Translation invariant models in QFT without ultraviolet cutoffs

2015/06/24 by Fumio Hiroshima, Hiroshima, Fumio
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1506.07514

This is a proceeding of 51 Winter School of Theoretical Physics Ladek Zdroj, Poland, 9 - 14 February 2015

arxiv created 2015/06/24 · arxiv updated 2015/06/25

Abstract

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 proven by functional integrations. As a corollary it can be shown that the Nelson Hamiltonian with zero total momentum has a ground state for arbitrary values of coupling constants in two dimension. Furthermore the ultraviolet renormalization of the polaron model is also studied.

Related

• Note on ultraviolet renormalization and ground state energy of the Nelson model
• Ultraviolet Renormalization of the Nelson Hamiltonian through Functional Integration
• Non-existence of ground states in the translation invariant Nelson model
• The Massless Nelson Hamiltonian and its Domain
• A fresh look at (non)renormalizable QFTs