New structures for physics:
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2011
|
| Schriftenreihe: | Lecture Notes in Physics
813 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XVIII, 1031 S. graph. Darst. |
| ISBN: | 9783642128202 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1805094993528881152 |
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| adam_text |
IMAGE 1
CONTENTS
FART I AN ABC ON COMPOSITIONALITY
1 INTRODUCTION TO CATEGORIES AND CATEGORICAL LOGIC 3
S. ABRAMSKY AND N. TZEVCLCKOS 1.1 INTRODUCTION 3
1.2 SOME BASIC CONSTRUCTIONS 13
1.3 FUNCTORS 23
1.4 NATURAL TRANSFORMATIONS 30
1.5 UNIVERSALITY AND ADJOINTS 37
1.6 THE CURRY-HOWARD CORRESPONDENCE 51
1.7 LINEARITY 68
1.8 MONADS AND COMONADS 79
REFERENCES 94
2 PHYSICS, TOPOLOGY, LOGIC AND COMPUTATION: A ROSETTA STONE 95 J. BAEZ
AND M. STAY 2.1 INTRODUCTION 95
2.2 THE ANALOGY BETWEEN PHYSICS AND TOPOLOGY 98
2.3 LOGIC ' 132
2.4 COMPUTATION 149
2.5 CONCLUSIONS 166
REFERENCES 1 68
3 CATEGORIES FOR THE PRACTISING PHYSICIST 173
B. COECKE AND E.O. PAQUETTE 3.1 PROLOGUE: COOKING WITH VEGETABLES 173
3.2 THE 1D CASE: NEW ARROWS FOR YOUR QUIVER 177
3.3 THE 2D CASE: MUSCLE POWER 194
3.4 QUANTUM-LIKE TENSORS 217
3.5 CLASSICAL-LIKE TENSORS 232
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1001251873
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
3.6 MONOIDAL FUNCTORIALITY, NATURALITY AND TQFTS 271
3.7 FURTHER READING 281
REFERENCES 283
PART II MANIFESTATIONS OF LINEARITY
4 A SURVEY OF GRAPHICAL LANGUAGES FOR MONOIDAL CATEGORIES 289 P.
SELINGER 4.1 INTRODUCTION 289
4.2 CATEGORIES 292
4.3 MONOIDAL CATEGORIES 296
4.4 AUTONOMOUS CATEGORIES 307
4.5 TRACED CATEGORIES 322
4.6 PRODUCTS, COPRODUCTS, AND BIPRODUCTS 332
4.7 DAGGER CATEGORIES 340
4.8 BICATEGORIES 350
4.9 BEYOND A SINGLE TENSOR PRODUCT 351
4.10 SUMMARY 352
REFERENCES 354
5 GEOMETRY OF INTERACTION AND THE DYNAMICS OF PROOF REDUCTION: A
TUTORIAL 357
E. HAGHVERDI AND P. SCOTT 5.1 INTRODUCTION 357
5.2 FROM MONOIDAL CATEGORIES TO *-AUTONOMY 359
5.3 LINEAR LOGIC AND CATEGORICAL PROOF THEORY 366
5.4 TRACED MONOIDAL CATEGORIES 375
5.5 WHAT IS THE GEOMETRY OF INTERACTION? 385
5.6 GOL INTERPRETATION OF MELL 389
5.7 PARTIAL TRACE AND ABSTRACT ORTHOGONALITY 398
5.8 TYPED GOL FOR MELL IN ^CATEGORIES 403
5.9 CONCLUDING REMARKS 412
APPENDIX 1: GRAPHICAL REPRESENTATION OF THE TRACE AXIOMS 412 APPENDIX 2:
COMPARING GOL NOTATION 414
REFERENCES 414
PART III MORE EXAMPLE APPLICATIONS
6 DAGGER CATEGORIES AND FORMAL DISTRIBUTIONS 421
R. BLUTE AND P. PANANGADEN 6.1 INTRODUCTION 421
6.2 DAGGER CATEGORIES AND NUCLEAR IDEALS 424
6.3 DISTRIBUTIONS AS RELATIONS 425
IMAGE 3
CONTENTS XV
6.4 CATEGORIES OF FORMAL DISTRIBUTIONS 428
6.5 VERTEX GROUPS AND CATEGORIES 433
6.6 CONCLUSION 435
REFERENCES 435
7 PROOF NETS AS FORMAL FEYNMAN DIAGRAMS 437
R. BLUTE AND P. PANANGADEN 7.1 INTRODUCTION 437
7.2 FUNCTIONAL INTEGRALS IN QUANTUM FIELD THEORY 438
