A Convergent Kinetic-Term Perturbation Expansion for $ϕ^4$ Theory
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917276291170304 |
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| author | Chen, Eugene |
| author_facet | Chen, Eugene |
| contents | We revisit scalar $ϕ^4$ theory and construct a reorganized perturbative expansion in which the kinetic operator, rather than the quartic interaction, is treated as the perturbation. Starting from the exactly solvable $0$-dimensional model, we show that the resulting series is convergent for positive coupling and can be written as an expansion in negative powers of the quartic coupling $λ$. We extend the construction to higher-dimensional field theory using an auxiliary field, and we formulate a discrete lattice version in which multi-site contributions are systematically organized. We explicitly compute the leading terms in the expansion, study their continuum limit, and compare against brute-force numerical evaluations of the partition function. We discuss the relation of this expansion to standard weak-coupling perturbation theory, strong-coupling expansions, and resummation techniques, and we outline possible applications to nonperturbative studies of scalar field theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13539 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Convergent Kinetic-Term Perturbation Expansion for $ϕ^4$ Theory Chen, Eugene High Energy Physics - Theory We revisit scalar $ϕ^4$ theory and construct a reorganized perturbative expansion in which the kinetic operator, rather than the quartic interaction, is treated as the perturbation. Starting from the exactly solvable $0$-dimensional model, we show that the resulting series is convergent for positive coupling and can be written as an expansion in negative powers of the quartic coupling $λ$. We extend the construction to higher-dimensional field theory using an auxiliary field, and we formulate a discrete lattice version in which multi-site contributions are systematically organized. We explicitly compute the leading terms in the expansion, study their continuum limit, and compare against brute-force numerical evaluations of the partition function. We discuss the relation of this expansion to standard weak-coupling perturbation theory, strong-coupling expansions, and resummation techniques, and we outline possible applications to nonperturbative studies of scalar field theories. |
| title | A Convergent Kinetic-Term Perturbation Expansion for $ϕ^4$ Theory |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2602.13539 |