Non Relativistic Limit in QFT: a Wilson Renormalization Group Approach in the Minkowski Space

Silva, A.J. da

doi:10.1590/s0103-97332001000200006

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“…In this section we will describe the manner in which we will implement the non-relativistic approximation for the Klein-Gordon theory described above. In the literature, there are different approaches for making this approximation; one can find methods using the WKB approximation or similar techniques [37][38][39], others using a group theoretic perspective [40,41], and yet others using a renormalization perspective [42][43][44]. Often in these approaches, one finds either the implicit or explicit assumption of an ultraviolet cutoff that can suitably impose the 'small momentum' condition.…”

Section: Aspects Of the Non-relativistic Approximationmentioning

confidence: 99%

Impact of relativity on particle localizability and ground state entanglement

Maria

Pye

2019

J. Phys. A: Math. Theor.

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Can a relativistic quantum field theory be consistently described as a theory of localizable particles? There are many known issues with such a description, indicating an answer in the negative. In this paper, we examine these obstructions by tracing how they (partially) subside in passing to an approximation of ordinary quantum mechanics in the non-relativistic regime. We undertake a recovery of the characteristic features of non-relativistic quantum mechanics beyond simply the Schrödinger equation. We find that once this is achieved, there are persisting issues in the localizability of particle states. A major focus is on the lingering discrepancy between two different localization schemes in quantum field theory. The non-relativistic approximation of the quantum field theory is achieved by introducing an ultraviolet cutoff set by the Compton scale. The other main undertaking of this paper is to quantify the fate of ground state entanglement and the Unruh effect in the non-relativistic regime. Observing that the Unruh temperature vanishes in the naive limit as the speed of light is taken to infinity motivates the question: is the Unruh effect relativistic? It happens that this is closely related to the former issues, as ground state entanglement causes obstructions to localizability through the Reeh-Schlieder theorem.

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