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A Integral de Feynman VIII Escola CBPF 2010

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Integral de Feynman
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   1 A INTEGRAL DE FEYNMAN DAS ORIGENS ÀS TEORIAS DE CAMPOS A TEMPERATURAS FINITAS Prof. Armando Flavio Rodrigues CBPF 2010     2 C󰁯󰁮󰁴󰁥󰃺󰁤󰁯 I. P󰁲󰁯󰁬󰁥󰁧󰃴󰁭󰁥󰁮󰁯󰁳 ............................................................................................................................ 6 I.0. I󰁮󰁴󰁲󰁯󰁤󰁵󰃧󰃣󰁯 ........................................................................................................................... 6 I.1. A󰁳 󰁯󰁲󰁩󰁧󰁥󰁮󰁳: 󰁵󰁭󰁡 󰁣󰁯󰁮󰁪󰁥󰁴󰁵󰁲󰁡 󰁤󰁥 D󰁩󰁲󰁡󰁣 󰁥 󰁡 󰁴󰁥󰁳󰁥 󰁤󰁥 F󰁥󰁹󰁮󰁭󰁡󰁮 .................................................. 8 I.2. A 󰁩󰁮󰁴󰁥󰁧󰁲󰁡󰁬 󰁤󰁥 F󰁥󰁹󰁮󰁭󰁡󰁮 󰁥 󰁡 󰁥󰁱󰁵󰁡󰃧󰃣󰁯 󰁤󰁥 S󰁣󰁨󰁲󰃶󰁤󰁩󰁮󰁧󰁥󰁲 ......................................................... 11 I.3. A󰁮󰁡󰁬󰁯󰁧󰁩󰁡󰁳 󰁦󰁯󰁲󰁭󰁡󰁩󰁳: 󰁡󰁳 󰁩󰁮󰁴󰁥󰁧󰁲󰁡󰁩󰁳 󰁤󰁥 󰁗󰁩󰁥󰁮󰁥󰁲 󰁥 I󰁴󰃴 ................................................................ 12 I.3.1. O 󰁭󰁯󰁶󰁩󰁭󰁥󰁮󰁴󰁯 󰁢󰁲󰁯󰁷󰁮󰁩󰁡󰁮󰁯 󰁲󰁥󰁶󰁩󰁳󰁩󰁴󰁡󰁤󰁯 ................................................................... 13 I.3.2. A 󰁩󰁮󰁴󰁥󰁧󰁲󰁡󰁬 󰁤󰁥 󰁗󰁩󰁥󰁮󰁥󰁲 .......................................................................................... 14 I.3.3. A 󰁩󰁮󰁴󰁥󰁧󰁲󰁡󰁬 󰁤󰁥 I󰁴󰃴 ................................................................................................... 15 I.3.4 A 󰁩󰁮󰁴󰁥󰁧󰁲󰁡󰁬 󰁤󰁥 S󰁴󰁲󰁡󰁴󰁯󰁮󰁯󰁶󰁩󰁣󰁨 ....................................................................................... 