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TMF, 2015, Volume 182, Number 1, Pages 103–111 (Mi tmf8731)  

This article is cited in 3 scientific papers (total in 3 papers)

Nontrivial quantization of $\phi^4_n$, $n\ge2$

J. R. Klauderab

a University of Florida, Department of Mathematics, Gainesville, FL, USA
b University of Florida, Department of Physics, Gainesville, FL, USA

Abstract: The conventional quantization of covariant $\phi^4_n$ scalar field models for space–time dimensions $n\ge5$ is trivial, and this may also be true for $n=4$. But an alternative $O(\hbar)$ counterterm leads to nontrivial results for all $n\ge4$ and also provides a different quantization for $n=2,3$. We determine the counterterm that provides these desirable properties as simply and directly as possible. The same counterterm also resolves models such as $\phi^p_n$ for all even $p$ including those where $p>2n/(n-2)$, which are traditionally regarded as nonrenormalizable.

Keywords: nontriviality of phi to the fourth, overcoming nonrenormalizability, mixed model

DOI: https://doi.org/10.4213/tmf8731

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English version:
Theoretical and Mathematical Physics, 2015, 182:1, 83–89

Bibliographic databases:

Received: 12.06.2014

Citation: J. R. Klauder, “Nontrivial quantization of $\phi^4_n$, $n\ge2$”, TMF, 182:1 (2015), 103–111; Theoret. and Math. Phys., 182:1 (2015), 83–89

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf8731
  • http://mi.mathnet.ru/eng/tmf/v182/i1/p103

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. J. R. Klauder, “Mixed models: combining incompatible scalar models in any space-time dimension”, Int. J. Mod. Phys. A, 32:1, SI (2017), 1750001  crossref  mathscinet  zmath  isi  scopus
    2. J. R. Klauder, “Quantum field theory with no zero-point energy”, J. High Energy Phys., 2018, no. 5, 191  crossref  zmath  isi
    3. J. R. Klauder, “Enhanced quantization: the right way to quantize everything”, Coherent States and Their Applications: a Contemporary Panorama, Springer Proceedings in Physics, 205, eds. J. Antoine, F. Bagarello, J. Gazeau, Springer-Verlag Berlin, 2018, 1–15  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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