On the effective action in presence of local non-linear constraints
| Autor: | Adam Rançon, Ivan Balog |
|---|---|
| Přispěvatelé: | Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 (PhLAM), Université de Lille-Centre National de la Recherche Scientifique (CNRS), ANR-16-IDEX-0004,ULNE,ULNE(2016) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
High Energy Physics - Theory
Statistics and Probability Statistical field theory Degrees of freedom (statistics) toy model FOS: Physical sciences nonperturbative 01 natural sciences Legendre transformation symbols.namesake Correlation function 0103 physical sciences Functional renormalization group Applied mathematics correlation function 010306 general physics Effective action Condensed Matter - Statistical Mechanics Mathematics Second derivative statistical field theory effective average action constraints Statistical Mechanics (cond-mat.stat-mech) 010308 nuclear & particles physics [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] Statistical and Nonlinear Physics Renormalization group 16. Peace & justice constraint: nonlinear [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph] High Energy Physics - Theory (hep-th) effective action symbols Statistics Probability and Uncertainty renormalization group field theory: statistical |
| Zdroj: | J.Stat.Mech. J.Stat.Mech., 2019, 1903 (3), pp.033215. ⟨10.1088/1742-5468/ab0c12⟩ |
| DOI: | 10.1088/1742-5468/ab0c12⟩ |
| Popis: | The conditions for the existence of the effective action in statistical field theory, the Legendre transform of the cumulant generating function, in presence of non-linear local constraints are discussed. This problem is of importance for non-perturbative approaches, such as the functional renormalization group. We show that the Legendre transform exists as long as the non-linear constraints do not imply linear constraints on the microscopic fields. We discuss how to handle the case of effectively linear constraints and we naturally obtain that the second derivative of the effective action is the Moore-Penrose pseudo-inverse of the correlation function. We illustrate our discussion with toy-models, and show that the correct counting of degrees of freedom in non-linearly constrained statistical field theories can be rather counter-intuitive. 13 pages; comments welcomed |
| Databáze: | OpenAIRE |
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