# Variational method in relativistic quantum field theory without cutoff

@article{Tilloy2021VariationalMI, title={Variational method in relativistic quantum field theory without cutoff}, author={Antoine Tilloy}, journal={Physical Review D}, year={2021} }

The variational method is a powerful approach to solve many-body quantum problems non perturbatively. However, in the context of relativistic quantum field theory (QFT), it needs to meet 3 seemingly incompatible requirements outlined by Feynman: extensivity, computability, and lack of UV sensitivity. In practice, variational methods break one of the 3, which translates into the need to have an IR or UV cutoff. In this letter, I introduce a relativistic modification of continuous matrix product…

## 4 Citations

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- 2021

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### Relativistic continuous matrix product states for quantum fields without cutoff

- 2021

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I introduce a modification of continuous matrix product states (CMPS) that makes them adapted to relativistic quantum field theories (QFT). These relativistic CMPS can be used to solve genuine 1+1…

## 38 References

### Phys

- 2015

Rev. D 91, 085011

### Relativistic continuous matrix product states for quantum fields without cutoff

- 2021

Physics

Physical Review D

I introduce a modification of continuous matrix product states (CMPS) that makes them adapted to relativistic quantum field theories (QFT). These relativistic CMPS can be used to solve genuine 1+1…

### and a at

- 2018

Chemistry

The William Makepeace Thackeray Library

The xishacorene natural products are structurally unique apolar diterpenoids that feature a bicyclo[3.3.1] framework. These secondary metabolites likely arise from the well-studied, structurally…

### Matrix product states and projected entangled pair states: Concepts, symmetries, theorems

- 2021

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Reviews of Modern Physics

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### Gaussian continuous tensor network states for simple bosonic field theories

- 2020

Physics

Tensor networks states allow to find the low energy states of local lattice Hamiltonians through variational optimization. Recently, a construction of such states in the continuum was put forward,…

### Fields Without Cutoffs

- 1981

Mathematics

The construction of P(φ)2 quantum fields given here is valid for semibounded interaction polynomials P of the form P = even + linear. Other constructions apply to general semibounded P; see also…

### Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory

- 1992

Physics

The subject of this book is equilibrium statistical mechanics, in particular the theory of critical phenomena, and quantum field theory. The central theme is the use of random-walk representations as…