On fermion grading symmetry for quasi-local systems

We discuss fermion grading symmetry for quasi-local systems with graded commutation relations. We introduce a criterion of spontaneously symmetry breaking (SSB) for general quasi-local systems. It is formulated based on the idea that each pair of distinct phases (appeared in spontaneous symmetry bre...

Full description

Saved in:
Bibliographic Details
Published in:Communications in mathematical physics 2006-06, Vol.264 (2), p.411-426
Main Author: MORIYA, Hajime
Format: Article
Language:English
Subjects:
Broken symmetry
Commutation
Exact sciences and technology
Fermions
Functional analysis
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Physics
Quantum statistical mechanics
Sciences and techniques of general use
Statistical physics, thermodynamics, and nonlinear dynamical systems
Symmetry
Thermal stability
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We discuss fermion grading symmetry for quasi-local systems with graded commutation relations. We introduce a criterion of spontaneously symmetry breaking (SSB) for general quasi-local systems. It is formulated based on the idea that each pair of distinct phases (appeared in spontaneous symmetry breaking) should be disjoint not only for the total system but also for every complementary outside system of a local region specified by the given quasi-local structure. Under a completely model independent setting, we show the absence of SSB for fermion grading symmetry in the above sense.We obtain some structural results for equilibrium states of lattice systems. If there would exist an even KMS state for some even dynamics that is decomposed into noneven KMS states, then those noneven states inevitably violate our local thermal stability condition.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-006-1550-7