Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:hep-ph/0212196 · Journal of High Energy Physics

Renormalization of hamiltonian field theory; a non-perturbative and non-unitarity approach

Amir H. Rezaeian, Niels R. Walet

Published Dec 17, 2003• 4 citations
arXivHTMLPDF
DOI
10.1088/1126-6708/2003/12/040

Related papers

Perturbative renormalization in quantum mechanics

Cristina Manuel, R. Tarrach

arXiv:hep-th/9309013•Physics Letters B•May 1, 1994•77 citations

Revisiting Schrödinger CFTs: Factorization, Massless Particles, and a Path to the Bootstrap

Mathieu Boisvert, Shehab Hossam Fadda, Justin Kulp +1 more

We revisit Schrödinger CFTs from a modern point of view. We introduce the ''harmonic trap geometry,'' analogous to the cylinder picture in relativistic CFTs, and demonstrate a state-operator correspondence that applies to all operators, including descendant, massless, and ''normal-ordered operators.'' A thermofield double construction plays an extremely important role. We systematically classify all physical spectra in the harmonic trap and their unitarity bounds, extending earlier results to include both massless and massive states of all spins, providing a new analytic treatment of unitarity bounds, and establishing foundations for a bootstrap. In our reformulation, previously known perturbative non-renormalization theorems follow immediately from non-perturbative factorization at fixed points and along RG flows. Massless states are described by an effective 1d CFT, as predicted by DLCQ, and violate the non-renormalization theorems. We include a self-consistent review of Schrödinger CFTs in our framework, making the paper accessible to anyone with a field theory background.

arXiv:2510.26872•Oct 30, 2025•0 citations

Renormalized Perturbation Theory and Field-Theoretic Renormalization Group

Lothar Schäfer

Springer eBooks•Jan 1, 1999•1 citation

A New Renormalization Group for Hamiltonian Field Theory

Robert J. Perry, S. Szpigel

The Schrodinger equation with a two-dimensional delta-function potential is a simple example of an asymptotically free theory that undergoes dimensional transmutation. Renormalization requires the introduction of a mass scale, which can be lowered perturbatively until an infrared cutoff produced by non-perturbative effects such as bound state formation is encountered. We outline the effective field theory and similarity renormalization group techniques for producing renormalized cutoff hamiltonians, and illustrate the control of logarithmic and inverse-power-law errors both techniques provide.

arXiv:nucl-th/9901079•To be published in the proceedings of•Jan 26, 1999•4 citations

Methods of Nonrelativistic Quantum Field Theory

K. W. Kehr

Springer eBooks•Jan 1, 1977•0 citations

Effective Field Theories for Nuclear and (Some) Atomic Physics

U. van Kolck

Abstract These lectures are a pedagogical—not comprehensive—introduction to the applications of effective field theory (EFT) in the context of nuclear and atomic physics. A common feature of these applications is the interplay between non-perturbative physics (needed at leading order to produce non-relativistic bound states and resonances) and controlled perturbative corrections (crucial for predictive power). The essential ideas are illustrated with the simplest nuclear EFT, pionless EFT, which contains only contact interactions and, with minor changes, can be adapted to certain atomic systems. This EFT exploits the two-body unitarity limit, where renormalization leads to discrete scale invariance in systems of three and more bodies. Remarkably complex structures then arise from very simple leading-order interactions. It briefly describes some of the challenges and rewards of including long-range forces—pion exchange in chiral EFT for nuclear systems or Van der Waals forces between atoms.

•Apr 30, 2020•3 citations
We revisit Schrödinger CFTs from a modern point of view. We introduce the ''harmonic trap geometry,'' analogous to the cylinder picture in relativistic CFTs, and demonstrate a state-operator correspondence that applies to all operators, including descendant, massless, and ''normal-ordered operators.'' A thermofield double construction plays an extremely important role. We systematically classify all physical spectra in the harmonic trap and their unitarity bounds, extending earlier results to include both massless and massive states of all spins, providing a new analytic treatment of unitarity bounds, and establishing foundations for a bootstrap. In our reformulation, previously known perturbative non-renormalization theorems follow immediately from non-perturbative factorization at fixed points and along RG flows. Massless states are described by an effective 1d CFT, as predicted by DLCQ, and violate the non-renormalization theorems. We include a self-consistent review of Schrödinger CFTs in our framework, making the paper accessible to anyone with a field theory background.
The Schrodinger equation with a two-dimensional delta-function potential is a simple example of an asymptotically free theory that undergoes dimensional transmutation. Renormalization requires the introduction of a mass scale, which can be lowered perturbatively until an infrared cutoff produced by non-perturbative effects such as bound state formation is encountered. We outline the effective field theory and similarity renormalization group techniques for producing renormalized cutoff hamiltonians, and illustrate the control of logarithmic and inverse-power-law errors both techniques provide.
Abstract These lectures are a pedagogical—not comprehensive—introduction to the applications of effective field theory (EFT) in the context of nuclear and atomic physics. A common feature of these applications is the interplay between non-perturbative physics (needed at leading order to produce non-relativistic bound states and resonances) and controlled perturbative corrections (crucial for predictive power). The essential ideas are illustrated with the simplest nuclear EFT, pionless EFT, which contains only contact interactions and, with minor changes, can be adapted to certain atomic systems. This EFT exploits the two-body unitarity limit, where renormalization leads to discrete scale invariance in systems of three and more bodies. Remarkably complex structures then arise from very simple leading-order interactions. It briefly describes some of the challenges and rewards of including long-range forces—pion exchange in chiral EFT for nuclear systems or Van der Waals forces between atoms.