Fluctuation Operators and Spontaneous Symmetry Breaking

Abstract

We develop an alternative approach to this field, which was to a large extent developed by Verbeure et al. It is meant to complement their approach, which is largely based on a non-commutative central limit theorem and coordinate space estimates. In contrast to that we deal directly with the limits of $l$-point truncated correlation functions and show that they typically vanish for $l\ge 3$ provided that the respective scaling exponents of the fluctuation observables are appropriately chosen. This direct approach is greatly simplified by the introduction of a smooth version of spatial averaging, which has a much nicer scaling behavior and the systematic developement of Fourier space and energy-momentum spectral methods. We both analyze the regime of normal fluctuations, the various regimes of poor clustering and the case of spontaneous symmetry breaking or Goldstone phenomenon.

30 pages, Latex, a more detailed discussion in section 7 as to possible scaling behavior of l-point functions

References in corpus (6)

• Scaling Algebras and Renormalization Group in Algebraic Quantum Field Theory
• Goldstone Boson Normal Coordinates
• The unmasking of thermal Goldstone bosons
• Goldstone Boson Normal Coordinates in Interacting Bose Gases
• Bounded Fluctuations and Translation Symmetry Breaking in One-Dimensional Particle Systems
• Scaling Limit and Renormalisation Group in General (Quantum) Many Body Theory

Cited by in corpus (9)

• Entanglement-Entropy for Groundstates, Low-lying and Highly Excited Eigenstates of General (Lattice) Hamiltonians
• Wormhole Spaces: the Common Cause for the Black Hole Entropy-Area Law,the Holographic Principle and Quantum Entanglement
• Bogoliubov quasi-averages: spontaneous symmetry breaking and algebra of fluctuations
• Planck Fluctuations, Measurement Uncertainties and the Holographic Principle
• Quantum Theory as emergent from an undulatory translocal Sub-Quantum Level
• Scaling Limit and Renormalisation Group in General (Quantum) Many Body Theory
• Scaling Limit and Renormalisation Group in the Critical Point Analysis of General (Quantum) Many Body Systems
• Slow decay of dynamical correlation functions for nonequilibrium quantum states
• Scaling Analysis and Renormalisation Group for General (Quantum) Many Body Systems in the Critical Regime