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Coarse-Graining as a Route to Microscopic Physics: The Renormalization Group in Quantum Field Theory

Published online by Cambridge University Press:  01 January 2022

Abstract

The renormalization group (RG) has been characterized as merely a coarse-graining procedure that does not illuminate the microscopic content of quantum field theory (QFT) but merely gets us from that content, as given by axiomatic QFT, to macroscopic predictions. I argue that in the constructive field theory tradition, RG techniques do illuminate the microscopic dynamics of a QFT, which are not automatically given by axiomatic QFT. RG techniques in constructive field theory are also rigorous, so one cannot object to their foundational import on grounds of lack of rigor.

Type
Quantum Physics
Copyright
Copyright © The Philosophy of Science Association

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References

Abdesselam, A. 2007. “A Complete Renormalization Group Trajectory between Two Fixed Points.” Communications in Mathematical Physics 276 (3): 727–72.CrossRefGoogle Scholar
Bagnuls, C., and Bervillier, C.. 2001. “Exact Renormalization Group Equations and the Field Theoretical Approach to Critical Phenomena.” International Journal of Modern Physics A 16 (11): 1825–45.CrossRefGoogle Scholar
Bain, J. 2013. “Effective Field Theories.” In The Oxford Handbook of Philosophy of Physics, ed. Batterman, R., 224–54. New York: Oxford University Press.Google Scholar
Balaban, T., Imbrie, J., and Jaffe, A.. 1984. “Exact Renormalization Group for Gauge Theories.” In Progress in Gauge Field Theory, ed. ‘t Hooft, G. et al., 79103. New York: Plenum.CrossRefGoogle Scholar
Benfatto, G., Cassandro, M., Gallavotti, G., Nicoló, F., Olivieri, E., Presutti, E., and Scacciatelli, E.. 1980. “Ultraviolet Stability in Euclidean Scalar Field Theories.” Communications in Mathematical Physics 71 (2): 95130.CrossRefGoogle Scholar
Brydges, D., Dimock, J., and Hurd, T. R.. 1995. “The Short Distance Behavior of (φ4)3.” Communications in Mathematical Physics 172 (1): 143–86.CrossRefGoogle Scholar
Douglas, M. 2011. “Foundations of Quantum Field Theory.” Proceedings of Symposia in Pure Mathematics 85:105–24.Google Scholar
Duncan, A. 2012. The Conceptual Framework of Quantum Field Theory. Oxford: Oxford University Press.CrossRefGoogle Scholar
Feldman, J., Magnen, J., Rivasseau, V., and Sénéor, R.. 1987. “Construction and Borel Summability of Infrared ϕ4 by a Phase Space Expansion.” Communications in Mathematical Physics 109 (3): 437–80.CrossRefGoogle Scholar
Fraser, D. 2011. “How to Take Particle Physics Seriously: A Further Defence of Axiomatic Quantum Field Theory. Studies in History and Philosophy of Science B 42 (2): 126–35.Google Scholar
Gawdzki, K., and Kupiainen, A.. 1983. “Non-Gaussian Fixed Points of the Block Spin Transformation: Hierarchical Model Approximation.” Communications in Mathematical Physics 89 (2): 191220.CrossRefGoogle Scholar
Gawdzki, K., and Kupiainen, A. 1985. “Exact Renormalization for the Gross-Neveu Model of Quantum Fields.” Physical Review Letters 54:2191–94.Google Scholar
Glimm, J., and Jaffe, A.. 1987. Quantum Physics: A Functional Integral Point of View. 2nd ed. New York: Springer.CrossRefGoogle Scholar
Gurau, R., Rivasseau, V., and Sfondrini, A.. 2014. “Renormalization: An Advanced Overview.” arXiv, Cornell University. http://arxiv.org/abs/1401.5003.pdf.Google Scholar
Horuzhy, S. S. 1990. Introduction to Algebraic Quantum Field Theory. Berlin: Springer.Google Scholar
Huggett, N., and Weingard, R.. 1995. “The Renormalisation Group and Effective Field Theories.” Synthese 102 (1): 171–94.CrossRefGoogle Scholar
Kuhlmann, M., Lyre, H., and Wayne, A.. 2002. “Introduction.” In Ontological Aspects of Quantum Field Theory, ed. Kuhlmann, M., Lyre, H., and Wayne, A., 129. Singapore: World Scientific.CrossRefGoogle Scholar
Pordt, A. 1994. “On Renormalization Group Flows and Polymer Algebras.” In Constructive Physics: Results in Field Theory, Statistical Mechanics and Condensed Matter Physics, ed. Rivasseau, V., 5181. Lecture Notes in Physics 446. Berlin: Springer.Google Scholar
Rivasseau, V. 1991. From Perturbative to Constructive Renormalization. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Rosten, O. J. 2012. “Fundamentals of the Exact Renormalization Group.” Physics Reports 511 (4): 177272.CrossRefGoogle Scholar
Wallace, D. 2011. “Taking Particle Physics Seriously: A Critique of the Algebraic Approach to Quantum Field Theory.” Studies in History and Philosophy of Science B 42 (2): 116–25.Google Scholar
Watanabe, H. 2000. “Renormalization Group Methods in Constructive Field Theories.” International Journal of Modern Physics B 14 (12–13): 1363–98.CrossRefGoogle Scholar
Wightman, A. S. 1976. “Hilbert’s Sixth Problem: Mathematical Treatment of the Axioms of Physics.” In Mathematical Developments Arising from Hilbert Problems, 147240. Providence, RI: American Mathematical Society.CrossRefGoogle Scholar
Zee, A. 2010. Quantum Field Theory in a Nutshell. 2nd ed. Princeton, NJ: Princeton University Press.Google Scholar