Introduction to Algebraic and Constructive Quantum Field Theory

Abstract

Wiener transform 41 1.8. The structure of r and wave-particle duality 1,9. Implications of wave-particle duality 1.10. Characterization of the free boson field 62 1.11. The complex wave representation 1.12. Analytic features of the complex wave representation 70 2, The Free Fermion Field 2, I. Clifford systems 2.2. Existence of the free fennion field 80 2.3. The real wave representation • 2.4. The complex wave representation 3. Properties of the Free Fields 3,1. lmroduction 3.2. The exponential laws 3.3. Irreducibility 3.4. Representation of the orthogonal group by measurepreserving transfonnations 100

Topics of Measure Theory on Infinite Dimensional Spaces

“…We review next some concepts and results from ergodic theory, following [1,31,32]. Only finite measures are considered.…”

Quantum fields with classical perturbations

“…Below we present computations only for E 2 , which is quadratically divergent. As a special case of (7.13) for n = 2 we write E 2 = |σ(k)| 2 π(k 2 ) dk (2π) 4 .…”

“…4) We say that Spin ↑ (1, 3) is a connected double covering of SO ↑ (1,3). The group Spin ↑ (1, 3) happens to be isomorphic to SL(2, C).…”

“…By saying that it is cyclic we will mean that it satisfies Axiom (4). To see this we recall that there are serious problems with commutation of unbounded operators [42].…”

Introduction to Representations of the Canonical Commutation and Anticommutation Relations

“…Modern exposition of the mathematical formalism of second quantization can be also found e.g. in [39,13]. We would also like to mention the book by Neretin [50], which describes infinite dimensional metaplectic and Pin groups, and review articles by Varilly and Gracia-Bondia [72,73].…”