The Bose Einstein Condensation Program

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The following papers are all associated with a program to construct, mathematically rigorously, a model of a Bose gas exhibiting Bose Einstein condensation and symmetry breaking. The collaborators in that program are T. Balaban (Rutgers), J. Feldman (UBC), H. Knörrer (ETH, Zürich) and E. Trubowitz (ETH, Zürich) and all of the papers have that authorship. We have divided the program into a number of stages.

The Functional Integral Representation

Yellow Ball A Functional Integral Representation for Many Boson Systems I: The Partition Function.
Annales Henri Poincaré, 9, 1229-1273 (2008).
[ pdf (275KB), published version (subscription required)]

Yellow Ball A Functional Integral Representation for Many Boson Systems II: Correlation Functions.
Annales Henri Poincaré, 9, 1275-1307 (2008).
[ pdf (221KB), published version (subscription required)]


A Simple High Temperature Expansion

Yellow Ball Power Series Representations for Bosonic Effective Actions.
Journal of Statistical Physics, 134, 839-857 (2009).
pdf (180KB)

Yellow Ball Power Series Representations for Complex Bosonic Effective Actions I: A Small Field Renormalization Group Step.
Journal of Mathematical Physics, 51, 053305 (2010).
[ pdf (309KB), AIP's official online abstract (subscription required)]
Copyright (2010) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

Yellow Ball Power Series Representations for Complex Bosonic Effective Actions. II: A Small Field Renormalization Group Flow.
Journal of Mathematical Physics, 51, 053306 (2010).
[ pdf (260KB), AIP's official online abstract (subscription required)]
Copyright (2010) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

Yellow Ball Power Series Representations for Complex Bosonic Effective Actions. III. Substitution and Fixed Point Equations.
[ preprint (222KB)]


The Temporal Ultraviolet Limit

Yellow Ball The Temporal Ultraviolet Limit for Complex Bosonic Many-body Models.
Annales Henri Poincaré, 11, 151-350 (2010).
[ pdf (1430KB), published version (subscription required)]

Yellow Ball The Temporal Ultraviolet Limit, Les Houches 2010.
This is a draft of Feldman's Les Houches 2010 course. It provides more pedagogical treatments of various aspects of the construction.
pdf (605KB)


The Small Field Part of the Parabolic Flow

Yellow Ball Complex Bosonic Many-body Models: Overview of the Small Field Parabolic Flow.
Annales Henri Poincaré, 18, 2873-2903 (2017).
[ preprint (307KB), published version]

Yellow Ball The Small Field Parabolic Flow for Bosonic Many-body Models: Part 1 - Main Results and Algebra.
[ preprint (506KB)]

Yellow Ball The Small Field Parabolic Flow for Bosonic Many--body Models: Part 2 - Fluctuation Integral and Renormalization.
[ preprint (450KB)]

Yellow Ball The Small Field Parabolic Flow for Bosonic Many--body Models: Part 3 - Nonperturbatively Small Errors.
[ preprint (175KB)]

Yellow Ball The Small Field Parabolic Flow for Bosonic Many--body Models: Part 4 - Background and Critical Field Estimates.
[ preprint (301KB)]

 

Yellow Ball Operators for Parabolic Block Spin Transformations.
[ preprint (448KB)]

Yellow Ball Bloch Theory for Periodic Block Spin Transformations.
[ preprint (207KB)]

 

Yellow Ball The Algebra of Block Spin Renormalization Group Transformations.
[ preprint (176KB)]


The Small Field Part of the Elliptic Flow

Yellow Ball Under (slow) construction.


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