16 I.4. O󰁳 E󰁰󰃭󰁧󰁯󰁮󰁯󰁳 󰁥 󰁯 󰁥󰁮󰁩󰁧󰁭󰁡 󰁭󰁡󰁴󰁥󰁭󰃡󰁴󰁩󰁣󰁯 ................................................................................ 18 II. A M󰁥󰁤󰁩󰁤󰁡 󰁥 󰁡 I󰁮󰁴󰁥󰁧󰁲󰁡󰁬 .............................................................................................................. 20 II.1. O󰁳 󰁣󰁯󰁮󰁣󰁥󰁩󰁴󰁯󰁳 󰁥 󰁯󰁳 󰁥󰁬󰁥󰁭󰁥󰁮󰁴󰁯󰁳 󰁤󰁡 󰁩󰁮󰁴󰁥󰁧󰁲󰁡󰃧󰃣󰁯 ..................................................................... 20 II.2. T󰁥󰁯󰁲󰁩󰁡 󰁤󰁡 M󰁥󰁤󰁩󰁤󰁡 (H. L󰁥󰁢󰁥󰁳󰁧󰁵󰁥) 󲀓 󰁵󰁭󰁡 󰁢󰁲󰁥󰁶󰁥 󰁥󰁸󰁰󰁯󰁳󰁩󰃧󰃣󰁯 ........................................... 21 II.3. A 󰁩󰁮󰁴󰁥󰁧󰁲󰁡󰁬 󰁤󰁥 R󰁩󰁥󰁭󰁡󰁮󰁮: 󰁡 󰁥󰁸󰁡󰁵󰁳󰁴󰃣󰁯 󰁤󰁡 A󰁮󰃡󰁬󰁩󰁳󰁥 R󰁥󰁡󰁬 ................................................... 26 II.4. A 󰁩󰁮󰁴󰁥󰁧󰁲󰁡󰁬 󰁤󰁥 L󰁥󰁢󰁥󰁳󰁧󰁵󰁥 󰁥 󰁡 󰁥󰁸󰁴󰁥󰁮󰁳󰃣󰁯 󰁡 󰁥󰁳󰁰󰁡󰃧󰁯󰁳 󰁡󰁢󰁳󰁴󰁲󰁡󰁴󰁯󰁳 ......................................... 31 II.4.1. A 󰁩󰁮󰁴󰁥󰁧󰁲󰁡󰁬 ............................................................................................................. 31 II.4.2. F󰁵󰁮󰃧󰃵󰁥󰁳 󰁩󰁮󰁴󰁥󰁧󰁲󰃡󰁶󰁥󰁩󰁳 ............................................................................................. 33 II.5. A󰁬󰁧󰁵󰁮󰁳 󰁥󰁸󰁥󰁭󰁰󰁬󰁯󰁳 󰁤󰁥 󰁭󰁥󰁤󰁩󰁤󰁡󰁳 󰁥󰁭 F󰃭󰁳󰁩󰁣󰁡 T󰁥󰃳󰁲󰁩󰁣󰁡 ........................................................ 37 II.5.1. A 󰁭󰁥󰁤󰁩󰁤󰁡 󰁤󰁥 D󰁩󰁲󰁡󰁣 ..................................................................................................... 37 II.5.2. I󰁮󰁴󰁥󰁧󰁲󰁡󰃧󰃣󰁯 󰁳󰁯󰁢󰁲󰁥 󰁧󰁲󰁵󰁰󰁯󰁳: 󰁡 󰁭󰁥󰁤󰁩󰁤󰁡 󰁤󰁥 H󰁡󰁡󰁲. ............................................................ 38 II.5.3. O󰁵󰁴󰁲󰁡󰁳 󰁭󰁥󰁤󰁩󰁤󰁡󰁳 󰁤󰁥 󰁩󰁮󰁴󰁥󰁧󰁲󰁡󰃧󰃣󰁯 .................................................................................. 44 III. 󰁕󰁭󰁡 T󰁥󰁯󰁲󰁩󰁡 G󰁥󰁲󰁡󰁬 󰁤󰁡 I󰁮󰁴󰁥󰁧󰁲󰁡󰁬 󰁤󰁥 F󰁥󰁹󰁮󰁭󰁡󰁮 ............................................................................ 