دانلود کتاب Factorization algebras and free field theories

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Acknowledgements
Chapter 1. Introduction
1.1. An overview of the chapters
1.2. Notations
Chapter 2. Motivation and algebraic techniques
2.1. Classical BV formalism: the derived critical locus
2.2. Quantum BV formalism: the twisted de Rham complex
2.3. Wick\'s lemma and Feynman diagrams, homologically
2.4. A compendium of essential definitions and constructions
2.5. The homological perturbation lemma in the BV formalism
2.6. Global observables and formal Hodge theory
Chapter 3. BV formalism as a determinant functor
3.1. Cotangent quantization of k-vector spaces
3.2. Recollections
3.3. Properties of cotangent quantization over any commutative dg algebra
3.4. Invertibility survives over artinian dg algebras
Chapter 4. Factorization algebras
4.1. Definitions
4.2. Associative algebras as factorization algebras on R
4.3. Associative algebras and the bar complex
4.4. The category of factorization algebras
4.5. General construction methods for factorization algebras
4.6. A novel construction of the universal enveloping algebra
4.7. Extension from a factorizing basis
4.8. Pushforward and Pullback
Chapter 5. Free fields and their observables
5.1. Introduction
5.2. Elliptic complexes and free BV theories
5.3. Observables as a factorization algebra
5.4. BV quantization as a Heisenberg Lie algebra construction
5.5. BV quantization as a determinant functor
5.6. Implications for interacting theories
5.7. Theories with a Poincaré lemma
Chapter 6. Free holomorphic field theories and vertex algebras
6.1. The system
6.2. The quantum observables of the system
6.3. Recovering a vertex algebra
6.4. Vertex algebras from Lie algebras
6.5. Definitions and a conjecture
Chapter 7. An index theorem
7.1. A motivating example
7.2. A precise statement of the theorem
7.3. Setting up the problem
7.4. Background about BV theories and renormalization
7.5. The proof
7.6. Global statements
Bibliography