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Fuzzy Actions and their Continuum Limits
| Content Provider | Semantic Scholar |
|---|---|
| Author | Martin, Xavier Connor, Denjoe O’ |
| Abstract | In contrast to conventional lattice discretizations, fuzzy physics [1–6] regulates quantum fields on a manifold M by quantizing the latter, treating it as a phase space. This method works because quantization implies a short distance cut–off: the number of states in a volume V on M is infinite in classical physics, but becomes about V/ ̃̄ h d on quantization, if ̃̄ h is the substitute for Planck’s constant and M has dimension d. The classical limit ̃̄ h→ 0 is then the continuum limit of interest. In past research, [7–16] several authors have explored this novel approach to discrete physics and established that it can correctly reproduce continuum topological features like instantons, θ–states and the axial anomaly. Even chiral fermions can be formulated without duplication [14]. When M is the two sphere S, this formulation shares common features with the Ginsparg-Wilson approach [15]. Proposals have also been made in previous work for certain novel fuzzy actions. They fulfill instanton-like bounds when such exist in the continuum and in all cases are compatible with the known scaling properties of the latter. They were conjectured to have correct continuum limits as well. This paper verifies those conjectures for the scalar and spinor fields. Gauge theories will be examined elsewhere, but the correctness of the conjectures in all instances looks plausible. The present work in this manner goes toward establishing that the actions of [13,14] in addition to retaining important topological features, also have the correct continuum limits. There is thus good reason to explore them further as alternatives to conventional lattice models. In section II, we review the motivations and structure of the proposed actions and indicate which of them we will study in this paper. Introductory developments and useful asymptotic estimates involving heat kernels methods are covered in sections III, IV and the Appendix. The remaining two sections successfully employ this material to establish the continuum limits. The concluding remarks are in section VII. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://cds.cern.ch/record/445970/files/0007030.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Anomaly detection Chirality (chemistry) Classical limit Correctness (computer science) Estimated Gene Duplication Abnormality Image scaling Lattice model (physics) Motivation Published Comment Spinor Test scaling Theory Triune continuum paradigm Vii manifold |
| Content Type | Text |
| Resource Type | Article |
