Symmetry rules: how science and nature are founded on symmetry
Modern theoretical physics suggests that symmetry is a, if not the, foundational principle of nature. Emphasizing the concepts, this book introduces symmetry and its applications. It is shown that the universe cannot possess exact symmetry, which is a principle of fundamental significance.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2008
|
| Schriftenreihe: | The frontiers collection
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Modern theoretical physics suggests that symmetry is a, if not the, foundational principle of nature. Emphasizing the concepts, this book introduces symmetry and its applications. It is shown that the universe cannot possess exact symmetry, which is a principle of fundamental significance. |
| Beschreibung: | XIV, 304 S. graph. Darst. |
| ISBN: | 9783540759720 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV023206844 | ||
| 003 | DE-604 | ||
| 005 | 20081009 | ||
| 007 | t | ||
| 008 | 080311s2008 d||| |||| 00||| eng d | ||
| 020 | |a 9783540759720 |9 978-3-540-75972-0 | ||
| 035 | |a (OCoLC)191754739 | ||
| 035 | |a (DE-599)BVBBV023206844 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-19 |a DE-29T |a DE-20 |a DE-91G |a DE-703 |a DE-706 |a DE-11 |a DE-355 |a DE-188 | ||
| 050 | 0 | |a Q172.5.S95 | |
| 082 | 0 | |a 500 |2 22 | |
| 084 | |a SK 950 |0 (DE-625)143273: |2 rvk | ||
| 084 | |a TB 6000 |0 (DE-625)143784: |2 rvk | ||
| 084 | |a TB 6500 |0 (DE-625)143789: |2 rvk | ||
| 084 | |a UO 1500 |0 (DE-625)146200: |2 rvk | ||
| 084 | |a UQ 1300 |0 (DE-625)146478: |2 rvk | ||
| 084 | |a PHY 012f |2 stub | ||
| 100 | 1 | |a Rosen, Joe |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Symmetry rules |b how science and nature are founded on symmetry |c Joe Rosen |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XIV, 304 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a The frontiers collection | |
| 520 | 3 | |a Modern theoretical physics suggests that symmetry is a, if not the, foundational principle of nature. Emphasizing the concepts, this book introduces symmetry and its applications. It is shown that the universe cannot possess exact symmetry, which is a principle of fundamental significance. | |
| 650 | 4 | |a Symmetry | |
| 650 | 0 | 7 | |a Symmetrie |0 (DE-588)4058724-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Symmetrie |0 (DE-588)4058724-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m SWB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016392982&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016392982 | ||
Datensatz im Suchindex
| _version_ | 1804137486561050624 |
|---|---|
| adam_text | CONTENTS 1 THE CONCEPT OF SYMMETRY . . . . . . . . . . . . . . . . . . .
. . . . . . . 1 1.1 THE ESSENCE OF SYMMETRY . . . . . . . . . . . . . .
. . . . . . . . . . . 1 1.2 SYMMETRY IMPLIES ASYMMETRY . . . . . . . . .
. . . . . . . . . . . . 8 1.3 ANALOGY AND CLASSIFICATION ARE SYMMETRY. .
. . . . . . . . . 10 1.4 SUMMARY . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 15 2 SCIENCE IS FOUNDED ON
SYMMETRY . . . . . . . . . . . . . . . . . . . 17 2.1 SCIENCE . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17 2.2 REDUCTION IS SYMMETRY . . . . . . . . . . . . . . . . . . . . . .
. . . . . 20 2.2.1 REDUCTION TO OBSERVER AND OBSERVED . . . . . . . . 22
2.2.2 REDUCTION TO QUASI-ISOLATED SYSTEM AND ENVIRONMENT . . . . . . . .
. . . . . . . . . . . . . . . . . . 25 2.2.3 REDUCTION TO INITIAL STATE
AND EVOLUTION . . . . . 26 2.3 REPRODUCIBILITY IS SYMMETRY . . . . . . .
. . . . . . . . . . . . . . . 29 2.4 PREDICTABILITY IS SYMMETRY . . . .
. . . . . . . . . . . . . . . . . . . . 32 2.5 ANALOGY IN SCIENCE . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.6 SYMMETRY
AT THE FOUNDATION OF SCIENCE . . . . . . . . . . . . . 37 2.7 SUMMARY .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 38 3 SYMMETRY IN PHYSICS . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 39 3.1 SYMMETRY OF EVOLUTION . . . . . . . . . . . . .
