2000 character limit reached
Continuum limit of the Green function in scaled affine $\varphi^4_4$ quantum Euclidean covariant relativistic field theory (2402.10903v2)
Published 29 Dec 2023 in hep-th, hep-lat, quant-ph, gr-qc, and physics.comp-ph
Abstract: We prove through path integral Monte Carlo computer experiments that the affine quantization of the $\varphi_44$ scaled Euclidean covariant relativistic scalar field theory is a valid quantum field theory with a well defined continuum limit of the one- and two-point-function. Affine quantization leads to a completely satisfactory quantization of field theories using situations that involve scaled behavior leading to an unexpected, $\hbar2/\varphi2$ which arises only in the quantum aspects.
- P. A. M. Dirac, The Principles of Quantum Mechanics (Claredon Press, Oxford, 1958) in a footnote on page 114.
- B. Freedman, P. Smolensky, and D. Weingarten, Monte Carlo Evaluation of the Continuum Limit of ϕ44superscriptsubscriptitalic-ϕ44\phi_{4}^{4}italic_ϕ start_POSTSUBSCRIPT 4 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT and ϕ34superscriptsubscriptitalic-ϕ34\phi_{3}^{4}italic_ϕ start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT, Physics Letters 113B, 481 (1982).
- M. Aizenman, Proof of the Triviality of ϕd4subscriptsuperscriptitalic-ϕ4𝑑\phi^{4}_{d}italic_ϕ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT Field Theory and Some Mean-Field Features of Ising Models for d>4𝑑4d>4italic_d > 4, Phys. Rev. Lett. 47, 886(E) (1981).
- J. Fröhlich, On the Triviality of λϕd4𝜆superscriptsubscriptitalic-ϕ𝑑4\lambda\phi_{d}^{4}italic_λ italic_ϕ start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT Theories and the Approach to the Critical Point in d≥4𝑑4d\geq 4italic_d ≥ 4 Dimensions, Nuclear Physics B 200, 281 (1982).
- J. Siefert and U. Wolff, Triviality of φ4superscript𝜑4\varphi^{4}italic_φ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT theory in a finite volume scheme adapted to the broken phase, Physics Letters B 733, 11 (2014).
- U. Wolff, Triviality of four dimensional ϕ4superscriptitalic-ϕ4\phi^{4}italic_ϕ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT theory on the lattice, Scholarpedia 9, 7367 (2014).
- J. R. Klauder, A Modern Approach to Functional Integration (Springer, 2010).
- J. R. Klauder, Beyond Conventional Quantization (Cambridge University Press, 2000) chap. 5.
- J. R. Klauder, The Benefits of Affine Quantization, Journal of High Energy Physics, Gravitation and Cosmology 6, 175 (2020a).
- J. R. Klauder, Using Affine Quantization to Analyze Non-renormalizable Scalar Fields and the Quantization of Einstein’s Gravity, (2020b), arXiv:2006.09156.
- J. R. Klauder, An Ultralocal Classical and Quantum Gravity Theory, Journal of High Energy Physics, Gravitation and Cosmology 6, 656 (2020c).
- R. Fantoni and J. R. Klauder, Affine quantization of (φ4)4subscriptsuperscript𝜑44(\varphi^{4})_{4}( italic_φ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT ) start_POSTSUBSCRIPT 4 end_POSTSUBSCRIPT succeeds while canonical quantization fails, Phys. Rev. D 103, 076013 (2021a).
- R. Fantoni, Monte carlo evaluation of the continuum limit of (ϕ12)3subscriptsuperscriptitalic-ϕ123(\phi^{12})_{3}( italic_ϕ start_POSTSUPERSCRIPT 12 end_POSTSUPERSCRIPT ) start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT, J. Stat. Mech. , 083102 (2021).
- R. Fantoni and J. R. Klauder, Monte carlo evaluation of the continuum limit of the two-point function of the euclidean free real scalar field subject to affine quantization, J. Stat. Phys. 184, 28 (2021b).
- R. Fantoni and J. R. Klauder, Monte carlo evaluation of the continuum limit of the two-point function of two euclidean higgs real scalar fields subject to affine quantization, Phys. Rev. D 104, 054514 (2021c).
- R. Fantoni and J. R. Klauder, Eliminating nonrenormalizability helps prove scaled affine quantization of φ44subscriptsuperscript𝜑44\varphi^{4}_{4}italic_φ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 4 end_POSTSUBSCRIPT is nontrivial, Int. J. Mod. Phys. A 37, 2250029 (2022a).
- R. Fantoni and J. R. Klauder, Kinetic factors in affine quantization and their role in field theory monte carlo, Int. J. Mod. Phys. A 37, 2250094 (2022b).
- R. Fantoni and J. R. Klauder, Scaled affine quantization of φ44subscriptsuperscript𝜑44\varphi^{4}_{4}italic_φ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 4 end_POSTSUBSCRIPT in the low temperature limit, Eur. Phys. J. C 82, 843 (2022c).
- R. Fantoni and J. R. Klauder, Scaled affine quantization of ultralocal φ24subscriptsuperscript𝜑42\varphi^{4}_{2}italic_φ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT a comparative path integral monte carlo study with scaled canonical quantization, Phys. Rev. D 106, 114508 (2022d).
- R. Fantoni, Scaled affine quantization of φ312subscriptsuperscript𝜑123\varphi^{12}_{3}italic_φ start_POSTSUPERSCRIPT 12 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT is nontrivial, Mod. Phys. Lett. A , 2350167 (2023).
- J. R. Klauder and R. Fantoni, A modest redirection of quantum field theory solves all current problems, J. Stat. Phys. (submitted) (2023b), arXiv:2308.13475.
- D. M. Ceperley, Rev. Mod. Phys. 67, 279 (1995).
- M. H. Kalos and P. A. Whitlock, Monte Carlo Methods (Wiley-Vch Verlag GmbH & Co., Germany, 2008).
- R. Fantoni, Localization of acoustic polarons at low temperatures: A path integral monte carlo approach, Phys. Rev. B 86, 144304 (2012).
Sponsored by Paperpile, the PDF & BibTeX manager trusted by top AI labs.
Get 30 days freePaper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.