Bose-Einstein condensation of quasiparticles is excluded in the van Hove model because time cluster properties on beta-KMS states preclude it and nonlinear dispersion with s greater than 2 reduces the observable algebra via infrared divergences.
A Note on the Resolvent Algebra and Functional Integral Approach to the Free Bose Einstein Condensation
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abstract
We present a systematic description of the structure of Bose-Einstein condensation (BEC) in the free Bose gas from the viewpoint of the correspondence between the operator-algebraic formulation based on the resolvent algebra and the functional integral representation. By clarifying the representation-theoretic structure of finite-temperature BEC states and rigorously analyzing the correspondence between their direct integral decomposition and the ergodic decomposition of the associated probability measures, we provide a framework in which general features of phase transitions-such as the emergence of order parameters, the decomposition of states, and clustering properties-are explicitly described using BEC in the free Bose gas as a concrete example. Furthermore, we construct in detail the correspondence between the decomposition of measures in the functional integral approach and that of operator-algebraic representations, thereby establishing the equivalence between the probabilistic and algebraic aspects, and providing a guiding principle for isolating the essential structures by disentangling the additional mathematical complications arising from the treatment of infrared singularities in interacting systems. These results lay a foundation for the rigorous analysis of phase transitions in non-relativistic constructive quantum field theory and quantum statistical mechanics, and serve as a starting point for extensions to interacting models.
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In the mean-field BEC regime of the imperfect Bose gas, zero-mode covariance defines a mean-field BEC ideal in the resolvent algebra, with occupation-number and Brownian-loop formulations recovering consistent density, excess, and ODLRO data while separating finite-density BEC from Buchholz's strict
No-go theorem for quasiparticle BEC in the spin-boson model is stated, with the observation that the model does not follow the referenced no-go criterion from arxiv:1207.4621.
Operator algebras and probability theory supply guiding principles for constructive quantum field theory and rigorous statistical mechanics.
The paper is a set of notes on the van Hove model that covers cutoff removal, existence of ground and KMS states for a point source, and Bose-Einstein condensation in infinite volume, but states it contains no essentially new results.
citing papers explorer
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No-Go Theorem for Quasiparticle BEC
Bose-Einstein condensation of quasiparticles is excluded in the van Hove model because time cluster properties on beta-KMS states preclude it and nonlinear dispersion with s greater than 2 reduces the observable algebra via infrared divergences.
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Mean-Field Bose--Einstein Condensation and Condensate Ideals in the Resolvent Algebra
In the mean-field BEC regime of the imperfect Bose gas, zero-mode covariance defines a mean-field BEC ideal in the resolvent algebra, with occupation-number and Brownian-loop formulations recovering consistent density, excess, and ODLRO data while separating finite-density BEC from Buchholz's strict
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No-Go Theorem for Quasiparticle BEC in the Spin-Boson Model
No-go theorem for quasiparticle BEC in the spin-boson model is stated, with the observation that the model does not follow the referenced no-go criterion from arxiv:1207.4621.
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Constructive Quantum Field Theory and Rigorous Statistical Mechanics via Operator Algebras and Probability Theory -- Guiding Principles and Research Perspectives
Operator algebras and probability theory supply guiding principles for constructive quantum field theory and rigorous statistical mechanics.
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A Note on the Resolvent Algebra and Functional Integral Approach to the van Hove Model
The paper is a set of notes on the van Hove model that covers cutoff removal, existence of ground and KMS states for a point source, and Bose-Einstein condensation in infinite volume, but states it contains no essentially new results.