. . . . . . . . . . . . . . 40 3.2 SYMMETRY OF STATES . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 44 3.3 REFERENCE FRAME . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.4 GLOBAL,
INERTIAL, AND LOCAL REFERENCE FRAMES . . . . . . . . 53 XII CONTENTS 3.5
GAUGE TRANSFORMATION . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 55 3.6 GAUGE SYMMETRY . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 58 3.7 SYMMETRY AND CONSERVATION . . . . . . . . . . .
. . . . . . . . . . . 65 3.7.1 CONSERVATION OF ENERGY . . . . . . . . .
. . . . . . . . . . . 66 3.7.2 CONSERVATION OF LINEAR MOMENTUM . . . . .
. . . . . 67 3.7.3 CONSERVATION OF ANGULAR MOMENTUM . . . . . . . . . 68
3.8 SYMMETRY AT THE FOUNDATION OF PHYSICS. . . . . . . . . . . . . 70
3.9 SYMMETRY AT THE FOUNDATION OF QUANTUM THEORY . . . . 71 3.9.1
ASSOCIATION OF A HILBERT SPACE WITH A PHYSICAL SYSTEM . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.9.2
CORRESPONDENCE OF OBSERVABLES TO HERMITIAN OPERATORS . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 73 3.9.3 COMPLETE SET OF
COMPATIBLE OBSERVABLES . . . . . 74 3.9.4 HEISENBERG COMMUTATION
RELATIONS . . . . . . . . . . 75 3.9.5 OPERATORS FOR CANONICAL VARIABLES
. . . . . . . . . . . 75 3.9.6 A MEASUREMENT RESULT IS AN EIGENVALUE . .
. . . . 75 3.9.7 EXPECTATION VALUES AND PROBABILITIES . . . . . . . . 76
3.9.8 THE HAMILTONIAN OPERATOR . . . . . . . . . . . . . . . . . 76
3.9.9 PLANCK*S CONSTANT AS A PARAMETER . . . . . . . . . . . 77 3.9.10
THE CORRESPONDENCE PRINCIPLE. . . . . . . . . . . . . . . 77 3.10
SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 77 4 THE SYMMETRY PRINCIPLE . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 81 4.1 CAUSAL RELATION. . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 81 4.2 EQUIVALENCE RELATION,
EQUIVALENCE CLASS . . . . . . . . . . . . 86 4.3 THE EQUIVALENCE
PRINCIPLE. . . . . . . . . . . . . . . . . . . . . . . . . 89 4.4 THE
SYMMETRY PRINCIPLE . . . . . . . . . . . . . . . . . . . . . . . . . .
97 4.5 CAUSE AND EFFECT IN QUANTUM SYSTEMS. . . . . . . . . . . . . .
102 4.6 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 104 5 APPLICATION OF SYMMETRY . . . . . . . . . .
. . . . . . . . . . . . . . . . . 107 5.1 MINIMALISTIC USE OF THE
SYMMETRY PRINCIPLE . . . . . . . . . 107 5.2 MAXIMALISTIC USE OF THE
SYMMETRY PRINCIPLE. . . . . . . . . 125 5.3 SUMMARY . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 CONTENTS
XIII 6 APPROXIMATE SYMMETRY, SPONTANEOUS SYMMETRY BREAKING . . . . . . .
. . . . . . . . . . . . 131 6.1 APPROXIMATE SYMMETRY . . . . . . . . . .
. . . . . . . . . . . . . . . . 131 6.2 SPONTANEOUS SYMMETRY BREAKING .
. . . . . . . . . . . . . . . . . 135 6.3 SUMMARY . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 7 COSMIC
CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 141 7.1 SYMMETRY OF THE LAWS OF NATURE . . . . . . . . . . . . . . . .
. . . 141 7.2 SYMMETRY OF THE UNIVERSE. . . . . . . . . . . . . . . . .
. . . . . . . . 144 7.3 NO COSMIC SYMMETRY BREAKING OR RESTORATION. . .
. . . . 147 7.4 THE QUANTUM ERA AND THE BEGINNING . . . . . . . . . . .
. . . 155 7.5 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 159 8 THE MATHEMATICS OF SYMMETRY: GROUP
THEORY . . . . . 161 8.1 GROUP . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 161 8.2 MAPPING . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
8.3 ISOMORPHISM . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 180 8.4 HOMOMORPHISM . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 186 8.5 SUBGROUP . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 192 8.6 SUMMARY .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 194 9 GROUP THEORY CONTINUED . . . . . . . . . . . . . . . . . . . .