56 III.1. A L󰁥󰁩 󰁤󰁥 M󰁯󰁶󰁩󰁭󰁥󰁮󰁴󰁯 󰁤󰁡 MQ ............................................................................................ 56 III.1.1. A A󰃧󰃣󰁯 C󰁬󰃡󰁳󰁳󰁩󰁣󰁡 ........................................................................................................ 56 III.1.2. A A󰁭󰁰󰁬󰁩󰁴󰁵󰁤󰁥 󰁤󰁥 P󰁲󰁯󰁢󰁡󰁢󰁩󰁬󰁩󰁤󰁡󰁤󰁥 󰁮󰁡 MQ .................................................................... 57 III.1.3. O 󰁬󰁩󰁭󰁩󰁴󰁥 󰁣󰁬󰃡󰁳󰁳󰁩󰁣󰁯 ....................................................................................................... 57 III.1.4. A 󰁳󰁯󰁭󰁡 󰁳󰁯󰁢󰁲󰁥 󰁴󰁲󰁡󰁪󰁥󰁴󰃳󰁲󰁩󰁡󰁳 .......................................................................................... 58 III.1.4.1. A 󰁡󰁮󰁡󰁬󰁯󰁧󰁩󰁡 󰁣󰁯󰁭 󰁡 󰁩󰁮󰁴󰁥󰁧󰁲󰁡󰁬 󰁤󰁥 R󰁩󰁥󰁭󰁡󰁮󰁮 .................................................................. 58 III.1.4.2. C󰁯󰁮󰁳󰁴󰁲󰁵󰁩󰁮󰁤󰁯 󰁡 󰁳󰁯󰁭󰁡 .............................................................................................. 59 III.1.4.3. A 󰁩󰁮󰁴󰁥󰁧󰁲󰁡󰁬 󰁤󰁥 󰁴󰁲󰁡󰁪󰁥󰁴󰃳󰁲󰁩󰁡 .......................................................................................... 60 III.1.4.4. A 󰁲󰁥󰁧󰁲󰁡 󰁰󰁡󰁲󰁡 󰁤󰁯󰁩󰁳 󰁥󰁶󰁥󰁮󰁴󰁯󰁳 󰁳󰁵󰁣󰁥󰁳󰁳󰁩󰁶󰁯󰁳 .................................................................... 60 III.2. A 󰁦󰃳󰁲󰁭󰁵󰁬󰁡 󰁤󰁥 T󰁲󰁯󰁴󰁴󰁥󰁲 ....................................................................................................... 61 III.3. O O󰁳󰁣󰁩󰁬󰁡󰁤󰁯󰁲 H󰁡󰁲󰁭󰃴󰁮󰁩󰁣󰁯 S󰁩󰁭󰁰󰁬󰁥󰁳 (OHS) 󰁥 󰁯 O󰁳󰁣󰁩󰁬󰁡󰁤󰁯󰁲 H󰁡󰁲󰁭󰃴󰁮󰁩󰁣󰁯 F󰁯󰁲󰃧󰁡󰁤󰁯 ..................... 66   3 III.3.1. I󰁮󰁴󰁥󰁧󰁲󰁡󰁩󰁳 󰁧󰁡󰁵󰁳󰁳󰁩󰁡󰁮󰁡󰁳 ................................................................................................. 