7.3 LINEAR REALIZABILITY ALGEBRA 442
7.4 THE ^-CALCULUS 445
7.5 EXPONENTIAL IDENTITIES FOR OPERATORS 453
7.6 INTERPRETING PROOF NETS 456
7.7 EXAMPLE CALCULATIONS 459
7.8 CONCLUSIONS 463
REFERENCES 465
8 COMPACT MONOIDAL CATEGORIES FROM LINGUISTICS TO PHYSICS 467 J. LAMBEK
8.1 COMPACT 2-CATEGORIES AND PREGROUPS 468
8.2 PREGROUPS FOR GRAMMAR 470
8.3 FREE COMPACT 2-CATEGORIES 471
8.4 IN SEARCH OF A COMPACT FEYNMAN CATEGORY 475
8.5 A POGROUP FOR QED 477
8.6 FROM QED TO THE STANDARD MODEL 479
8.7 FROM 2-CATEGORIES TO BICATEGORIES 481
8.8 OTHER OPERATIONS IN BILINEAR LOGIC 485
8.9 POSTSCRIPT 486
REFERENCES 487
PART IV INFORMATIE GEOMETRY
9 DOMAIN THEORY AND MEASUREMENT 491
K. MARTIN 9.1 INTRODUCTION 491
9.2 THE BASIC ELEMENTS 494
9.3 FIXED POINTS 508
9.4 INSTANCES OF PARTIALITY 524
9.5 THE INFORMATIE DERIVATIVE 539
9.6 FORMS OF PROCESS EVOLUTION 559
9.7 PROVOCATION 587
REFERENCES 589
IMAGE 4
XVI CONTENTS
10 A PARTIAL ORDER ON CLASSICAL AND QUANTUM STATES 593
B. COECKE AND K. MARTIN 10.1 INTRODUCTION 593
10.2 CLASSICAL STATES 595
10.3 QUANTUM STATES 630
10.4 SYNTHESIS 655
10.5 APPLICATIONS 672
REFERENCES 682
PART V SPATIO-TEMPORAL GEOMETRY
11 DOMAIN THEORY AND GENERAL RELATIVITY 687
K. MARTIN AND P. PANANGADEN 11.1 INTRODUCTION 687
11.2 DOMAINS, CONTINUOUS POSETS AND TOPOLOGY 689
11.3 THE CAUSAL STRUCTURE OF SPACETIME 691
11.4 GLOBAL HYPERBOLICITY 692
11.5 SPACETIME FROM A DISCRETE CAUSAL SET 694
11.6 SPACETIME AS A DOMAIN 695
11.7 TIME AND MEASUREMENT 699
11.8 SPACETIME GEOMETRY FROM A DISCRETE CAUSAL SET 701
11.9 CONCLUSIONS 702
REFERENCES 703
12 PROCESS, DISTINCTION, GROUPOIDS AND CLIFFORD ALGEBRAS: AN ALTERNATIVE
VIEW OF THE QUANTUM FORMALISM 705
B.J. HILEY 12.1 THE ALGEBRA OF PROCESS 705
12.2 SOME SPECIFIC ALGEBRAS OF PROCESS 709
12.3 CONNECTIONS WITH OTHER MATHEMATICAL APPROACHES 715
12.4 SOME RADICAL NEW IDEAS 719
12.5 THE CONFORMAI CLIFFORD C 2A 731
12.6 CONNECTIONS IN THE CLIFFORD BUNDLE 736
12.7 EXPECTATION VALUES 740
12.8 THE SYMPLECTIC GROUP 744
12.9 GENERAL CONCLUSIONS 749
REFERENCES 750
13 "WHAT IS A THING?": TOPOS THEORY IN THE FOUNDATIONS OF PHYSICS 753 A.
DOERING AND C. ISHAM 13.1 INTRODUCTION 754
13.2 THE CONCEPTUAL BACKGROUND OF OUR SCHEME 762
13.3 PROPOSITIONAL LANGUAGES AND THEORIES OF PHYSICS 770
IMAGE 5
CONTENTS
13.4 A HIGHER-ORDER, TYPED LANGUAGE FOR PHYSICS 778
13.5 QUANTUM PROPOSITIONS AS SUB-OBJECTS OF THE SPECTRAL PRESHEAF . . .
788 13.6 TRUTH VALUES IN TOPOS PHYSICS 809
13.7 THE DE GROOTE PRESHEAVES OF PHYSICAL QUANTITIES 827
13.8 THE PRESHEAVES SP(A)^, K^ AND R^ 837
13.9 EXTENDING THE QUANTITY-VALUE PRESHEAF TO AN ABELIAN GROUP OBJECT
858
13.10 THE ROLE OF UNITARY OPERATORS 863
13.11 THE CATEGORY OF SYSTEMS 871
13.12 THEORIES OF PHYSICS IN A GENERAL TOPOS 886
13.13 THE GENERAL SCHEME APPLIED TO QUANTUM THEORY 894
13.14 CHARACTERISTIC PROPERTIES OF E^, 11$ AND T, TU 904
13.15 CONCLUSION 911
APPENDIX 1 : SOME THEOREMS AND CONSTRUCTIONS USED IN THE MAIN TEXT .