. . . . . . . 195 9.1 CONJUGACY, INVARIANT SUBGROUP, KERNEL . . . . . .
. . . . . . . 195 9.2 COSET DECOMPOSITION . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 203 9.3 FACTOR GROUP . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 207 9.4 ANATOMY OF
HOMOMORPHISM . . . . . . . . . . . . . . . . . . . . . . . 209 9.5
GENERATOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 215 9.6 DIRECT PRODUCT . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 217 9.7 PERMUTATION, SYMMETRIC GROUP .
. . . . . . . . . . . . . . . . . . . 220 9.8 CAYLEY*S THEOREM . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 224 9.9 SUMMARY .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 226 10 THE FORMALISM OF SYMMETRY . . . . . . . . . . . . . . . . . .
. . . . . . 227 10.1 SYSTEM, STATE . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 227 10.2 TRANSFORMATION, TRANSFORMATION
GROUP . . . . . . . . . . . . . 229 XIV CONTENTS 10.3 TRANSFORMATIONS IN
SPACE, TIME, AND SPACE-TIME . . . . 236 10.4 STATE EQUIVALENCE . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 240 10.5 SYMMETRY
TRANSFORMATION, SYMMETRY GROUP . . . . . . . . 243 10.6 APPROXIMATE
SYMMETRY TRANSFORMATION . . . . . . . . . . . . 251 10.7 QUANTIFICATION
OF SYMMETRY . . . . . . . . . . . . . . . . . . . . . . . 253 10.8
QUANTUM SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 255 10.9 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 258 11 SYMMETRY IN PROCESSES . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 261 11.1 SYMMETRY OF THE LAWS
OF NATURE . . . . . . . . . . . . . . . . . . . 261 11.2 SYMMETRY OF
INITIAL AND FINAL STATES, THE GENERAL SYMMETRY EVOLUTION PRINCIPLE . . .
. . . . . . . 270 11.3 THE SPECIAL SYMMETRY EVOLUTION PRINCIPLE AND
ENTROPY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 274 11.4 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 280 12 SUMMARY OF PRINCIPLES . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 283 12.1 SYMMETRY AND
ASYMMETRY . . . . . . . . . . . . . . . . . . . . . . . . 283 12.2
SYMMETRY IMPLIES ASYMMETRY . . . . . . . . . . . . . . . . . . . . . 283
12.3 NO EXACT SYMMETRY OF THE UNIVERSE . . . . . . . . . . . . . . . .
284 12.4 COSMOLOGICAL IMPLICATIONS . . . . . . . . . . . . . . . . . . .
. . . . . . 285 12.5 THE EQUIVALENCE PRINCIPLE. . . . . . . . . . . . .
. . . . . . . . . . . . 285 12.6 THE SYMMETRY PRINCIPLE . . . . . . . .
. . . . . . . . . . . . . . . . . . 285 12.7 THE EQUIVALENCE PRINCIPLE
FOR PROCESSES. . . . . . . . . . . . . 286 12.8 THE SYMMETRY PRINCIPLE
FOR PROCESSES . . . . . . . . . . . . . . 286 12.9 THE GENERAL SYMMETRY
EVOLUTION PRINCIPLE . . . . . . . . . 286 12.10 THE SPECIAL SYMMETRY
EVOLUTION PRINCIPLE . . . . . . . . . . 286 REFERENCES . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 289 FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 293 INDEX . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
297
|
| adam_txt |
CONTENTS 1 THE CONCEPT OF SYMMETRY . . . . . . . . . . . . . . . . . . .
. . . . . . . 1 1.1 THE ESSENCE OF SYMMETRY . . . . . . . . . . . . . .
. . . . . . . . . . . 1 1.2 SYMMETRY IMPLIES ASYMMETRY . . . . . . . . .
. . . . . . . . . . . . 8 1.3 ANALOGY AND CLASSIFICATION ARE SYMMETRY. .
. . . . . . . . . 10 1.4 SUMMARY . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 15 2 SCIENCE IS FOUNDED ON
SYMMETRY . . . . . . . . . . . . . . . . . . . 17 2.1 SCIENCE . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17 2.2 REDUCTION IS SYMMETRY . . . . . . . . . . . . . . . . . . . . . .
. . . . . 20 2.2.1 REDUCTION TO OBSERVER AND OBSERVED . . . . . . . . 22
2.2.2 REDUCTION TO QUASI-ISOLATED SYSTEM AND ENVIRONMENT . . . . . . . .
. . . . . . . . . . . . . . . . . . 25 2.2.3 REDUCTION TO INITIAL STATE
AND EVOLUTION . . . . . 26 2.3 REPRODUCIBILITY IS SYMMETRY . . . . . . .
