# A Hilbert Space Setting for Interacting Higher Spin Fields and the Higgs Issue

@article{Schroer2014AHS, title={A Hilbert Space Setting for Interacting Higher Spin Fields and the Higgs Issue}, author={Bert Schroer}, journal={Foundations of Physics}, year={2014}, volume={45}, pages={219-252} }

Wigner’s famous 1939 classification of positive energy representations, combined with the more recent modular localization principle, has led to a significant conceptual and computational extension of renormalized perturbation theory to interactions involving fields of higher spin. Traditionally the clash between pointlike localization and the the Hilbert space was resolved by passing to a Krein space setting which resulted in the well-known BRST gauge formulation. Recently it turned out that…

## 12 Citations

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Positive energy ray representations of the Poincar\'e group are naturally subdivided into three classes according to their mass and spin content: m>0, m=0 finite helicity and m=0 infinite helicity.…

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The almost 7 decades lasting futile attempts to understand the possible physical content of the third Wigner representation class (the infinite spin class) came to a partial solution with the 2006…

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dx.doi.org/10.7437/NF2318-4957/2013.01.002 Modular localization is the concise conceptual formulation of causal localizationin the setting of local quantum physics. Unlike QM it does not refer to…

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## References

SHOWING 1-10 OF 39 REFERENCES

### An Alternative to the Gauge Theoretic Setting

- Physics
- 2011

The standard formulation of quantum gauge theories results from the Lagrangian (functional integral) quantization of classical gauge theories. A more intrinsic quantum theoretical access in the…

### String-Localized Quantum Fields, Modular Localization, and Gauge Theories

- Physics
- 2009

The concept of modular localization introduced by Brunetti, Guido and Longo, and Schroer, can be used to construct quantum fields. It combines Wigner’s particle concept with the Tomita-Takesaki…

### The foundational origin of integrability in quantum field theory

- Mathematics
- 2011

The main aim of this work is to relate integrability in QFT with a complete particle interpretation directly to the principle of causal localization, circumventing the standard method of finding…

### New Light on Infrared Problems: Sectors, Statistics, Symmetries and Spectrum

- Physics
- 2014

A new approach to the analysis of the physical state space of a theory is presented within the general setting of local quantum physics. It also covers theories with long range forces, such as…

### Modular localization and wigner particles

- Mathematics
- 2002

We propose a framework for the free field construction of algebras of local observables which uses as an input the Bisognano–Wichmann relations and a representation of the Poincare group on the…

### Renormalization of the abelian Higgs-Kibble model

- Physics
- 1975

This article is devoted to the perturbative renormalization of the abelian Higgs-Kibble model, within the class of renormalizable gauges which are odd under charge conjugation. The Bogoliubov…

### Dark matter and Wigner's third positive-energy representation class

- Physics
- 2013

The almost 7 decades lasting futile attempts to understand the possible physical content of the third Wigner representation class (the infinite spin class) came to a partial solution with the 2006…

### String-Localized Quantum Fields and Modular Localization

- Physics, Mathematics
- 2005

We study free, covariant, quantum (Bose) fields that are associated with irreducible representations of the Poincaré group and localized in semi-infinite strings extending to spacelike infinity.…

### Modular localization and the holistic structure of causal quantum theory, a historical perspective

- Physics
- 2011

### The ongoing impact of modular localization on particle theory To the memory of Hans-Jürgen Borchers (1926-2011)

- Physics
- 2013

dx.doi.org/10.7437/NF2318-4957/2013.01.002 Modular localization is the concise conceptual formulation of causal localizationin the setting of local quantum physics. Unlike QM it does not refer to…