916 APPENDIX 2: A SHORT INTRODUCTION TO THE RELEVANT PARTS OF TOPOS
THEORY . 925 REFERENCES 934
PART VI GEOMETRY AND TOPOLOGY IN COMPUTATION
14 CAN A QUANTUM COMPUTER RUN THE VON NEUMANN ARCHITECTURE? . . 941 P.
HINES 14.1 INTRODUCTION 941
14.2 THE VON NEUMANN ARCHITECTURE 942
14.3 RELEVANT QUANTUM INFORMATION THEORY 944
14.4 DATA/CODE INTERCHANGEABILITY, AND EVALUATION 948
14.5 EVALUATION IN THE ONE-BIT COMPUTER 950
14.6 IMPLEMENTING EVALUATION BY UNITARY OPERATIONS? 950
14.7 EVALUATION AS CURRYING 953
14.8 BASIC CATEGORY THEORY 955
14.9 CATEGORICAL CLOSURE AND HUBERT SPACES 960
14.10 ABRAMSKY AND COECKE'S CATEGORICAL FOUNDATIONS FOR QUANTUM
MECHANICS 964
14.11 EVALUATION BY TELEPORTATION, AND THE VN ARCHITECTURE 966 14.12
NAMING AN UNKNOWN ARROW 970
14.13 OTHER ASPECTS 972
APPENDIX 976
REFERENCES 978
15 A CATEGORICAL PRESENTATION OF QUANTUM COMPUTATION WITH ANYONS . 983
P. PANANGADEN AND E.O. PAQUETTE 15.1 INTRODUCTION 983
15.2 SPIN AND STATISTICS 987
15.3 ANYONS AND BRAIDS 989
IMAGE 6
XVIII CONTENTS
15.4 THE ALGEBRA OF ANYONS: MODULAR TENSOR CATEGORIES 992
15.5 AN EXAMPLE: FIBONACCI ANYONS 1014
15.6 UNIVERSAL QUANTUM COMPUTATION WITH FIBONACCI ANYONS 1020 15.7
CONCLUSIONS 1022
REFERENCES 1023
INDEX 1027 |
| any_adam_object | 1 |
| author2 | Coecke, Bob |
| author2_role | edt |
| author2_variant | b c bc |
| author_facet | Coecke, Bob |
| building | Verbundindex |
| bvnumber | BV036785683 |
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| dewey-full | 530.15 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15 |
| dewey-search | 530.15 |
| dewey-sort | 3530.15 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| spelling | New structures for physics B. Coecke (ed.) Berlin [u.a.] Springer 2011 XVIII, 1031 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture Notes in Physics 813 Kategorientheorie (DE-588)4120552-2 gnd rswk-swf Quantencomputer (DE-588)4533372-5 gnd rswk-swf Quantengravitation (DE-588)4124012-1 gnd rswk-swf Bereichstheorie (DE-588)4382803-6 gnd rswk-swf Kategorientheorie (DE-588)4120552-2 s Bereichstheorie (DE-588)4382803-6 s Quantencomputer (DE-588)4533372-5 s Quantengravitation (DE-588)4124012-1 s DE-604 Coecke, Bob edt Lecture Notes in Physics 813 (DE-604)BV000003166 813 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3449996&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020702196&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | New structures for physics Lecture Notes in Physics Kategorientheorie (DE-588)4120552-2 gnd Quantencomputer (DE-588)4533372-5 gnd Quantengravitation (DE-588)4124012-1 gnd Bereichstheorie (DE-588)4382803-6 gnd |
| subject_GND | (DE-588)4120552-2 (DE-588)4533372-5 (DE-588)4124012-1 (DE-588)4382803-6 |
| title | New structures for physics |
| title_auth | New structures for physics |
| title_exact_search | New structures for physics |
| title_full | New structures for physics B. Coecke (ed.) |
| title_fullStr | New structures for physics B. Coecke (ed.) |
| title_full_unstemmed | New structures for physics B. Coecke (ed.) |
| title_short | New structures for physics |
| title_sort | new structures for physics |
| topic | Kategorientheorie (DE-588)4120552-2 gnd Quantencomputer (DE-588)4533372-5 gnd Quantengravitation (DE-588)4124012-1 gnd Bereichstheorie (DE-588)4382803-6 gnd |
| topic_facet | Kategorientheorie Quantencomputer Quantengravitation Bereichstheorie |
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