. . . . . . . . . . . . . . . 29 2.4 PREDICTABILITY IS SYMMETRY . . . .
. . . . . . . . . . . . . . . . . . . . 32 2.5 ANALOGY IN SCIENCE . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.6 SYMMETRY
AT THE FOUNDATION OF SCIENCE . . . . . . . . . . . . . 37 2.7 SUMMARY .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 38 3 SYMMETRY IN PHYSICS . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 39 3.1 SYMMETRY OF EVOLUTION . . . . . . . . . . . . .
. . . . . . . . . . . . . . 40 3.2 SYMMETRY OF STATES . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 44 3.3 REFERENCE FRAME . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.4 GLOBAL,
INERTIAL, AND LOCAL REFERENCE FRAMES . . . . . . . . 53 XII CONTENTS 3.5
GAUGE TRANSFORMATION . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 55 3.6 GAUGE SYMMETRY . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 58 3.7 SYMMETRY AND CONSERVATION . . . . . . . . . . .
. . . . . . . . . . . 65 3.7.1 CONSERVATION OF ENERGY . . . . . . . . .
. . . . . . . . . . . 66 3.7.2 CONSERVATION OF LINEAR MOMENTUM . . . . .
. . . . . 67 3.7.3 CONSERVATION OF ANGULAR MOMENTUM . . . . . . . . . 68
3.8 SYMMETRY AT THE FOUNDATION OF PHYSICS. . . . . . . . . . . . . 70
3.9 SYMMETRY AT THE FOUNDATION OF QUANTUM THEORY . . . . 71 3.9.1
ASSOCIATION OF A HILBERT SPACE WITH A PHYSICAL SYSTEM . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.9.2
CORRESPONDENCE OF OBSERVABLES TO HERMITIAN OPERATORS . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 73 3.9.3 COMPLETE SET OF
COMPATIBLE OBSERVABLES . . . . . 74 3.9.4 HEISENBERG COMMUTATION
RELATIONS . . . . . . . . . . 75 3.9.5 OPERATORS FOR CANONICAL VARIABLES
. . . . . . . . . . . 75 3.9.6 A MEASUREMENT RESULT IS AN EIGENVALUE . .
. . . . 75 3.9.7 EXPECTATION VALUES AND PROBABILITIES . . . . . . . . 76
3.9.8 THE HAMILTONIAN OPERATOR . . . . . . . . . . . . . . . . . 76
3.9.9 PLANCK*S CONSTANT AS A PARAMETER . . . . . . . . . . . 77 3.9.10
THE CORRESPONDENCE PRINCIPLE. . . . . . . . . . . . . . . 77 3.10
SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 77 4 THE SYMMETRY PRINCIPLE . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 81 4.1 CAUSAL RELATION. . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 81 4.2 EQUIVALENCE RELATION,
EQUIVALENCE CLASS . . . . . . . . . . . . 86 4.3 THE EQUIVALENCE
PRINCIPLE. . . . . . . . . . . . . . . . . . . . . . . . . 89 4.4 THE
SYMMETRY PRINCIPLE . . . . . . . . . . . . . . . . . . . . . . . . . .
97 4.5 CAUSE AND EFFECT IN QUANTUM SYSTEMS. . . . . . . . . . . . . .
102 4.6 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 104 5 APPLICATION OF SYMMETRY . . . . . . . . . .
. . . . . . . . . . . . . . . . . 107 5.1 MINIMALISTIC USE OF THE
SYMMETRY PRINCIPLE . . . . . . . . . 107 5.2 MAXIMALISTIC USE OF THE
SYMMETRY PRINCIPLE. . . . . . . . . 125 5.3 SUMMARY . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 CONTENTS
XIII 6 APPROXIMATE SYMMETRY, SPONTANEOUS SYMMETRY BREAKING . . . . . . .
. . . . . . . . . . . . 131 6.1 APPROXIMATE SYMMETRY . . . . . . . . . .
. . . . . . . . . . . . . . . . 131 6.2 SPONTANEOUS SYMMETRY BREAKING .
. . . . . . . . . . . . . . . . . 135 6.3 SUMMARY . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 7 COSMIC
CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 141 7.1 SYMMETRY OF THE LAWS OF NATURE . . . . . . . . . . . . . . . .
