Power Series Representations for Bosonic Effective Actions
We develop a power series representation and estimates for an effective action of the form Here, f ( φ , ψ ) is an analytic function of the real fields φ ( x ), ψ ( x ) indexed by x in a finite set X , and d μ ( φ ) is a compactly supported product measure. Such effective actions occur in the small...
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| Published in | Journal of statistical physics Vol. 134; no. 5-6; pp. 839 - 857 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Boston
Springer US
01.03.2009
|
| Subjects | |
| Online Access | Get full text |
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| Abstract | We develop a power series representation and estimates for an effective action of the form
Here,
f
(
φ
,
ψ
) is an analytic function of the real fields
φ
(
x
),
ψ
(
x
) indexed by
x
in a finite set
X
, and
d
μ
(
φ
) is a compactly supported product measure. Such effective actions occur in the small field region for a renormalization group analysis. The customary way to analyze them is a cluster expansion, possibly preceded by a decoupling expansion. Using methods similar to a polymer expansion, we estimate the power series of the effective action without introducing an artificial decomposition of the underlying space into boxes. |
|---|---|
| AbstractList | We develop a power series representation and estimates for an effective action of the form
Here,
f
(
φ
,
ψ
) is an analytic function of the real fields
φ
(
x
),
ψ
(
x
) indexed by
x
in a finite set
X
, and
d
μ
(
φ
) is a compactly supported product measure. Such effective actions occur in the small field region for a renormalization group analysis. The customary way to analyze them is a cluster expansion, possibly preceded by a decoupling expansion. Using methods similar to a polymer expansion, we estimate the power series of the effective action without introducing an artificial decomposition of the underlying space into boxes. |
| Author | Feldman, Joel Balaban, Tadeusz Trubowitz, Eugene Knörrer, Horst |
| Author_xml | – sequence: 1 givenname: Tadeusz surname: Balaban fullname: Balaban, Tadeusz organization: Department of Mathematics, Rutgers, The State University of New Jersey – sequence: 2 givenname: Joel surname: Feldman fullname: Feldman, Joel organization: Department of Mathematics, University of British Columbia – sequence: 3 givenname: Horst surname: Knörrer fullname: Knörrer, Horst email: knoerrer@math.ethz.ch organization: Mathematik, ETH-Zentrum – sequence: 4 givenname: Eugene surname: Trubowitz fullname: Trubowitz, Eugene organization: Mathematik, ETH-Zentrum |
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| Cites_doi | 10.1007/BF00531932 10.1007/BF01403502 10.1007/s00023-008-0387-3 10.1007/s00023-008-0388-2 10.1515/9781400862085 10.1007/978-3-662-03873-4 10.1007/s10955-008-9634-8 10.1515/9781400863433 |
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| Keywords | Polymer expansion Renormalization group |
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| References | Seiler (CR9) 1982 Cammarota (CR5) 1982; 85 Simon (CR10) 1993 Rota (CR7) 1964; 2 Rivasseau (CR6) 1991 CR4 CR3 Balaban, Feldman, Knörrer, Trubowitz (CR2) 2008; 9 Balaban, Feldman, Knörrer, Trubowitz (CR1) 2008; 9 Salmhofer (CR8) 1999 9634_CR3 T. Balaban (9634_CR1) 2008; 9 V. Rivasseau (9634_CR6) 1991 9634_CR4 M. Salmhofer (9634_CR8) 1999 E. Seiler (9634_CR9) 1982 G.-C. Rota (9634_CR7) 1964; 2 T. Balaban (9634_CR2) 2008; 9 C. Cammarota (9634_CR5) 1982; 85 B. Simon (9634_CR10) 1993 |
| References_xml | – year: 1982 ident: CR9 publication-title: Gauge Theories as a Problem of Constructive Quantum Field Theory and Statistical Mechanics contributor: fullname: Seiler – volume: 2 start-page: 340 year: 1964 ident: CR7 article-title: On the foundations of combinatorial theory. I. Theory of Möbius functions publication-title: Z. Wahrscheinlichkeitstheor. Verw. Geb. doi: 10.1007/BF00531932 contributor: fullname: Rota – year: 1999 ident: CR8 publication-title: Renormalization, An Introduction contributor: fullname: Salmhofer – volume: 85 start-page: 517 year: 1982 end-page: 528 ident: CR5 article-title: Decay of correlations for infinite range interactions in unbounded spin systems publication-title: Commun. Math. Phys. doi: 10.1007/BF01403502 contributor: fullname: Cammarota – ident: CR3 – ident: CR4 – volume: 9 start-page: 1229 year: 2008 end-page: 1273 ident: CR1 article-title: A functional integral representation for many boson systems. I: The partition function publication-title: Ann. Henri Poincaré doi: 10.1007/s00023-008-0387-3 contributor: fullname: Trubowitz – year: 1991 ident: CR6 publication-title: From Perturbative to Constructive Renormalization contributor: fullname: Rivasseau – volume: 9 start-page: 1275 year: 2008 end-page: 1307 ident: CR2 article-title: A functional integral representation for many boson systems. II: Correlation functions publication-title: Ann. Henri Poincaré doi: 10.1007/s00023-008-0388-2 contributor: fullname: Trubowitz – year: 1993 ident: CR10 publication-title: The Statistical Mechanics of Lattice Gases contributor: fullname: Simon – volume: 9 start-page: 1275 year: 2008 ident: 9634_CR2 publication-title: Ann. Henri Poincaré doi: 10.1007/s00023-008-0388-2 contributor: fullname: T. Balaban – volume-title: From Perturbative to Constructive Renormalization year: 1991 ident: 9634_CR6 doi: 10.1515/9781400862085 contributor: fullname: V. Rivasseau – volume-title: Renormalization, An Introduction year: 1999 ident: 9634_CR8 doi: 10.1007/978-3-662-03873-4 contributor: fullname: M. Salmhofer – volume-title: Gauge Theories as a Problem of Constructive Quantum Field Theory and Statistical Mechanics year: 1982 ident: 9634_CR9 contributor: fullname: E. Seiler – volume: 85 start-page: 517 year: 1982 ident: 9634_CR5 publication-title: Commun. Math. Phys. doi: 10.1007/BF01403502 contributor: fullname: C. Cammarota – volume: 2 start-page: 340 year: 1964 ident: 9634_CR7 publication-title: Z. Wahrscheinlichkeitstheor. Verw. Geb. doi: 10.1007/BF00531932 contributor: fullname: G.-C. Rota – volume: 9 start-page: 1229 year: 2008 ident: 9634_CR1 publication-title: Ann. Henri Poincaré doi: 10.1007/s00023-008-0387-3 contributor: fullname: T. Balaban – ident: 9634_CR3 doi: 10.1007/s10955-008-9634-8 – ident: 9634_CR4 doi: 10.1007/s10955-008-9634-8 – volume-title: The Statistical Mechanics of Lattice Gases year: 1993 ident: 9634_CR10 doi: 10.1515/9781400863433 contributor: fullname: B. Simon |
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| Snippet | We develop a power series representation and estimates for an effective action of the form
Here,
f
(
φ
,
ψ
) is an analytic function of the real fields
φ
(
x... |
| SourceID | crossref springer |
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| SubjectTerms | Mathematical and Computational Physics Physical Chemistry Physics Physics and Astronomy Quantum Physics Statistical Physics and Dynamical Systems Theoretical |
| Title | Power Series Representations for Bosonic Effective Actions |
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