On Self-Consistency in Quantum Field Theory
Keywords:
quantum field theory, effective action, self-consistency, bootstrap
Abstract
A bootstrap approach to the effective action in quantum field theory is discussed which entails the invariance
under quantum fluctuations of the effective action describing physical reality (via the S-matrix).
References
[1] J. F. Donoghue, E. Golowich, B. R. Holstein: Dynamics of the Standard Model. 1. ed.: Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology, Vol. 2. Cambridge University Press, Cambridge, 1992 (DOI: 10.1017/CBO9780511524370); 2. ed.: Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology, Vol. 35. Cambridge University Press, Cambridge, 2014 (DOI: 10.1017/9781009291033).
[2] P. J. Mohr, B. N. Taylor: Tests of fundamental physics. Chap. 28, Part B: Atoms, in: G. W. F. Drake (Ed.): Springer Handbook of Atomic, Molecular, and Optical Physics. Springer Handbooks of Atomic, Molecular, and Optical Physics. Springer-Verlag, New York, NY, 2006, pp. 429-447 (DOI: 10.1007/978-0-387-26308-3_28).
[3] T. Kinoshita (Ed.): Quantum Electrodynamics. Advanced Series on Directions in High Energy Physics, Vol. 7. World Scientific, Singapore, 1990 (DOI: 10.1142/0495).
[4] Tian Yu Cao (Ed.): Conceptual Foundations of Quantum Field Theory. Cambridge University Press, Cambridge, 1999, 2004, 2009 (DOI: 10.1017/CBO9780511470813).
[5] D. Poland, L. Rastelli: Snowmass Topical Summary: Formal QFT. To appear in the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021). [arXiv:2210.03128 (https://arxiv.org/abs/2210.03128)].
[6] R. P. Feynman: The development of the space-time view of quantum electrodynamics. Science 153:3737(1966)699-708 (DOI: 10.1126/science.153.3737.699); Physics Today 19:8(1966)31-44 (DOI: 10.1063/1.3048404). The text is freely available online at the Nobel Foundation URL: http://nobelprize.org/nobel_prizes/physics/laureates/1965/feynman-lecture.html. Also printed in: 1. Nobelstiftelsen (Nobel Foundation): Les Prix Nobel en 1965. Almqvist & Wiksell International, Stockholm, 1966, pp. 172-191. 2. Nobelstiftelsen (Nobel Foundation): Nobel Lectures, Including Presentation Speeches and Laureates’ Biographies: Physics, 1963-1970. Elsevier, Amsterdam, 1972, pp. 155-178. Reprinted: World Scientific Publishing, Singapore, 1998 (DOI: 10.1142/3729). 3. L. M. Brown (Ed.): Selected Papers of Richard Feynman, with Commentary. World Scientific Series in 20th Century Physics, Vol. 27. World Scientific Publishing, Singapore, 2000, pp. 9-32 (DOI: 10.1142/9789812385468_0002).
[7] R. P. Feynman: QED – The Strange Theory of Light and Matter. Alix G. Mautner Memorial Lectures. Princeton University Press, Princeton, NJ, 1985, 1988; Penguin Books, London, 1985, 1990, 2008; expanded 2. ed., Princeton Science Library, 2006, 2013, 2014.
[8] P. A. M. Dirac: Directions in Physics. John Wiley & Sons, New York, 1978.
[9] P. A. M. Dirac: The origin of quantum field theory. In: L. M. Brown, L. Hoddeson (Eds.): The Birth of Particle Physics. Cambridge University Press, Cambridge, 1983, pp. 39-55.
[10] K. von Meyenn (Ed.): Wolfgang Pauli. Wissenschaftlicher Briefwechsel mit Bohr, Einstein, Heisenberg u.a.. Band III: 1940-1949. Scientific Correspondence with Bohr, Einstein, Heisenberg a.o.. Volume III: 1940-1949. Sources in the History of Mathematics and Physical Sciences, Vol. 11. Springer-Verlag, Berlin, 1993, 2014 (DOI: 10.1007/978-3-540-78802-7).
[11] Л. Д. Фаддеев [L. D. Faddeev], А. А. Славнов [A. A. Slavnov]: Введение в квантовую теорию калибровочных полей [Vvedenie v kvantovuyu teoriyu kalibrovochnykh poleĭ]. Наука [Nauka], Moscow, 1. ed.: 1978, 2. rev. & ext. ed.: 1988; УРСС [URSS], Moscow, 2022. [in Russian] English translation: Gauge Fields: Introduction to Quantum Theory. Frontiers in Physics, 1. ed.: Vol. 50, 2nd rev. & ext. ed., Vol. 83. 1. ed.: Benjamin/Cummings Publ., Reading, MA, 1980, 2nd rev. & ext. ed.: Addison-Wesley, Redwood City, CA, 1990; Westview Press, Boulder, CO, 1991; CRC Press, Boca Raton, FL, 2018, 2019 (DOI: 10.1201/9780429493829).