. . . 141 7.2 SYMMETRY OF THE UNIVERSE. . . . . . . . . . . . . . . . .
. . . . . . . . 144 7.3 NO COSMIC SYMMETRY BREAKING OR RESTORATION. . .
. . . . 147 7.4 THE QUANTUM ERA AND THE BEGINNING . . . . . . . . . . .
. . . 155 7.5 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 159 8 THE MATHEMATICS OF SYMMETRY: GROUP
THEORY . . . . . 161 8.1 GROUP . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 161 8.2 MAPPING . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
8.3 ISOMORPHISM . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 180 8.4 HOMOMORPHISM . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 186 8.5 SUBGROUP . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 192 8.6 SUMMARY .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 194 9 GROUP THEORY CONTINUED . . . . . . . . . . . . . . . . . . . .
. . . . . . . 195 9.1 CONJUGACY, INVARIANT SUBGROUP, KERNEL . . . . . .
. . . . . . . 195 9.2 COSET DECOMPOSITION . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 203 9.3 FACTOR GROUP . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 207 9.4 ANATOMY OF
HOMOMORPHISM . . . . . . . . . . . . . . . . . . . . . . . 209 9.5
GENERATOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 215 9.6 DIRECT PRODUCT . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 217 9.7 PERMUTATION, SYMMETRIC GROUP .
. . . . . . . . . . . . . . . . . . . 220 9.8 CAYLEY*S THEOREM . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 224 9.9 SUMMARY .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 226 10 THE FORMALISM OF SYMMETRY . . . . . . . . . . . . . . . . . .
. . . . . . 227 10.1 SYSTEM, STATE . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 227 10.2 TRANSFORMATION, TRANSFORMATION
GROUP . . . . . . . . . . . . . 229 XIV CONTENTS 10.3 TRANSFORMATIONS IN
SPACE, TIME, AND SPACE-TIME . . . . 236 10.4 STATE EQUIVALENCE . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 240 10.5 SYMMETRY
TRANSFORMATION, SYMMETRY GROUP . . . . . . . . 243 10.6 APPROXIMATE
SYMMETRY TRANSFORMATION . . . . . . . . . . . . 251 10.7 QUANTIFICATION
OF SYMMETRY . . . . . . . . . . . . . . . . . . . . . . . 253 10.8
QUANTUM SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 255 10.9 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 258 11 SYMMETRY IN PROCESSES . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 261 11.1 SYMMETRY OF THE LAWS
OF NATURE . . . . . . . . . . . . . . . . . . . 261 11.2 SYMMETRY OF
INITIAL AND FINAL STATES, THE GENERAL SYMMETRY EVOLUTION PRINCIPLE . . .
. . . . . . . 270 11.3 THE SPECIAL SYMMETRY EVOLUTION PRINCIPLE AND
ENTROPY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 274 11.4 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 280 12 SUMMARY OF PRINCIPLES . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 283 12.1 SYMMETRY AND
ASYMMETRY . . . . . . . . . . . . . . . . . . . . . . . . 283 12.2
SYMMETRY IMPLIES ASYMMETRY . . . . . . . . . . . . . . . . . . . . . 283
12.3 NO EXACT SYMMETRY OF THE UNIVERSE . . . . . . . . . . . . . . . .
284 12.4 COSMOLOGICAL IMPLICATIONS . . . . . . . . . . . . . . . . . . .
. . . . . . 285 12.5 THE EQUIVALENCE PRINCIPLE. . . . . . . . . . . . .
. . . . . . . . . . . . 285 12.6 THE SYMMETRY PRINCIPLE . . . . . . . .