66 III.3.2. C󰃡󰁬󰁣󰁵󰁬󰁯 󰁤󰁡 󰁡󰃧󰃣󰁯 󰁤󰁯 OHS ............................................................................................ 67 III.3.3. C󰃡󰁬󰁣󰁵󰁬󰁯 󰁤󰁡 󰁦󰁵󰁮󰃧󰃣󰁯 ( ) OHS  F T   .................................................................................... 68 III.3.4. OHS 󰁦󰁯󰁲󰃧󰁡󰁤󰁯 󰁥 󰁡󰁳 󰁦󰁯󰁮󰁴󰁥󰁳 ( )  J t   󰁤󰁥 S󰁣󰁨󰁷󰁩󰁮󰁧󰁥󰁲 .......................................................... 71 III.4. D󰁥󰁲󰁩󰁶󰁡󰁤󰁡󰁳 󰁦󰁵󰁮󰁣󰁩󰁯󰁮󰁡󰁩󰁳 ....................................................................................................... 74 III.5. O 󰁣󰃡󰁬󰁣󰁵󰁬󰁯 󰁰󰁥󰁲󰁴󰁵󰁲󰁢󰁡󰁴󰁩󰁶󰁯 ..................................................................................................... 75 III.5.1. O 󰁦󰁵󰁮󰁣󰁩󰁯󰁮󰁡󰁬 󰁧󰁥󰁲󰁡󰁤󰁯󰁲 .................................................................................................. 75 III.5.2. O 󰁰󰁲󰁯󰁰󰁡󰁧󰁡󰁤󰁯󰁲 󰁤󰁥 F󰁥󰁹󰁮󰁭󰁡󰁮 ...................................................................................... 77 III.5.3. C󰃡󰁬󰁣󰁵󰁬󰁯 󰁰󰁥󰁲󰁴󰁵󰁲󰁢󰁡󰁴󰁩󰁶󰁯 󰁤󰁡 󰁴󰁥󰁯󰁲󰁩󰁡 3 φ   .......................................................................... 81 III.5.3.1. C󰃡󰁬󰁣󰁵󰁬󰁯 󰁤󰁡󰁳 󰁦󰁵󰁮󰃧󰃵󰁥󰁳 󰁤󰁥 G󰁲󰁥󰁥󰁮 󰁰󰁡󰁲󰁡 󰁵󰁭 󰁰󰁯󰁴󰁥󰁮󰁣󰁩󰁡󰁬 󰁡󰁲󰁢󰁩󰁴󰁲󰃡󰁲󰁩󰁯 ................................ 81 III.5.3.2. C󰃡󰁬󰁣󰁵󰁬󰁯 󰁤󰁡 󰁳󰃩󰁲󰁩󰁥 󰁰󰁥󰁲󰁴󰁵󰁲󰁢󰁡󰁴󰁩󰁶󰁡 󰁰󰁡󰁲󰁡 󰁯 󰁰󰁯󰁴󰁥󰁮󰁣󰁩󰁡󰁬 ( ) 3 3! gV   φ φ  = −  .......................... 83 III.5.3.3. I󰁮󰁴󰁥󰁲󰁰󰁲󰁥󰁴󰁡󰃧󰃣󰁯 󰁤󰁩󰁡󰁧󰁲󰁡󰁭󰃡󰁴󰁩󰁣󰁡 󰁤󰁡 󰁴󰁥󰁯󰁲󰁩󰁡 3 φ   ............................................................. 86 I󰁖. T󰃩󰁣󰁮󰁩󰁣󰁡󰁳 󰁥 A󰁰󰁬󰁩󰁣󰁡󰃧󰃵󰁥󰁳 󰁤󰁡 I󰁮󰁴󰁥󰁧󰁲󰁡󰁬 F󰁵󰁮󰁣󰁩󰁯󰁮󰁡󰁬 .................................................................. 95 I󰁖.1. C󰃡󰁬󰁣󰁵󰁬󰁯 P󰁥󰁲󰁴󰁵󰁲󰁢󰁡󰁴󰁩󰁶󰁯: 󰁭󰃩󰁴󰁯󰁤󰁯󰁳 󰁥 󰁴󰃩󰁣󰁮󰁩󰁣󰁡󰁳 󰁧󰁥󰁲󰁡󰁩󰁳 ............................................................ 