Quantum Field Theory and Critical Phenomena

By J. Zinn-Justin. 2002

2,090 citations recorded by the source corpus.

Introduced as a quantum extension of Maxwell's classical theory, quantum electrodynamic (QED) has been the first example of a quantum field theory (QFT). Eventually, QFT has become the framework for the discussion of all fundamental interactions at the microscopic scale except, possibly, gravity. More surprisingly, it has also provided a framework for the understanding of second order phase transitions in statistical mechanics. In fact, as hopefully this work illustrates, QFT is the natural framework for the discussion of most systems involving an infinite number of degrees of freedom with local couplings. These systems range from cold Bose gases at the condensation temperature (about ten nanokelvin) to conventional phase transitions (from a few degrees to several hundred) and high energy particle physics up to a TeV, altogether more than twenty orders of magnitude in the energy scale. Therefore, although excellent textbooks about QFT had already been published, I thought, many years ago, that it might not be completely worthless to present a work in which the strong formal relations between particle physics and the theory of critical phenomena are systematically emphasized. This option explains some of the choices made in the presentation. A formulation in terms of field integrals has been adopted to study the properties of QFT. The language of partition and correlation functions has been used throughout, even in applications of QFT to particle physics. Renormalization and renormalization group (RG) properties are systematically discussed. The notion of effective field theory (EFT) and the emergence of renormalizable theories are described. The consequences for fine-tuning and triviality issue are emphasized. This fifth edition has been updated and fully revised.

Subfields: Applied Mathematics, Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/45079a4dfb5360c348d8f6987058d7110a7c579f

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Citations in the corpus

An Introduction to the Nonperturbative Renormalization Group (2007, background): “espond to a controlled approximation whereas approximations performed in the NPRG framework seemed uncontrolled. However, this is completely wrong. Renormalized perturbation series are not convergent.[41, 5] They are asymptotic series, at best.2 For the O(N) model at l − 1 loops, the coeﬃcient in fr”
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Nonperturbative effects and nonperturbative definitions in matrix models and topological strings (2008, background): “This has been also pointed out for the case of the double-well potential in quantum mechanics, where the multi-instanton corrections play a crucial role in reconstructing the exact answer for the energies [ 82 , 83].”
First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories (2008, methodology): “In principle, we can now use the tools of dynamical field theory [ 49 ] to incorporate fluctuations around the saddle points, and to calculate spatiotemporal correlation functions in the s-ensemble, For example, defining a density field n(x, τ ) through a continuum limit of the original occupation v”
Critical phenomena in microgravity: Past, present, and future (2007, background): “…RG theory can be obtained from textbooks and extensive reviews on the subject and references therein Fisher, 1974, 1998; Ma, 1976; Parisi, 1988; Itzykson and DrouHe, 1989; Binney et al., 1993; Cardy, 1996; Kleinert and Schulte-Frohlinde, 2001; Zinn-Justin, 2001, 2002; Pelissetto and Vicari, 2002 .”
Irreversibility in Active Matter Systems: Fluctuation Theorem and Mutual Information (2018, methodology): “Gaussian path integrals of this form are ubiquitous in field theories [84, 113] with well-established results.”
An introduction to spontaneous symmetry breaking (2019, background): “The study of the renormalisation group is consequently a major field of study on its own, for which several excellent textbooks are available [20,67,70,75].”
Heisenberg-Euler Effective Lagrangians : Basics and Extensions (2004, neutral): “, the expansion coeﬃcients behave for large kas c(j) k = (−1)j+kΓ(2k+j)Γ(2k+j+2)B 2k+2j+2 Γ(2k+3)Γ(2k+j+ 5 2 ) ∼ 2 Γ(2k+3j− 1 2 ) (2π)2j+2k+2 , k→ ∞ . (2.52) Using standard Borel dispersion relations [67,68], one ﬁnds [66] ImS(j) ∼ 1 j! πm4ω2 4e3E3 j exp − m2π eE (2.53) Remarkably, the sum over j”
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