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Shojaei-Fard, Ali
- Application of Deformed Lie Algebras to Non-Perturbative Quantum Field Theory
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1 Independent Scholar, Mathematician, Tehran, 1461863596, Marzdaran Blvd, IR
1 Independent Scholar, Mathematician, Tehran, 1461863596, Marzdaran Blvd, IR
Source
The Journal of the Indian Mathematical Society, Vol 84, No 1-2 (2017), Pagination: 109-129Abstract
The manuscript implements Connes-Kreimer Hopf algebraic renormalization of Feynman diagrams and Dubois-Violette type noncommutative differential geometry to discover a new class of differential calculi with respect to infinite formal expansions of Feynman diagrams which are generated by Dyson-Schwinger equations.Keywords
Hopf Algebraic Renormalization, Dyson-Schwinger Equations, Dubois-Violette Noncommutative Differential Forms, Non-Perturbative Renormalization Group.
References
- C. M. Bender, Perturbation Theory In Large Order, Adv. in Math., vol. 30 no. 3 (1978), 250-267.
- C. Bergbauer, D. Kreimer, Hopf algebras in renormalization theory: Locality and Dyson-Schwinger equations from Hochschild cohomology, IRMA Lectures in Mathematics and Theoretical Physics, 10 (2006), 133-164.
- F. Brown, D. Kreimer, Angles, scales and parametric renormalization, Lett. Math. Phys., vol. 103 no. 9 (2013), 933-1007.
- G. Baditoiu, S. Rosenberg, Lax pair equations and Connes-Kreimer renormalization, Commun. Math. Phys., vol. 296 no. 3 (2010), 655-680.
- J. C. Collins, Renormalization: an introduction to renormalization, the renormalization group and the operator-product expansion, Cambridge University Press, 1986.
- A. Connes, D. Kreimer, Renormalization in quantum field theory and the Riemann-Hilbert problem. I. The Hopf algebra structure of graphs and the main theorem, Commun. Math. Phys., vol. 210 no. 1 (2000), 249-273.
- A. Connes, D. Kreimer, Renormalization in quantum field theory and the Riemann-Hilbert problem. II. The -function, diffeomorphisms and the renormalization group, Commun. Math. Phys., vol. 216 no. 1 (2001), 215-241.
- J. F. Carinena, J. Grabowski, G. Marmo, Quantum bi-Hamiltonian systems, Internat. J. Modern Phys. A, vol. 15 no. 30 (2000), 4797-4810.
- A. Connes, M. Marcolli, Noncommutative geometry, quantum fields and motives, Colloquium Publications, American Mathematical Society, vol. 55 (2008).
- A.E.F. Djemai, Introduction to Dubois-Violette's noncommutative differential geometry, Int. J. Theoret. Phys., vol. 34 no. 6 (1995), 801-887.
- I. Dorfman, Dirac structures and integrability of nonlinear evolution equations, Nonlinear science: Theory and applications, John Wiley & Sons Ltd. (1993).
- M. Dubois-Violette, Lectures on graded differential algebras and noncommutative geometry, Proceedings of the workshop on noncommutative differential geometry and its application to physics, Shonan-Kokusaimura 1999, Series: Mathematical Physics Studies, vol. 23 (2001).
- K. Ebrahimi-Fard, On the associative Nijenhuis relation, Electron. J. Combin., vol. 11 no.1 (2004), Research Paper 38, 13 pp. (electronic).
- K. Ebrahimi-Fard, L. Guo, Mixable shuffles, quasi-shuffles and Hopf algebras, J. Algebraic Combin., vol. 24 no. 1 (2006), 83-101.
- K. Ebrahimi-Fard, L. Guo, Rota-Baxter algebras in renormalization of perturbative quantum field theory. universality and renormalization, Fields Inst. Commun., vol. 50 (2007), 47-105.
- L. Foissy, Faa di Bruno subalgebras of the Hopf algebra of planar trees from combinatorial Dyson-Schwinger equations, Adv. in Math., vol. 218 (2008), 136-162.
- L. Guo, An introduction to Rota-Baxter algebra, Surveys of modern mathematics, International Press, Somerville, MA; Higher Education Press, Beijing, Vol. 4 (2012).