95 I󰁖.1.1. R󰁥󰁧󰁲󰁡󰁳 󰁤󰁥 F󰁥󰁹󰁮󰁭󰁡󰁮 󰁰󰁡󰁲󰁡 󰁯 󰁰󰁯󰁴󰁥󰁮󰁣󰁩󰁡󰁬 4 φ   ............................................................ 98 I󰁖.2. A P󰁡󰁲󰁴󰃭󰁣󰁵󰁬󰁡 L󰁩󰁶󰁲󰁥 󰁮󰁵󰁭 󰁥󰁳󰁰󰁡󰃧󰁯 󰁥󰁵󰁣󰁬󰁩󰁤󰁩󰁡󰁮󰁯 D󰀭󰁤󰁩󰁭󰁥󰁮󰁳󰁩󰁯󰁮󰁡󰁬 .............................................. 101 I󰁖.3. O O󰁳󰁣󰁩󰁬󰁡󰁤󰁯󰁲 H󰁡󰁲󰁭󰃴󰁮󰁩󰁣󰁯 󰁮󰁵󰁭 󰁥󰁳󰁰󰁡󰃧󰁯 󰁥󰁵󰁣󰁬󰁩󰁤󰁩󰁡󰁮󰁯 D󰀭󰁤󰁩󰁭󰁥󰁮󰁳󰁩󰁯󰁮󰁡󰁬................................... 102 I󰁖.4. Q󰁵󰁡󰁮󰁴󰁩󰁺󰁡󰃧󰃣󰁯 F󰁵󰁮󰁣󰁩󰁯󰁮󰁡󰁬 󰁤󰁥 C󰁡󰁭󰁰󰁯󰁳 E󰁳󰁣󰁡󰁬󰁡󰁲󰁥󰁳 .......................................................... 104 I󰁖.4.1. F󰁵󰁮󰃧󰃵󰁥󰁳 󰁤󰁥 C󰁯󰁲󰁲󰁥󰁬󰁡󰃧󰃣󰁯 .......................................................................................... 104 I󰁖.5. A A󰁮󰁡󰁬󰁯󰁧󰁩󰁡 󰁥󰁮󰁴󰁲󰁥 T󰁥󰁯󰁲󰁩󰁡 Q󰁵󰃢󰁮󰁴󰁩󰁣󰁡 󰁤󰁯󰁳 C󰁡󰁭󰁰󰁯󰁳 󰁥 F󰃭󰁳󰁩󰁣󰁡 E󰁳󰁴󰁡󰁴󰃭󰁳󰁴󰁩󰁣󰁡 .............................. 108 I󰁖.6. Q󰁵󰁡󰁮󰁴󰁩󰁺󰁡󰃧󰃣󰁯 F󰁵󰁮󰁣󰁩󰁯󰁮󰁡󰁬 󰁤󰁯 C󰁡󰁭󰁰󰁯 E󰁬󰁥󰁴󰁲󰁯󰁭󰁡󰁧󰁮󰃩󰁴󰁩󰁣󰁯 (󰁣󰁡󰁭󰁰󰁯 󰁤󰁥 M󰁡󰁸󰁷󰁥󰁬󰁬) .................. 109 I󰁖.7. Q󰁵󰁡󰁮󰁴󰁩󰁺󰁡󰃧󰃣󰁯 F󰁵󰁮󰁣󰁩󰁯󰁮󰁡󰁬 󰁤󰁯 C󰁡󰁭󰁰󰁯 E󰁳󰁰󰁩󰁮󰁯󰁲󰁩󰁡󰁬 ............................................................... 113 I󰁖.7.1 C󰃡󰁬󰁣󰁵󰁬󰁯 G󰁥󰁯󰁭󰃩󰁴󰁲󰁩󰁣󰁯, 󰁯󰁵 󰃁󰁬󰁧󰁥󰁢󰁲󰁡 󰁤󰁥 G󰁲󰁡󰁳󰁳󰁭󰁡󰁮󰁮 .................................................... 113 I󰁖.7.2. 󲀓 O 󰁦󰁵󰁮󰁣󰁩󰁯󰁮󰁡󰁬 󰁧󰁥󰁲󰁡󰁤󰁯󰁲 󰁰󰁡󰁲󰁡 󰁯 󰁣󰁡󰁭󰁰󰁯 󰁤󰁥 D󰁩󰁲󰁡󰁣 ....................................................... 115 I󰁖.8. QED: E󰁬󰁥󰁴󰁲󰁯󰁤󰁩󰁮󰃢󰁭󰁩󰁣󰁡 Q󰁵󰃢󰁮󰁴󰁩󰁣󰁡 .................................................................................. 116 I󰁖.9. D󰁥󰁴󰁥󰁲󰁭󰁩󰁮󰁡󰁮󰁴󰁥󰁳 F󰁵󰁮󰁣󰁩󰁯󰁮󰁡󰁩󰁳 ........................................................................................ 117 L󰁩󰁳󰁴󰁡 󰁤󰁥 󰁥󰁸󰁥󰁲󰁣󰃭󰁣󰁩󰁯󰁳 󰁤󰁯 M󰃳󰁤󰁵󰁬󰁯 A ................................................................................................ 