# Removal of UV Cutoff for the Nelson Model with Variable Coefficients

@article{Grard2012RemovalOU, title={Removal of UV Cutoff for the Nelson Model with Variable Coefficients}, author={Christian G{\'e}rard and Fumio Hiroshima and Annalisa Panati and Akito Suzuki}, journal={Letters in Mathematical Physics}, year={2012}, volume={101}, pages={305-322} }

We consider the Nelson model with variable coefficients. Nelson models with variable coefficients arise when one replaces in the usual Nelson model the flat Minkowski metric by a static metric, allowing also the boson mass to depend on position. We study the removal of the ultraviolet cutoff.

## 13 Citations

### Translation invariant models in QFT without ultraviolet cutoffs

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The translation invariant model in quantum field theory is considered by functional integrations. Ultraviolet renormalization of the translation invariant Nelson model with a fixed total momentum is…

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In this article we consider the ground state of the renormalized Nelson Hamiltonian in quantum field theory by using the integral kernel of the semigroup generated by the Hamiltonian. By introducing…

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Ultraviolet (UV) renormalization of the Nelson model He in quantum field theory is considered. E. Nelson proved that lime!0e T(H" E ren " ) converges to e THren in [Nel64a]. A relationship between a…

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In this article we consider the ground state of the renormalized Nelson Hamil‐ tonian in quantum field theory by using the integral kernel of the semigroup gen‐ erated by the Hamiltonian. By…

### The Nelson Model on Static Spacetimes

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The Nelson model describes the interaction of nonrelativistic quantum particles with a relativistic quantum field of scalar bosons. Nelson rigorously demonstrated in 1964 the existence of a…

### Functional Central Limit Theorems and P(ϕ)1-Processes for the Relativistic and Non-Relativistic Nelson Models

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We construct P(ϕ)1-processes indexed by the full time-line, separately derived from the functional integral representations of the relativistic and non-relativistic Nelson models in quantum field…

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The Nelson Hamiltonian is unitarily equivalent to a Hamiltonian defined through a closed, semibounded quadratic form, the unitary transformation being explicitly known and due to Gross. In this paper…

### Functional central limit theorems and $P(phi)_{1}$-processes for the classical and relativistic Nelson models

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We construct $P(phi)_1$-processes indexed by the full time-line, separately derived from the functional integral representations of the relativistic and non-relativistic Nelson models in quantum…

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We consider a model describing the coupling of a vector-valued and a scalar homogeneous Markovian random field over R4, interpreted as expressing the interaction between a charged scalar quantum…

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This lecture note consists of three parts. Fundamental facts on Boson Fock space are introduced in Part I. Ref. 1.and 3. are reviewed in Part II and, Ref. 2. and 4. in Part III.
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