- S. Gra, V. Grecchi, B. Simon, Borel summability: application to the anharmonic oscillator, Phys. Lett. B, vol. 32B (1970), 631-634.
- M. E. Ho man, Quasi-shuffle products, J. Algebraic Combin., vol. 11 no. 1 (2000), 49-68.
- Z. Horvath, L. Palla, Non-perturbative QFT methods and their applications, Proceedings of the 24th Johns Hopkins Workshop, Bolyai College, Budapest, Hungary, 19-21 August 2000. World Scientific.
- D. Kreimer, On the Hopf algebra structure of perturbative quantum field theories, Adv. Theor. Math. Phys., vol. 2 no. 2 (1998), 303-334.
- D. J. Broadhurst, D. Kreimer, Renormalization automated by Hopf algebra, J. Symbolic Comput., vol. 27 no. 6 (1999), 581-600.
- D. Kreimer, Structures in Feynman graphs - Hopf algebras and symmetries, Proc. Symp. Pure Math., vol. 73 (2005), 43-78.
- D. Kreimer, Anatomy of a gauge theory, Ann. Phys., vol. 321 no. 12 (2006), 2757-2781.
- D. Kreimer, Dyson-Schwinger equations: from Hopf algebras to number theory, Universality and renormalization, Fields Inst. Commun., vol. 50 (2007), 225-248.
- Y. Kosmann-Schwarzbach, F. Magri, Poisson-Nijenhuis structures, Ann. Inst. Henri Poincare., vol. 53 no. 1 (1990), 35-81.
- P.P. Kulish, E.K. Sklyanin, Solutions of the Yang-Baxter equations, J. Soviet Math., vol. 19 (1982), 1596-1620.
- J. Madore, An introduction to noncommutative geometry and its physical applications, Cam- bridge University Press, 1999.
- M. Marino, Non-perturbative effects and non-perturbative definitions in matrix models and topological strings, Journal of High Energy Physics, vol. 2008 (2008), JHEP12(2008).
- A. Morozov, Integrability in non-perturbative QFT, AIP Proc., vol. 1562 (2013), 167-176.
- M.E. Peskin, D.V. Schroeder, An introduction to quantum field theory, Addison-Wesley Publishing Company, 1995
- J. Polchinski, Renormalization and effective Lagrangians, Nucl. Phys. B, vol. 231 Issue 2 (1984), 269-295.
- P. Ramond, Field Theory : A Modern Primer (Frontiers in Physics Series, Vol 74), Westview Press, 2001
- M. Sakakibara, On the differential equations of the characters for the renormalization group, Mod. Phys. Lett. A., vol. 19 no. 19 (2004), 1453-1456.
- M.A. Semenov-Tian-Shansky, What is a classical r-matrix?, Funct. Anal. Appl., vol. 17 (1983), 259-272.
- M.A. Semenov-Tian-Shansky, Integrable Systems and factorization problems. Factorization and integrable systems, Oper. Theory Adv. Appl., vol. 141 (2003), 155-218.
- A. Shojaei-Fard, From Dyson-Schwinger equations to the Riemann-Hilbert correspondence, Int. J. Geom. Methods Mod. Phys., vol. 7 no. 4 (2010), 519-538.
- A. Shojaei-Fard, Riemann-Hilbert problem and Quantum Field Theory: integrable renormalization, Dyson-Schwinger equations, Monograph, Lambert Academic Publishing, ISBN 978-3-8473-4067-6, (2012), 136 pages.
- A. Shojaei-Fard, What is a quantum equation of motion?, Electronic Journal of Theoretical Physics, vol. 10 no. 28 (2013), 1-8.
- A. Shojaei-Fard, A geometric perspective on counterterms related to Dyson-Schwinger equations, Internat. J. Modern Phys. A, vol. 28 no. 32 (2013), 1350170 (15 pages).
- A. Shojaei-Fard, The global beta-functions from solutions of Dyson-Schwinger equations, Modern Phys. Lett. A, vol. 28 no. 34 (2013), 1350152 (12 pages).
- T. Schafer, E. V. Shuryak, Instantons in QCD, Rev. Modern Phys., vol. 70 no. 2 (1998), 323-425.
- K. Yeats, Rearranging Dyson-Schwinger Equations, Memoirs of the American Mathematical Society, vol. 211 (2011).