]r\,a  126
5.X. Symplectic     p. Spial Line,a Group} and Loientz !2roup     128
Chapter 6. The IielinIr (Groilp and N tural (7'-Alg4iras  a (A   \   fi!l
in 3-SPce                                              13!
6.1. ThI Heisenberg Gr,oup Bundle of Vncto! Field                 132
62. IMoftine Dim-nsional Heisenberg Alg Iobras and  ,fini1 D1i)HsioNnal
teisN,r g (GlCroups of  ct1or Field                       135
6.3. Ilya >s eitbrmiied by H5lomm1)irphilms                       1 40
6.J.  G(ou1p Algfbras of Infinite [) nsional ieisenbcrlg (Group1s  131
6.). The (? -Group Al-gra and the Twisted i nvoluwohNh. thp \\NVY
Itbra and Mhe PWhisson AlgW%3a                             1).
Chapter 7. 1lh SclhrlM dinger Repres-elntaltion and thMi Nh-lu]]e3Qtil
Repq r>ysentw1thlOl                                    1361
7i. Dw)initin, of 1he Schr6dinger Represej-ntation and] Phase Spae- 1c 131i
7.2. Clar;icleristic Ingr01edienis of the Slchrding0t r Bip1res'enta tion  I t66
7.3  Thle nfinitesinmal Schr6din ger Rcpresentation 3aid Phase Space  175
7..  Anroje(:tive Rlepresenta ions of' the Splneuti]iA  (roup (onsirulted i  a
t1hw Schri-dinger Riprtesentation                           176
7.5. A    ;ealization of the Mleta)plectic G1-oup and] the Metaplecif
R epresena tion t                                          1 0
Chqter s. T1'i Heisenberg Group: 2A Basi CG eom3-itric Backgeround of Signal
Analvsis and Gcomeiric Optics                          191
8.1. The Notion of a Signal                                       192
-.2. Tinme-Frequency Analysis and lhe Ui nci(rtainty Principle    193
8.3. Furnher Tools of Tirne-]Irequency Analysis                   196
8.4. Reconstruc1ion Forimulae                                     201
8.N. The Geometry 1Underlying Time-Frequency Analysis             202
8.6. The Radar Ambiguliy tunlction                                201
8.7. IThe Stone-von Neumiann Theoremn in 1-iine-Frequency Analysis  205
8.8. Geometric Optics                                             206
S.9. Holography                                                   210
Chapter 9. Quantization of Quadratic PolynoVniais                   21
9.1. Elementary Observations on Information and its Transmission  215
9.2. Pieservation of Information                                  217
9.3. The Po-isson Algebra, of all Hlomogeineous QuadratVi 1"iyno01ian in
Two Variab-- L                                             221
9.. .The Quanliza;ion of Inhomogeneous Quadratic Polynomials      230



Library of Congress subject headings for this publication: Heisenberg uncertainty principle Mathematics, Quantum theory Mathematics