A Combinatorial Perspective on Quantum Field Theory - download pdf or read online

By Karen Yeats

ISBN-10: 3319475509

ISBN-13: 9783319475509

ISBN-10: 3319475517

ISBN-13: 9783319475516

This publication explores combinatorial difficulties and insights in quantum box idea. it isn't complete, yet quite takes a travel, formed by means of the author’s biases, via a few of the vital ways in which a combinatorial viewpoint will be delivered to undergo on quantum box thought. one of the results are either actual insights and engaging mathematics.

The ebook starts off via taking into account perturbative expansions as varieties of producing capabilities after which introduces renormalization Hopf algebras. the remaining is damaged into elements. the 1st half appears at Dyson-Schwinger equations, stepping steadily from the basically combinatorial to the extra actual. the second one half seems to be at Feynman graphs and their periods.

The flavour of the publication will entice mathematicians with a combinatorics heritage in addition to mathematical physicists and different mathematicians.

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Incidence Hopf algebras. J. Pure Appl. Algebra 96(3), 299–330 (1994) 3. : On the multiplication of causal functions in the quantum theory of fields. Acta Math. 97, 227–266 (1957) 4. : Convergence of Bogoliubovs method of renormalization in momentum space. Commun. Math. Phys. 15, 208–234 (1969) 5. : Hopf algebra approach to Feynman diagram calculations. J. Phys. A 38, R285–R406 (2005). arXiv:hep-th/0510202 6. : On the Hopf algebra structure of perturbative quantum field theories. Adv. Theor. Math.

50 5 Feynman Graphs Fig. 2 The solid edges give a planar embedding of a graph G; the dotted edges give the dual graph G ∗ Finally, we need the notion of planar duality. A graph is planar if it can be drawn on the plane with each vertex a distinct point and each edge a curve where the edges only intersect at their ends. Such a drawing of a planar graph is a planar embedding. Cutting on the edges divides the plane into regions which are the faces of the embedding, including the one external or infinite face.

Commun. Math. Phys. 199, 203–242 (1998). arXiv:hep-th/9808042 20. : Faà di Bruno subalgebras of the Hopf algebra of planar trees from combinatorial Dyson-Schwinger equations. Adv. Math. 218(1), 136–162 (2007). 1204 21. : A Lie theoretic approach to renormalization. Commun. Math. Phys. 276(2), 519–549 (2007). arXiv:hep-th/0609035 22. : The residues of quantum field theory-numbers we should know. , Marcolli, M. ) Noncommutative Geometry and Number Theory, pp. 187–204. Vieweg (2006). arXiv:hep-th/0404090 23.

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A Combinatorial Perspective on Quantum Field Theory by Karen Yeats

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