By Karen Yeats
This publication explores combinatorial difficulties and insights in quantum box idea. it isn't complete, yet particularly takes a journey, formed via the author’s biases, via many of the very important ways in which a combinatorial viewpoint may be dropped at undergo on quantum box thought. one of the results are either actual insights and fascinating mathematics.
The e-book starts off via considering perturbative expansions as types 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 only combinatorial to the extra actual. the second one half seems to be at Feynman graphs and their periods.
The flavour of the publication will attract mathematicians with a combinatorics heritage in addition to mathematical physicists and different mathematicians.
Read or Download A Combinatorial Perspective on Quantum Field Theory PDF
Similar discrete mathematics books
This publication takes readers via all of the steps invaluable for fixing difficult difficulties in continuum mechanics with delicate particle equipment. Pedagogical difficulties make clear the iteration of preliminary stipulations, the remedy of boundary stipulations, the mixing of the equations of movement, and the research of the implications.
This quantity includes 9 survey articles in line with the invited lectures given on the twenty third British Combinatorial convention, held at Exeter in July 2011. This biennial convention is a well-established foreign occasion, with audio system from worldwide. by means of its nature, this quantity offers an up to date assessment of present examine task in different components of combinatorics, together with extremal graph idea, the cyclic sieving phenomenon and transversals in Latin squares.
This ebook is a festschrift in honor of Professor Anthony Gaglione's 60th birthday. This quantity offers a superb mixture of examine and expository articles on a number of elements of countless staff conception. The papers provide a extensive assessment of current learn in limitless crew thought commonly, and combinatorial team thought and non-Abelian group-based cryptography particularly.
- Mathematics: A Discrete Introduction
- An Engineer's Guide to Mathematica
- Flow Networks: Analysis and Optimization of Repairable Flow Networks, Networks with Disturbed Flows, Static Flow Networks and Reliability Networks (Elsevier Insights)
- The Finite Element Method in Charged Particle Optics (The Springer International Series in Engineering and Computer Science)
- Fibonacci numbers and matrices, Edition: version 9 Jan 2016
Extra info for A Combinatorial Perspective on Quantum Field Theory
Number Theory Phys. 7(2), 251–291 (2013). 5457 27. : Quantum periods: a census of φ 4 -transcendentals. Commun. Number Theory Phys. 4(1), 1–48 (2010). 2856 28. : Renormalization of gauge fields: a Hopf algebra approach. Commun. Math. Phys. 276, 773–798 (2007). arXiv:0610137 29. : A few c2 invariants of circulant graphs. Commun. Number Theor. Phys. 10(1), 63–86 (2016). 06974 30. : Hopf-algebraic renormalization of Kreimer’s toy model. Master’s thesis, HumboldtUniversität zu Berlin (2011) 31. : Integrable renormalization ii: the general case.
Commun. Math. Phys. 204(3), 669–689 (1999). arXiv:hep-th/9810022 8. : Parametric Feynman integrals and determinant hypersurfaces. Adv. Theor. Math. Phys. 14(3), 911–964 (2010). 2107 2 Personal communication with Spencer Bloch and Dirk Kreimer. pdf; my understanding of the connection between the convolution property and the exponential map is based on personal communication with Jason Bell and Julian Rosen. 3 Some References 33 9. : The QED beta-function from global solutions to Dyson-Schwinger equations.
Feynman graphs, rooted trees, and Ringel-Hall algebras. Commun. Math. Phys. 289(2), 561–577 (2009). 1179 26. : A chord diagram expansion coming from some Dyson-Schwinger equations. Commun. Number Theory Phys. 7(2), 251–291 (2013). 5457 27. : Quantum periods: a census of φ 4 -transcendentals. Commun. Number Theory Phys. 4(1), 1–48 (2010). 2856 28. : Renormalization of gauge fields: a Hopf algebra approach. Commun. Math. Phys. 276, 773–798 (2007). arXiv:0610137 29. : A few c2 invariants of circulant graphs.