Effective action for the Yukawa2 quantum field theory

Lesniewski, Andrzej

doi:10.1007/bf01212319

Cited by 96 publications

(82 citation statements)

References 16 publications

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“…A very natural development was then to apply such techniques to condensed matter models, [25], [26] with the final aim at obtaining a full non perturbative control of the ground state properties of interacting systems. However, while the interaction in the models considered in [22] or [23] is marginally irrelevant or dimensionally irrelevant, this is not the case in interacting non relativistic fermionic models in one dimension, or in dimensions greater than one with extended Fermi surface. This is due to the fact that the ground state properties of the interacting system are generically different with respect to the non interacting case.…”

Section: Introductionmentioning

confidence: 99%

“…It was realized in the eighties that such methods can be indeed used to get a full non-perturbative control of certain fermionic Quantum Field Theories in d = 1 + 1, [22], [23] using Gram bounds and Brydges formula for truncated expectation [24]. A very natural development was then to apply such techniques to condensed matter models, [25], [26] with the final aim at obtaining a full non perturbative control of the ground state properties of interacting systems.…”

Section: Introductionmentioning

confidence: 99%

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Weyl Semimetallic Phase in an Interacting Lattice System

Mastropietro

2014

J Stat Phys

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By using Wilsonian Renormalization Group (RG) methods we rigorously establish the existence of a Weyl semimetallic phase in an interacting three dimensional fermionic lattice system, by showing that the zero temperature Schwinger functions are asymptotically close to the ones of massless Dirac fermions. This is done via an expansion which is convergent in a region of parameters, which includes the quantum critical point discriminating between the semimetallic and the insulating phase.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Weyl Semimetallic Phase in an Interacting Lattice System

Mastropietro

2014

J Stat Phys

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“…via the Hadamard inequality. The basic technique for achieving these bounds is well established after the work [Le87]. A second non trivial result is Proposition 2 (short range and asymptotics of the beta function): Let G 0 = ( g , g , .…”

Section: /Agosto/2017; 20:47mentioning

confidence: 99%

Renormalization group in statistical mechanics and mechanics: gauge symmetries and vanishing beta functions

Gallavotti

2001

Physics Reports

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Abstract:Two very different problems that can be studied by renormalization group methods are discussed with the aim of showing the conceptual unity that renormalization group has introduced in some areas of theoretical Physics. The two problems are: the ground state theory of a one dimensional quantum Fermi liquid and the existence of quasi periodic motions in classical mechanical systems close to integrable ones. I summarize here the main ideas and show that the two treatments, although completely independent of each other, are strikingly similar. §1. Introduction. . In all such examples there is a basic difficulty to overcome: namely the samples of the fields can be unboundedly large: this does not destroy the method because such large values have extremely small probability, [Ga85]. The necessity of a different treatment of the large and the small field values hides, to some extent, the intrinsic simplicity and elegance of the approach: unnecessarily so as the end result is that one can essentially ignore (to the extent that it is not even mentioned in most application oriented discussions) the large field values and treat the renormalization problem perturbatively, as if the large fields were not possible.Here I shall discuss two (non trivial) problems in which the large field difficulties are not at all present, and the theory leads to a convergent perturbative solution of the problem (unlike the the above mentioned classical cases, in which the perturbation expansion cannot be analytic in the perturbation parameter). The problems are:(1) the theory of the ground state of a system of (spinless, for simplicity) fermions inThe two problems will be treated independently, for completeness, although it will appear that they are closely related. Since the discussion of problem (1) is quite technical we summarize it at the end (in §3) in a form that shows the generality of the method that will then be applied to the problem (2) in §4. The analysis of the above examples suggests methods to study and solve several problems in the theory of rapidly perturbed quasi periodic unstable motion, [Ga95], [GGM99]: but for brevity we shall only refer to the literature for such applications.

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“…Recall that it is possible to rearrange Fermionic perturbation theory in a convergent expansion order by order by grouping together pieces of Feynman graphs which share a common tree [16,17]. But bosonic constructive theory cannot be simply rearranged in such a convergent way order by order, because all graphs at a given order have the same sign.…”

Section: Introductionmentioning

confidence: 99%