120 󰁖. O F󰁯󰁲󰁭󰁡󰁬󰁩󰁳󰁭󰁯 󰁤󰁥 T󰁥󰁭󰁰󰁯 I󰁭󰁡󰁧󰁩󰁮󰃡󰁲󰁩󰁯 .................................................................................... 121 󰁖.1. S󰁩󰁳󰁴󰁥󰁭󰁡󰁳 󰁥󰁭 󰁥󰁱󰁵󰁩󰁬󰃭󰁢󰁲󰁩󰁯: 󰁴󰁥󰁭󰁰󰁯 󰁩󰁭󰁡󰁧󰁩󰁮󰃡󰁲󰁩󰁯 .................................................................... 121 󰁖.1.1. 󰁕󰁭󰁡 B󰁲󰁥󰁶󰁥 R󰁥󰁶󰁩󰁳󰃣󰁯 󰁤󰁥 T󰁥󰁲󰁭󰁯󰁤󰁩󰁮󰃢󰁭󰁩󰁣󰁡 E󰁳󰁴󰁡󰁴󰃭󰁳󰁴󰁩󰁣󰁡 󰁮󰁯 E󰁱󰁵󰁩󰁬󰃭󰁢󰁲󰁩󰁯 ........................... 121 󰁖.1.2. O F󰁯󰁲󰁭󰁡󰁬󰁩󰁳󰁭󰁯 󰁤󰁥 M󰁡󰁴󰁳󰁵󰁢󰁡󰁲󰁡 .................................................................................. 123 󰁖.1.3. A󰁳 F󰁲󰁥󰁱󰁵󰃪󰁮󰁣󰁩󰁡󰁳 󰁤󰁥 M󰁡󰁴󰁳󰁵󰁢󰁡󰁲󰁡 ................................................................................. 126   4 󰁖.1.4. A F󰁯󰁲󰁭󰁵󰁬󰁡󰃧󰃣󰁯 I󰁮󰁴󰁥󰁧󰁲󰁡󰁬 F󰁵󰁮󰁣󰁩󰁯󰁮󰁡󰁬 ............................................................................ 129 󰁖.1.5. R󰁥󰁰󰁲󰁥󰁳󰁥󰁮󰁴󰁡󰃧󰃣󰁯 I󰁮󰁴󰁥󰁧󰁲󰁡󰁬 F󰁵󰁮󰁣󰁩󰁯󰁮󰁡󰁬 󰁤󰁡 F󰁵󰁮󰃧󰃣󰁯 󰁤󰁥 P󰁡󰁲󰁴󰁩󰃧󰃣󰁯 ................................ 131 󰁖.1.5.1. A󰁭󰁰󰁬󰁩󰁴󰁵󰁤󰁥 󰁤󰁥 T󰁲󰁡󰁮󰁳󰁩󰃧󰃣󰁯 󰁰󰁡󰁲󰁡 B󰃳󰁳󰁯󰁮󰁳 ............................................................ 131 󰁖.1.5.2. A F󰁵󰁮󰃧󰃣󰁯 󰁤󰁥 P󰁡󰁲󰁴󰁩󰃧󰃣󰁯 B󰁯󰁳󰃴󰁮󰁩󰁣󰁡 ............................................................................ 133 󰁖.1.5.3. C󰁡󰁭󰁰󰁯 󰁥󰁳󰁣󰁡󰁬󰁡󰁲 󰁮󰁥󰁵󰁴󰁲󰁯 ................................................................................... 134 󰁖.1.5.4. F󰃩󰁲󰁭󰁩󰁯󰁮󰁳 .............................................................................................................. 137 󰁖.1.6. A󰁰󰁬󰁩󰁣󰁡󰃧󰃵󰁥󰁳 󰁤󰁯 󰁦󰁯󰁲󰁭󰁡󰁬󰁩󰁳󰁭󰁯 󰁤󰁥 M󰁡󰁴󰁳󰁵󰁢󰁡󰁲󰁡 ............................................................... 141 󰁖.1.6.1. A C󰁯󰁲󰁲󰁥󰃧󰃣󰁯 󰁤󰁥 M󰁡󰁳󰁳󰁡 󰁥󰁭 󰁕󰁭 L󰁡󰃧󰁯 󰁰󰁡󰁲󰁡 󰁡 󰁴󰁥󰁯󰁲󰁩󰁡 4 φ   ........................................... 142 󰁖.1.6.2. A A󰁵󰁴󰁯󰀭󰁥󰁮󰁥󰁲󰁧󰁩󰁡 󰁥󰁭 T󰁥󰁭󰁰󰁥󰁲󰁡󰁴󰁵󰁲󰁡 F󰁩󰁮󰁩󰁴󰁡 ............................................................... 