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Exam (elaborations) TEST BANK FOR Polchinski's String Theory By Headri

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TEST BANK FOR Polchinski\'s String Theory By Headri

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Maastricht University (UM)

Exam (elaborations) TEST BANK FOR Polchinski's String Theory By Headri The following pages contain detailed solutions to 81 of the 202 problems in J. Polchinski’s twovolume textbook String Theory [1, 2]. I originally wrote up these solutions while teaching myself the subject, and then later d...

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, A solution manual for Polchinski’s String Theory
Matthew Headrick
arXiv:0812.4408v1 [hep-th] 23 Dec 2008

Martin Fisher School of Physics
Brandeis University
mph@brandeis.edu

Abstract
We present detailed solutions to 81 of the 202 problems in J. Polchinski’s two-volume text-
book String Theory.

BRX-TH-604

,CONTENTS 1

Contents
0 Preface 4

1 Chapter 1 5
1.1 Problem 1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Problem 1.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Problem 1.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Problem 1.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Problem 1.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Chapter 2 11
2.1 Problem 2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Problem 2.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Problem 2.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Problem 2.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5 Problem 2.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.6 Problem 2.11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.7 Problem 2.13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.8 Problem 2.15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.9 Problem 2.17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3 Chapter 3 21
3.1 Problem 3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Problem 3.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3 Problem 3.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.4 Problem 3.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.5 Problem 3.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.6 Problem 3.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.7 Problem 3.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.8 Problem 3.11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.9 Problem 3.13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4 Chapter 4 33
4.1 Problem 4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5 Chapter 5 35
5.1 Problem 5.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

, CONTENTS 2

6 Chapter 6 40
6.1 Problem 6.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
6.2 Problem 6.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
6.3 Problem 6.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
6.4 Problem 6.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
6.5 Problem 6.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
6.6 Problem 6.11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
6.7 Problem 6.12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

7 Chapter 7 52
7.1 Problem 7.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
7.2 Problem 7.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
7.3 Problem 7.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
7.4 Problem 7.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
7.5 Problem 7.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
7.6 Problem 7.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
7.7 Problem 7.10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
7.8 Problem 7.11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
7.9 Problem 7.13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.10 Problem 7.15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

8 Chapter 8 69
8.1 Problem 8.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
8.2 Problem 8.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
8.3 Problem 8.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
8.4 Problem 8.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
8.5 Problem 8.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
8.6 Problem 8.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
8.7 Problem 8.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
8.8 Problem 8.11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

9 Appendix A 78
9.1 Problem A.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
9.2 Problem A.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
9.3 Problem A.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

10 Chapter 10 83
10.1 Problem 10.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
10.2 Problem 10.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

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