Master Dissertation

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Bibliography [1] J. Foster and J.D. Nightingale: A Short Course in General Relativity 2nd edition Springer-Verlag, New York, 1995. [2] Gerd Grubb: Introduction to Distribution Theory - Lecture Notes, ”http://www.math.ku.dk/∼grubb/distribution.htm”, Copenhagen, 2003. [3] Romeo Brunetti and Klaus Fredenhagen: Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds, http://arxiv.org/abs/math-ph/9903028, Hamburg, 1999. [4] Asger Jacobsen and Morten Bakkedal: Wave Front Sets, ”http://www.ajac.dk/projects/wavefront/wavefront.pdf”, Copenhagen, 2005. [5] Robert J. Zimmer Essential Results of Functional Analysis, The University of Chicago Press, Chicago, 1990. [6] G. Scharf: Finite Quantum Electrodynamics - The Causal Approach 2nd edition, Springer-Verlag, Berlin, 1995. [7] Richard L. Liboff: Introductory Quantum Mechanics 3rd edition, Addison-Wesley, 1998. [8] J.J. Sakurai: Modern Quantum Mechanics Revised Edition, Addison-Wesley, 1994. [9] Huzihiro Araki: Mathematical Theory of Quantum Fields, Oxford University Press, Oxford, 1999. [10] G. Freidlander and M. Joshi: The Theory of Distributions 2nd edition, Cambridge University Press, Cambridge, 1998. [11] Lars Hörmander: The Analysis of Linear Partial Differential Operators I - Distribution Theory and Fourier Analysis 2nd edition, Springer-Verlag, Berlin Heidelberg, 1990 77
[12] Walter Rudin: Functional Analysis - 2nd edition McGraw-Hill, Inc. New York, 1991. 78
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Master Dissertation The Method of E
Page 3 and 4:
9 The Microlocal Approach - A Condi
Page 5 and 6:
Preface Overview This dissertation
Page 7 and 8:
Chapter 8 In Chapter 8 we will turn
Page 9 and 10:
Chapter 1 Introductory Theory 1.1 N
Page 11 and 12:
1.2 Formal Power Series The concept
Page 13 and 14:
Theorem 1.6. Let anX n be a formal
Page 15 and 16:
1.3 Affine Transformations of Distr
Page 17 and 18:
Chapter 2 The Poincaré Group 2.1 T
Page 19 and 20:
Definition 2.2. Given some point x
Page 21 and 22:
〈y, y〉 = det σ(y) = det A det
Page 23 and 24:
Note that 〈Woutφ, ψ〉 = 〈 li
Page 25 and 26:
Chapter 4 The Mathematical Setting
Page 27 and 28:
where ψ is the time-dependent Dira
Page 29 and 30: The Wightman Axioms. Axiom 1 (quant
Page 31 and 32: Axiom 0 (Well-definedness) Let g =
Page 33 and 34: Expected properties of the S-matrix
Page 35 and 36: equal powers must have equal coeffi
Page 37 and 38: We see that the Tn’s are time-ord
Page 39 and 40: 5.2 Example - In the Hilbert Space
Page 41 and 42: 5.3 Splitting of Distributions In o
Page 43 and 44: A proof of this is found in [6] pag
Page 45 and 46: Lemma 6.3. Let f : [x0, ∞) → R
Page 47 and 48: We want to show by induction that f
Page 49 and 50: substituting t := s − x. We may w
Page 51 and 52: Proof. Reduce ρ to be slowly varyi
Page 53 and 54: In our setting this is not defined,
Page 55 and 56: Let n, m ∈ N then and Hence mf( n
Page 57 and 58: 7.2 Case I: Negative Singular Order
Page 59 and 60: Therefore φ(x)d(x) also has quasi-
Page 61 and 62: Corollary 7.10. The limit exists.
Page 63 and 64: It is obvious for k = 0 and k = 1.
Page 65 and 66: By compactness of the unit-ball and
Page 67 and 68: 7.3 Case II: Positive Singular Orde
Page 69 and 70: Chapter 8 Application to QED 8.1 Us
Page 71 and 72: Finally we can calculate the differ
Page 73 and 74: Theorem 8.1. Identify ˆg(k) with t
Page 75 and 76: in the sense that if h ∈ D(M), th
Page 77 and 78: Note that the definition agrees wit
Page 79: Proof. Let xm be a maximal point, t
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Master Dissertation

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