146 󰁖.1.6.3. C󰁯󰁮󰁤󰁥󰁮󰁳󰁡󰃧󰃣󰁯 󰁤󰁥 B󰁯󰁳󰁥󰀭E󰁩󰁮󰁳󰁴󰁥󰁩󰁮 ..................................................................... 151 󰁖I. O F󰁯󰁲󰁭󰁡󰁬󰁩󰁳󰁭󰁯 󰁤󰁥 T󰁥󰁭󰁰󰁯 R󰁥󰁡󰁬 .............................................................................................. 157 󰁖I.1. I󰁮󰁴󰁲󰁯󰁤󰁵󰃧󰃣󰁯 ..................................................................................................................... 157 󰁖I.2. O F󰁯󰁲󰁭󰁡󰁬󰁩󰁳󰁭󰁯 CTP ......................................................................................................... 157 󰁖I.3. P󰁲󰁯󰁰󰁡󰁧󰁡󰁤󰁯󰁲󰁥󰁳 󰁥 󰁳󰁵󰁡 E󰁳󰁴󰁲󰁵󰁴󰁵󰁲󰁡 M󰁡󰁴󰁲󰁩󰁣󰁩󰁡󰁬 ....................................................................... 161 󰁖I.4. P󰁲󰁯󰁰󰁲󰁩󰁥󰁤󰁡󰁤󰁥󰁳 󰁤󰁥 A󰁮󰁡󰁬󰁩󰁴󰁩󰁣󰁩󰁤󰁡󰁤󰁥 ...................................................................................... 171 󰁖I.5. O P󰁲󰁯󰁰󰁡󰁧󰁡󰁤󰁯󰁲 󰁡 󰁕󰁭 L󰁡󰃧󰁯 .............................................................................................. 172 󰁖II. F󰁯󰁲󰁭󰁡󰁬󰁩󰁳󰁭󰁯 󰁤󰁥 T󰁥󰁭󰁰󰁯 R󰁥󰁡󰁬 󰁣󰁯󰁭 C󰁡󰁭󰁰󰁯󰁳 T󰃩󰁲󰁭󰁩󰁣󰁯󰁳 ........................................................... 176 󰁖II.1. I󰁮󰁴󰁲󰁯󰁤󰁵󰃧󰃣󰁯 .................................................................................................................... 176 󰁖II.2. F󰁯󰁲󰁭󰁡󰁬󰁩󰁳󰁭󰁯 TFD ........................................................................................................... 177 󰁖II.2.1. T󰁲󰁡󰁮󰁳󰁦󰁯󰁲󰁭󰁡󰃧󰃣󰁯 󰁤󰁥 B󰁯󰁧󰁯󰁬󰁩󰁵󰁢󰁯󰁶 󰁥 󰁖󰃡󰁣󰁵󰁯󰁳 T󰃩󰁲󰁭󰁩󰁣󰁯󰁳 ............................................... 177 󰁖II.2.1.1. C󰁯󰁲󰁲󰁥󰁬󰁡󰃧󰃣󰁯 󰁮󰁯 󰁖󰃡󰁣󰁵󰁯 .......................................................................................... 