. . . . . . . . . . . . . . . . . . 285 12.7 THE EQUIVALENCE PRINCIPLE
FOR PROCESSES. . . . . . . . . . . . . 286 12.8 THE SYMMETRY PRINCIPLE
FOR PROCESSES . . . . . . . . . . . . . . 286 12.9 THE GENERAL SYMMETRY
EVOLUTION PRINCIPLE . . . . . . . . . 286 12.10 THE SPECIAL SYMMETRY
EVOLUTION PRINCIPLE . . . . . . . . . . 286 REFERENCES . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 289 FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 293 INDEX . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
297 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Rosen, Joe |
| author_facet | Rosen, Joe |
| author_role | aut |
| author_sort | Rosen, Joe |
| author_variant | j r jr |
| building | Verbundindex |
| bvnumber | BV023206844 |
| callnumber-first | Q - Science |
| callnumber-label | Q172 |
| callnumber-raw | Q172.5.S95 |
| callnumber-search | Q172.5.S95 |
| callnumber-sort | Q 3172.5 S95 |
| callnumber-subject | Q - General Science |
| classification_rvk | SK 950 TB 6000 TB 6500 UO 1500 UQ 1300 |
| classification_tum | PHY 012f |
| ctrlnum | (OCoLC)191754739 (DE-599)BVBBV023206844 |
| dewey-full | 500 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 500 - Natural sciences and mathematics |
| dewey-raw | 500 |
| dewey-search | 500 |
| dewey-sort | 3500 |
| dewey-tens | 500 - Natural sciences and mathematics |
| discipline | Allgemeine Naturwissenschaft Physik Mathematik |
| discipline_str_mv | Allgemeine Naturwissenschaft Physik Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01855nam a2200433 c 4500</leader><controlfield tag="001">BV023206844</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20081009 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">080311s2008 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783540759720</subfield><subfield code="9">978-3-540-75972-0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)191754739</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV023206844</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-19</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">Q172.5.S95</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">500</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 950</subfield><subfield code="0">(DE-625)143273:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">TB 6000</subfield><subfield code="0">(DE-625)143784:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">TB 6500</subfield><subfield code="0">(DE-625)143789:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">UO 1500</subfield><subfield code="0">(DE-625)146200:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">UQ 1300</subfield><subfield code="0">(DE-625)146478:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">PHY 012f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Rosen, Joe</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Symmetry rules</subfield><subfield code="b">how science and nature are founded on symmetry</subfield><subfield code="c">Joe Rosen</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2008</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIV, 304 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">The frontiers collection</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="a">Modern theoretical physics suggests that symmetry is a, if not the, foundational principle of nature. Emphasizing the concepts, this book introduces symmetry and its applications. It is shown that the universe cannot possess exact symmetry, which is a principle of fundamental significance.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Symmetry</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Symmetrie</subfield><subfield code="0">(DE-588)4058724-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Symmetrie</subfield><subfield code="0">(DE-588)4058724-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">SWB Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016392982&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-016392982</subfield></datafield></record></collection> |
| id | DE-604.BV023206844 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:10:22Z |
| indexdate | 2024-07-09T21:13:04Z |
| institution | BVB |
| isbn | 9783540759720 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016392982 |
| oclc_num | 191754739 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-29T DE-20 DE-91G DE-BY-TUM DE-703 DE-706 DE-11 DE-355 DE-BY-UBR DE-188 |
| owner_facet | DE-19 DE-BY-UBM DE-29T DE-20 DE-91G DE-BY-TUM DE-703 DE-706 DE-11 DE-355 DE-BY-UBR DE-188 |
| physical | XIV, 304 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series2 | The frontiers collection |
| spelling | Rosen, Joe Verfasser aut Symmetry rules how science and nature are founded on symmetry Joe Rosen Berlin [u.a.] Springer 2008 XIV, 304 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The frontiers collection Modern theoretical physics suggests that symmetry is a, if not the, foundational principle of nature. Emphasizing the concepts, this book introduces symmetry and its applications. It is shown that the universe cannot possess exact symmetry, which is a principle of fundamental significance. Symmetry Symmetrie (DE-588)4058724-1 gnd rswk-swf Symmetrie (DE-588)4058724-1 s DE-604 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016392982&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rosen, Joe Symmetry rules how science and nature are founded on symmetry Symmetry Symmetrie (DE-588)4058724-1 gnd |
| subject_GND | (DE-588)4058724-1 |
| title | Symmetry rules how science and nature are founded on symmetry |
| title_auth | Symmetry rules how science and nature are founded on symmetry |
| title_exact_search | Symmetry rules how science and nature are founded on symmetry |
| title_exact_search_txtP | Symmetry rules how science and nature are founded on symmetry |
| title_full | Symmetry rules how science and nature are founded on symmetry Joe Rosen |
| title_fullStr | Symmetry rules how science and nature are founded on symmetry Joe Rosen |
| title_full_unstemmed | Symmetry rules how science and nature are founded on symmetry Joe Rosen |
| title_short | Symmetry rules |
| title_sort | symmetry rules how science and nature are founded on symmetry |
| title_sub | how science and nature are founded on symmetry |
| topic | Symmetry Symmetrie (DE-588)4058724-1 gnd |
| topic_facet | Symmetry Symmetrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016392982&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT rosenjoe symmetryruleshowscienceandnaturearefoundedonsymmetry |