[12] A. Jevicki, C. Lee: The S-matrix generating functional and effective action. Physical Review D 37:6(1988)1485-1491 (DOI: 10.1103/PhysRevD.37.1485) [Brown University report BROWN-HET-634].
[13] C. Itzykson, J.-B. Zuber: Quantum field theory. International Series in Pure and Applied Physics. McGraw-Hill, New York, 1980, 1985, 1986, 1987, 1988, 1990. Reprint: Dover Books on Physics. Dover Publications, Mineola, NY, 2005, 2006, 2012.
[14] Л. В. Прохоров [L. V. Prokhorov]: Уравнения для эффективных лагранжианов [Uravneniya dlya èffektivnykh lagranzhianov]. Ядерная Физика [Yadernaya Fizika] 16:4(1972)854-862. [in Russian] English translation: Equations for effective Lagrangians. Soviet Journal of Nuclear Physics 16:4(1973)473-477.
[15] K. Scharnhorst: Functional integral equation for the complete effective action in quantum field theory. International Journal of Theoretical Physics 36:2(1997)281-343 (DOI: 10.1007/BF02435737) [University of Leipzig report NTZ-16-1993, arXiv:hep-th/9312137 (https://arxiv.org/abs/hep-th/9312137)].
[16] J. S. Arponen: Independent-cluster methods as mappings of quantum theory into classical mechanics. Theoretica Chimica Acta 80:2-3(1991)149-179 (DOI: 10.1007/BF01119618) [University of Helsinki report HU-TFT-90-75].
[17] K. Scharnhorst: A Grassmann integral equation. Journal of Mathematical Physics 44:11(2003)5415-5449 (DOI: 10.1063/1.1612896, errata sheet at the URL: http://www.nat.vu.nl/~scharnh/mea30.pdf) [arXiv:math-ph/0206006 (https://arxiv.org/abs/math-ph/0206006)].
[18] B. Pioline: Cubic free field theory. In: L. Baulieu, E. Rabinovici, J. Harvey, B. Pioline, P. Windey (Eds.): Progress in String, Field and Particle Theory. Proceedings of the NATO Advanced Study Institute, Cargèse, Corsica, France, May 27-June 8, 2002. NATO Science Series II: Mathematics, Physics and Chemistry, Vol. 104. Kluwer Academic Publishers, Dordrecht, 2003, pp. 453-456 (DOI: 10.1007/978-94-010-0211-0_37) [LPTHE Paris report LPTHE-P03-01, arXiv:hep-th/0302043 (https://arxiv.org/abs/hep-th/0302043)].
[19] V. A. Alebastrov, G. V. Efimov: A proof of the unitarity of S-matrix in a nonlocal quantum field theory. Communications in Mathematical Physics 31:1(1973)1-24 (DOI: 10.1007/BF01645588, the article is freely available online from the Project Euclid website: http://projecteuclid.org/euclid.cmp/1103858926) [Institute of Theoretical Physics, Kiev, report ИТФ-72-110Р [ITF-72-110R] [in Russian]].
[20] V. A. Alebastrov, G. V. Efimov: Causality in quantum field theory with nonlocal interaction. Communications in Mathematical Physics 38:1(1974)11-28 (DOI: 10.1007/BF01651546, the article is freely available online from the Project Euclid website: http://projecteuclid.org/euclid.cmp/1103859964) [Joint Institute of Nuclear Resarch, Dubna, report Р2-7572 [R2-7572] [in Russian]].
[21] T. Kühn, M. Helias: Expansion of the effective action around non-Gaussian theories. Journal of Physics A: Mathematical and Theoretical 51:37(2018)375004, 35 pp. (DOI: 10.1088/1751-8121/aad52e), erratum ibid. 51:45(2018)459502, 1
p. (DOI: 10.1088/1751-8121/aae1d7) [arXiv:1711.05599 (https://arxiv.org/abs/1711.05599)].
[22] J. Rosaler, R. Harlander: Naturalness, Wilsonian renormalization, and “fundamental parameters” in quantum field theory. Studies in History and Philosophy of Modern Physics 66(2019)118-134 (DOI: 10.1016/j.shpsb.2018.12.003) [RWTH Aachen report TTK-19-04, ELHC research group report ELHC_2018-005, arXiv:1809.09489 (https://arxiv.org/abs/1809.09489)].
