• Corpus ID: 51743460

Living with Infinities

@article{Weinberg2009LivingWI,
  title={Living with Infinities},
  author={Steven Weinberg},
  journal={arXiv: High Energy Physics - Theory},
  year={2009}
}
  • S. Weinberg
  • Published 3 March 2009
  • Physics
  • arXiv: High Energy Physics - Theory
This is the written version of a talk given in memory of Gunnar Kallen, at the Departments of Theoretical Physics, Physics, and Astronomy of Lund University on February 13, 2009. It will be published in a collection of the papers of Gunnar Kallen, edited by C. Jarlskog and A. C. T. Wu. I discuss some of Kallen's work, especially regarding the problem of infinities in quantum field theory, and recount my own interactions with him. In addition, I describe for non-specialists the current status of… 
View PDF on arXiv
55 Citations
Background Citations
8

55 Citations

Introduction to a Quantum Theory over a Galois Field

A quantum theory based on a Galois field where infinities cannot exist, the cosmological constant problem does not arise, and there can be no neutral elementary particles and the spin-statistics theorem can be treated simply as a requirement that standard quantum theory should be based on complex numbers.

Towards a more algebraic footing for quantum field theory

The predictions of the standard model of particle physics are highly successful in spite of the fact that several parts of the underlying quantum field theoretical framework are analytically…

Non-Diophantine arithmetic as the mathematical foundation for quantum field theory

The problem of infinities in quantum field theory (QFT) is a long standing problem in particle physics. For solving this problem, different renormalization techniques have been suggested but the…

Quantum fields in the non-perturbative regime - Yang-Mills theory and gravity

In this thesis we investigate two different sets of physics questions, aiming at a better understanding of the low-energy behaviour of Yang-Mills theories, and the properties connected to…

Crisis in Quantum Theory and Its Possible Resolution

It is argued that the main reason of crisis in quantum theory is that nature, which is fundamentally discrete, is described by continuous mathematics. Moreover, no ultimate physical theory can be…

Supersymmetry - Roots That Didn't Grow

This article is about early roots of supersymmetry, as found in the literature from 1940s and early 1950s. There were models where the power of "partners" in alleviating divergences in quantum field…

Finite Quantum Theory and Applications to Gravity and Particle Theory

We argue that the main reason of crisis in quantum theory is that nature, which is fundamentally discrete and even finite, is described by continuous mathematics. Moreover, no ultimate physical…

QED coupled to QEG

We discuss the non-perturbative renormalization group flow of Quantum Electrodynamics (QED) coupled to Quantum Einstein Gravity (QEG) and explore the possibilities for defining its continuum limit at…

Discussion of foundation of mathematics and quantum theory

  • F. Lev
  • Mathematics, Physics
  • 2022
Abstract Following the results of our recently published book [F. Lev, Finite Mathematics as the Foundation of Classical Mathematics and Quantum Theory. With Applications to Gravity and Particle…

Gravity as a Manifestation of de Sitter Invariance over a Galois Field

We consider a system of two free bodies in de Sitter invariant quantum mechanics. De Sitter invariance is understood such that representation operators satisfy commutation relations of the de Sitter…
...