177 󰁖II.2.1.1.1. R󰁥󰁰󰁲󰁥󰁳󰁥󰁮󰁴󰁡󰃧󰃣󰁯 󰁤󰁥 N󰃺󰁭󰁥󰁲󰁯 (󰁤󰁥 O󰁳󰁣󰁩󰁬󰁡󰁤󰁯󰁲󰁥󰁳) ................................................. 177 󰁖II.2.1.1.2. E󰁳󰁴󰁡󰁤󰁯󰁳 C󰁯󰁥󰁲󰁥󰁮󰁴󰁥󰁳........................................................................................... 179 󰁖II.2.1.1.3. E󰁳󰁴󰁡󰁤󰁯󰁳 C󰁯󰁭󰁰󰁲󰁩󰁭󰁩󰁤󰁯󰁳 ( 󰁳󰁱󰁵󰁥󰁥󰁺󰁥󰁤 󰁳󰁴󰁡󰁴󰁥󰁳 ) ........................................................ 181 󰁖II.2.1.1.4. E󰁳󰁴󰁡󰁤󰁯󰁳 󰁣󰁯󰁭󰁰󰁲󰁩󰁭󰁩󰁤󰁯󰁳 󰁣󰁯󰁭 󰁤󰁯󰁩󰁳 󰁭󰁯󰁤󰁯󰁳 .......................................................... 183 󰁖II.2.2. A󰁢󰁯󰁲󰁤󰁡󰁧󰁥󰁭 󰁰󰁯󰁲 O󰁰󰁥󰁲󰁡󰁤󰁯󰁲󰁥󰁳: D󰁵󰁰󰁬󰁩󰁣󰁡󰃧󰃣󰁯 󰁤󰁯 E󰁳󰁰󰁡󰃧󰁯 󰁤󰁥 H󰁩󰁬󰁢󰁥󰁲󰁴 ........................... 185 󰁖II.2.3. O󰁳󰁣󰁩󰁬󰁡󰁤󰁯󰁲󰁥󰁳 B󰁯󰁳󰃴󰁮󰁩󰁣󰁯󰁳 󰁥 F󰁥󰁲󰁭󰁩󰃴󰁮󰁩󰁣󰁯󰁳 ................................................................... 187 󰁖II.2.3.1. O󰁳󰁣󰁩󰁬󰁡󰁤󰁯󰁲 B󰁯󰁳󰃴󰁮󰁩󰁣󰁯 ............................................................................................. 187 󰁖II.2.3.2. O󰁳󰁣󰁩󰁬󰁡󰁤󰁯󰁲 F󰁥󰁲󰁭󰁩󰃴󰁮󰁩󰁣󰁯 ......................................................................................... 189 󰁖II.2.4. T󰁥󰁯󰁲󰁩󰁡 L󰁩󰁶󰁲󰁥 󰁤󰁯 C󰁡󰁭󰁰󰁯 󰁤󰁥 S󰁣󰁨󰁲󰃶󰁤󰁩󰁮󰁧󰁥󰁲: O󰁰󰁥󰁲󰁡󰁤󰁯󰁲󰁥󰁳 T󰃩󰁲󰁭󰁩󰁣󰁯󰁳 ............................ 194 󰁖II.2.5. O P󰁲󰁯󰁰󰁡󰁧󰁡󰁤󰁯󰁲 󰁤󰁡 T󰁥󰁯󰁲󰁩󰁡 L󰁩󰁶󰁲󰁥 󰁤󰁯 C󰁡󰁭󰁰󰁯 󰁤󰁥 K󰁬󰁥󰁩󰁮󰀭G󰁯󰁲󰁤󰁯󰁮................................... 198 󰁖II.2.6. A C󰁯󰁮󰁤󰁩󰃧󰃣󰁯 KMS .................................................................................................... 201 󰁖II.2.7. R󰁥󰁬󰁡󰃧󰃵󰁥󰁳 󰁤󰁥 D󰁩󰁳󰁰󰁥󰁲󰁳󰃣󰁯 󰁰󰁡󰁲󰁡 P󰁲󰁯󰁰󰁡󰁧󰁡󰁤󰁯󰁲󰁥󰁳 A󰁲󰁢󰁩󰁴󰁲󰃡 rios  ........................................ 202 󰁖II.2.7. O T󰁥󰁯󰁲󰁥󰁭󰁡 󰁤󰁥 G󰁯󰁬󰁤󰁳󰁴󰁯󰁮󰁥 󰁮󰁡 TFD .......................................................................... 204
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