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The \(c_2\) Invariant

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A Combinatorial Perspective on Quantum Field Theory

Part of the book series: SpringerBriefs in Mathematical Physics ((BRIEFSMAPHY,volume 15))

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Abstract

Schnetz [1] defined the \(c_2\) invariant based on counting points on the affine variety defined by the vanishing of \(\varPsi _G\).

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References

  1. Schnetz, O.: Quantum field theory over \({\mathbb{F}}_q\). Electr. J. Combin. 18 (2011). arXiv:0909.0905

  2. Brown, F., Schnetz, O.: A K3 in \(\phi ^4\). Duke Math J. 161(10), 1817–1862 (2012). arXiv:1006.4064

  3. Broadhurst, D., Kreimer, D.: Knots and numbers in \(\phi ^4\) theory to 7 loops and beyond. Int. J. Mod. Phys. C6(519–524) (1995). arXiv:hep-ph/9504352

  4. Belkale, P., Brosnan, P.: Matroids, motives, and a conjecture of Kontsevich. Duke Math. J. 116(1), 147–188 (2003). arXiv:math/0012198

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  5. Doryn, D.: On one example and one counterexample in counting rational points on graph hypersurfaces. p. 91. arXiv:1006.3533

  6. Brown, F., Schnetz, O.: Modular forms in quantum field theory. p. 33. arXiv:1304.5342

  7. Logan, A.: New realizations of modular forms in Calabi-Yau threefolds arising from \(\phi ^4\) theory. arXiv:1604.04918

  8. Brown, F., Schnetz, O., Yeats, K.: Properties of \(c_2\) invariants of Feynman graphs. Adv. Theor. Math. Phys. 18(2), 323–362 (2014). arXiv:1203.0188

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  9. Doryn, D.: The \(c_2\) invariant is invariant. arXiv:1312.7271

  10. Yeats, K.: A few \(c_2\) invariants of circulant graphs. p. 33. arXiv:1507.06974

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Authors and Affiliations

  1. Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada

    Karen Yeats

  2. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, Canada

    Karen Yeats

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  1. Karen Yeats
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Correspondence to Karen Yeats .

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Yeats, K. (2017). The \(c_2\) Invariant. In: A Combinatorial Perspective on Quantum Field Theory. SpringerBriefs in Mathematical Physics, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-319-47551-6_15

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