[2] P. J. Mohr, B. N. Taylor: Tests of fundamental physics. Chap. 28, Part B: Atoms, in: G. W. F. Drake (Ed.): Springer Handbook of Atomic, Molecular, and Optical Physics. Springer Handbooks of Atomic, Molecular, and Optical Physics. Springer-Verlag, New York, NY, 2006, pp. 429-447 (DOI: 10.1007/978-0-387-26308-3_28).
[3] T. Kinoshita (Ed.): Quantum Electrodynamics. Advanced Series on Directions in High Energy Physics, Vol. 7. World Scientific, Singapore, 1990 (DOI: 10.1142/0495).
[4] Tian Yu Cao (Ed.): Conceptual Foundations of Quantum Field Theory. Cambridge University Press, Cambridge, 1999, 2004, 2009 (DOI: 10.1017/CBO9780511470813).
[5] D. Poland, L. Rastelli: Snowmass Topical Summary: Formal QFT. To appear in the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021). [arXiv:2210.03128 (https://arxiv.org/abs/2210.03128)].
[6] R. P. Feynman: The development of the space-time view of quantum electrodynamics. Science 153:3737(1966)699-708 (DOI: 10.1126/science.153.3737.699); Physics Today 19:8(1966)31-44 (DOI: 10.1063/1.3048404). The text is freely available online at the Nobel Foundation URL: http://nobelprize.org/nobel_prizes/physics/laureates/1965/feynman-lecture.html. Also printed in: 1. Nobelstiftelsen (Nobel Foundation): Les Prix Nobel en 1965. Almqvist & Wiksell International, Stockholm, 1966, pp. 172-191. 2. Nobelstiftelsen (Nobel Foundation): Nobel Lectures, Including Presentation Speeches and Laureates’ Biographies: Physics, 1963-1970. Elsevier, Amsterdam, 1972, pp. 155-178. Reprinted: World Scientific Publishing, Singapore, 1998 (DOI: 10.1142/3729). 3. L. M. Brown (Ed.): Selected Papers of Richard Feynman, with Commentary. World Scientific Series in 20th Century Physics, Vol. 27. World Scientific Publishing, Singapore, 2000, pp. 9-32 (DOI: 10.1142/9789812385468_0002).
[7] R. P. Feynman: QED – The Strange Theory of Light and Matter. Alix G. Mautner Memorial Lectures. Princeton University Press, Princeton, NJ, 1985, 1988; Penguin Books, London, 1985, 1990, 2008; expanded 2. ed., Princeton Science Library, 2006, 2013, 2014.
[8] P. A. M. Dirac: Directions in Physics. John Wiley & Sons, New York, 1978.
[9] P. A. M. Dirac: The origin of quantum field theory. In: L. M. Brown, L. Hoddeson (Eds.): The Birth of Particle Physics. Cambridge University Press, Cambridge, 1983, pp. 39-55.
[10] K. von Meyenn (Ed.): Wolfgang Pauli. Wissenschaftlicher Briefwechsel mit Bohr, Einstein, Heisenberg u.a.. Band III: 1940-1949. Scientific Correspondence with Bohr, Einstein, Heisenberg a.o.. Volume III: 1940-1949. Sources in the History of Mathematics and Physical Sciences, Vol. 11. Springer-Verlag, Berlin, 1993, 2014 (DOI: 10.1007/978-3-540-78802-7).
[11] Л. Д. Фаддеев [L. D. Faddeev], А. А. Славнов [A. A. Slavnov]: Введение в квантовую теорию калибровочных полей [Vvedenie v kvantovuyu teoriyu kalibrovochnykh poleĭ]. Наука [Nauka], Moscow, 1. ed.: 1978, 2. rev. & ext. ed.: 1988; УРСС [URSS], Moscow, 2022. [in Russian] English translation: Gauge Fields: Introduction to Quantum Theory. Frontiers in Physics, 1. ed.: Vol. 50, 2nd rev. & ext. ed., Vol. 83. 1. ed.: Benjamin/Cummings Publ., Reading, MA, 1980, 2nd rev. & ext. ed.: Addison-Wesley, Redwood City, CA, 1990; Westview Press, Boulder, CO, 1991; CRC Press, Boca Raton, FL, 2018, 2019 (DOI: 10.1201/9780429493829).
[12] A. Jevicki, C. Lee: The S-matrix generating functional and effective action. Physical Review D 37:6(1988)1485-1491 (DOI: 10.1103/PhysRevD.37.1485) [Brown University report BROWN-HET-634].
[13] C. Itzykson, J.-B. Zuber: Quantum field theory. International Series in Pure and Applied Physics. McGraw-Hill, New York, 1980, 1985, 1986, 1987, 1988, 1990. Reprint: Dover Books on Physics. Dover Publications, Mineola, NY, 2005, 2006, 2012.
