The functional integral in the Hubbard model

Zharkov, V. M.

doi:10.1007/s11232-012-0115-5

Cited by 2 publications

(2 citation statements)

References 22 publications

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“…Originally p-adic concepts have been introduced in string theory [1][2][3][4][5][6] as a model of spacetime beyond the Planck distance, where one should not expect the Archimedean axiom to hold true. The concept of ultrametric spaces and the corresponding mathematical machinery percolated into other fields of knowledge from high-energy [7][8][9] to condensed matter physics [10][11][12][13] and biology [14,15], since they were appreciated for being a natural language to describe hierarchical systems [16,17].…”

Section: Introductionmentioning

confidence: 99%

Coleman–Weinberg potential in p-adic field theory

2020

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In this paper, we study $$\lambda \phi ^4$$ λ ϕ 4 scalar field theory defined on the unramified extension of p-adic numbers $${\mathbb {Q}}_{p^n}$$ Q p n . For different “space-time” dimensions n, we compute one-loop quantum corrections to the effective potential. Surprisingly, despite the unusual properties of non-Archimedean geometry, the Coleman–Weinberg potential of p-adic field theory has structure very similar to that of its real cousin. We also study two formal limits of the effective potential, $$p \rightarrow 1$$ p → 1 and $$p \rightarrow \infty $$ p → ∞ . We show that the $$p\rightarrow 1$$ p → 1 limit allows to reconstruct the canonical result for real field theory from the p-adic effective potential and provide an explanation of this fact. On the other hand, in the $$p\rightarrow \infty $$ p → ∞ limit, the theory exhibits very peculiar behavior with emerging logarithmic terms in the effective potential, which has no analogue in real theories.

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Section: Introductionmentioning

confidence: 99%

Coleman–Weinberg potential in p-adic field theory

2020

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Section: Introductionmentioning

confidence: 99%

Coleman-Weinberg potential in $p$-adic field theory

Ageev,

Bagrov,

Iliasov

2020

Preprint

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In this paper, we study λφ 4 scalar field theory defined on the unramified extension of p-adic numbers Q p n . For different "space-time" dimensions n, we compute one-loop quantum corrections to the effective potential. Surprisingly, despite the unusual properties of non-Archimedean geometry, the Coleman-Weinberg potential of p-adic field theory has structure very similar to that of its real cousin. We also study two formal limits of the effective potential, p → 1 and p → ∞. We show that the p → 1 limit allows to reconstruct the canonical result for real field theory from the padic effective potential and provide an explanation of this fact. On the other hand, in the p → ∞ limit, the theory exhibits very peculiar behavior with emerging logarithmic terms in the effective potential, which has no analogue in real theories.

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The functional integral in the Hubbard model

Cited by 2 publications

References 22 publications

Coleman–Weinberg potential in p-adic field theory

Coleman–Weinberg potential in p-adic field theory

Coleman-Weinberg potential in $p$-adic field theory

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