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Algebraic Approach to the 1 / N Expansion in Quantum Field Theory
| Content Provider | Semantic Scholar |
|---|---|
| Author | Hollands, Stefan |
| Copyright Year | 2004 |
| Abstract | The 1/N expansion in quantum field theory is formulated within an algebraic framework. For a scalar field taking values in the N by N hermitian matrices, we rigorously construct the gauge invariant interacting quantum field operators in the sense of power series in 1/N and the ‘t Hooft coupling parameter as members of an abstract *-algebra. The key advantages of our algebraic formulation over the usual formulation of the 1/N expansion in terms of Green’s functions are (i) that it is completely local so that infra-red divergencies in massless theories are avoided on the algebraic level and (ii) that it admits a generalization to quantum field theories on general Lorentzian curved spacetimes. We expect that our constructions are also applicable in models possessing local gauge invariance such as Yang-Mills theories. The 1/N expansion of the renormalization group flow is constructed on the algebraic level via a family of *-isomorphisms between the algebras of interacting field observables corresponding to different scales. We also consider k-parameter deformations of the interacting field algebras that arise from reducing the symmetry group of the model to a diagonal subgroup with k factors. These parameters smoothly interpolate between situations of different symmetry. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/math-ph/0309042v2.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math-ph/0309042v1.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Byers-Yang theorem Canonical quantization Generalization (Psychology) Hospital admission Interaction Interpolation Linear algebra Observable Population Parameter Quantum field theory Smoothing Subgroup A Nepoviruses YANG |
| Content Type | Text |
| Resource Type | Article |