[14] Л. В. Прохоров [L. V. Prokhorov]: Уравнения для эффективных лагранжианов [Uravneniya dlya èffektivnykh lagranzhianov]. Ядерная Физика [Yadernaya Fizika] 16:4(1972)854-862. [in Russian] English translation: Equations for effective Lagrangians. Soviet Journal of Nuclear Physics 16:4(1973)473-477.
[15] K. Scharnhorst: Functional integral equation for the complete effective action in quantum field theory. International Journal of Theoretical Physics 36:2(1997)281-343 (DOI: 10.1007/BF02435737) [University of Leipzig report NTZ-16-1993, arXiv:hep-th/9312137 (https://arxiv.org/abs/hep-th/9312137)].
[16] J. S. Arponen: Independent-cluster methods as mappings of quantum theory into classical mechanics. Theoretica Chimica Acta 80:2-3(1991)149-179 (DOI: 10.1007/BF01119618) [University of Helsinki report HU-TFT-90-75].
[17] K. Scharnhorst: A Grassmann integral equation. Journal of Mathematical Physics 44:11(2003)5415-5449 (DOI: 10.1063/1.1612896, errata sheet at the URL: http://www.nat.vu.nl/~scharnh/mea30.pdf) [arXiv:math-ph/0206006 (https://arxiv.org/abs/math-ph/0206006)].
[18] B. Pioline: Cubic free field theory. In: L. Baulieu, E. Rabinovici, J. Harvey, B. Pioline, P. Windey (Eds.): Progress in String, Field and Particle Theory. Proceedings of the NATO Advanced Study Institute, Cargèse, Corsica, France, May 27-June 8, 2002. NATO Science Series II: Mathematics, Physics and Chemistry, Vol. 104. Kluwer Academic Publishers, Dordrecht, 2003, pp. 453-456 (DOI: 10.1007/978-94-010-0211-0_37) [LPTHE Paris report LPTHE-P03-01, arXiv:hep-th/0302043 (https://arxiv.org/abs/hep-th/0302043)].
[19] V. A. Alebastrov, G. V. Efimov: A proof of the unitarity of S-matrix in a nonlocal quantum field theory. Communications in Mathematical Physics 31:1(1973)1-24 (DOI: 10.1007/BF01645588, the article is freely available online from the Project Euclid website: http://projecteuclid.org/euclid.cmp/1103858926) [Institute of Theoretical Physics, Kiev, report ИТФ-72-110Р [ITF-72-110R] [in Russian]].
[20] V. A. Alebastrov, G. V. Efimov: Causality in quantum field theory with nonlocal interaction. Communications in Mathematical Physics 38:1(1974)11-28 (DOI: 10.1007/BF01651546, the article is freely available online from the Project Euclid website: http://projecteuclid.org/euclid.cmp/1103859964) [Joint Institute of Nuclear Resarch, Dubna, report Р2-7572 [R2-7572] [in Russian]].
[21] T. Kühn, M. Helias: Expansion of the effective action around non-Gaussian theories. Journal of Physics A: Mathematical and Theoretical 51:37(2018)375004, 35 pp. (DOI: 10.1088/1751-8121/aad52e), erratum ibid. 51:45(2018)459502, 1
p. (DOI: 10.1088/1751-8121/aae1d7) [arXiv:1711.05599 (https://arxiv.org/abs/1711.05599)].
[22] J. Rosaler, R. Harlander: Naturalness, Wilsonian renormalization, and “fundamental parameters” in quantum field theory. Studies in History and Philosophy of Modern Physics 66(2019)118-134 (DOI: 10.1016/j.shpsb.2018.12.003) [RWTH Aachen report TTK-19-04, ELHC research group report ELHC_2018-005, arXiv:1809.09489 (https://arxiv.org/abs/1809.09489)].
Published
2023-10-20
Issue
Section
Regular Issue
This work is licensed under a Creative Commons Attribution 4.0 International License.
Letters in High Energy Physics (LHEP) is an open access journal published by Andromeda Publishing and Education Services. The articles in LHEP are distributed according to the terms of the creative commons license CC-BY 4.0. Under the terms of this license, copyright is retained by the author while use, distribution and reproduction in any medium are permitted provided proper credit is given to original authors and sources.
Terms of Submission
By submitting an article for publication in LHEP, the submitting author asserts that:
1. The article presents original contributions by the author(s) which have not been published previously in a peer-reviewed medium and are not subject to copyright protection.
2. The co-authors of the article, if any, as well as any institution whose approval is required, agree to the publication of the article in LHEP.
