arXiv subjects

Tadeusz Balaban

Publications and source records attributed to Tadeusz Balaban.

9 recordsLinked to original sources

arXiv2016

Power Series Representations for Complex Bosonic Effective Actions. III. Substitution and Fixed Point Equations

We have previously developed a polymer-like expansion that applies when the (effective) action in a functional integral is an analytic function of the fields being integrated. Here, we develop methods to aid the application of this technique when the method of steepest descent is used to analyze the functional integral. We develop a version of the Banach fixed point theorem that can be used to construct and control the critical fields, as analytic functions of external fields, and substitution formulae to control the change in norms that occurs when one replaces the integration fields by the sum of the critical fields and the fluctuation fields.

math-ph↗

arXiv2016

Bloch Theory for Periodic Block Spin Transformations

Block spin renormalization group is the main tool used in our program to see symmetry breaking in a weakly interacting many Boson system on a three dimensional lattice at low temperature. It generates operators, like the fluctuation integral covariance, that act on some lattice but are translation invariant only with respect to a proper sublattice. This paper constructs a Bloch/Floquet framework that is appropriate for bounding such operators.

math-ph↗

arXiv2016

The Algebra of Block Spin Renormalization Group Transformations

Block spin renormalization group is the main tool used in our program to see symmetry breaking in a weakly interacting many Boson system on a three dimensional lattice at low temperature. In this paper, we discuss some of its purely algebraic aspects in an abstract setting. For example, we derive some "well known" identities like the composition rule and the relation between critical fields and background fields.

math-ph↗

arXiv2016

Operators for Parabolic Block Spin Transformations

This paper is a contribution to a program to see symmetry breaking in a weakly interacting many Boson system on a three dimensional lattice at low temperature. It is part of an analysis of the "small field" approximation to the "parabolic flow" which exhibits the formation of a "Mexican hat" potential well. Bounds on the fluctuation integral covariance, as well as on some other linear operators, are an important ingredient in our renormalization group step analysis. These bounds are proven here.

math-ph↗

arXiv2016

The Small Field Parabolic Flow for Bosonic Many-body Models: Part 1 - Main Results and Algebra

This paper is a contribution to a program to see symmetry breaking in a weakly interacting many Boson system on a three dimensional lattice at low temperature. It is part of an analysis of the "small field" approximation to the "parabolic flow" which exhibits the formation of a "Mexican hat" potential well. Here we state the main result of this analysis, outline the strategy of the proof, which uses a renormalization group flow, and perform the first, algebraic, part of a renormalization group step.

math-ph↗

arXiv2016

The Small Field Parabolic Flow for Bosonic Many-body Models: Part 2 - Fluctuation Integral and Renormalization

This paper is a contribution to a program to see symmetry breaking in a weakly interacting many Boson system on a three dimensional lattice at low temperature. It is part of an analysis of the "small field" approximation to the "parabolic flow" which exhibits the formation of a "Mexican hat" potential well. Here we complete the analysis of a renormalization group step by "evaluating" the fluctuation integral and renormalizing the chemical potential.

math-ph↗

arXiv2016

The Small Field Parabolic Flow for Bosonic Many-body Models: Part 3 - Nonperturbatively Small Errors

This paper is a contribution to a program to see symmetry breaking in a weakly interacting many Boson system on a three dimensional lattice at low temperature. It is part of an analysis of the "parabolic flow" which exhibits the formation of a "Mexican hat" potential well. Here we provide arguments that suggest, but do not completey prove, that the difference between the "small field" approximation and the full model is nonperturbatively small.

math-ph↗

arXiv2016

The Small Field Parabolic Flow for Bosonic Many-body Models: Part 4 - Background and Critical Field Estimates

This paper is a contribution to a program to see symmetry breaking in a weakly interacting many Boson system on a three dimensional lattice at low temperature. It is part of an analysis of the "small field" approximation to the "parabolic flow" which exhibits the formation of a "Mexican hat" potential well. Here we prove the existence of and bounds on the background and critical fields that arise from the steepest descent attack that is at the core of our renormalization group step anaylsis of these models.

math-ph↗

arXiv2016

Complex Bosonic Many-body Models: Overview of the Small Field Parabolic Flow

This paper is a contribution to a program to see symmetry breaking in a weakly interacting many Boson system on a three dimensional lattice at low temperature. It provides an overview of our analysis of the "small field" approximation to the "parabolic flow" which exhibits the formation of a "Mexican hat" potential well.

math-ph↗