Flow equations without mean field ambiguity

Jaeckel, Joerg; Wetterich, C.

doi:10.1103/physrevd.68.025020

Cited by 78 publications

(109 citation statements)

References 41 publications

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“…The B -dependence ofā or c therefore depends on the splitting of the microscopic interaction into the two pieces λ ψ,Λ and −h 2 φ /ν Λ . Since all our results depend only on c the B -dependence of the observables is now affected by an unphysical "Fierz ambiguity" [60]. This is clearly a shortcoming of the approximation, in particular of our neglection of the molecule fluctuations for the computation of Z φ and the renormalization effects forh φ .…”

Section: Appendix A: Renormalization Of Feshbach Couplingmentioning

confidence: 99%

Universality in phase transitions for ultracold fermionic atoms

2006

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We describe the gas of ultracold fermionic atoms by a functional integral for atom and molecule fields. The crossover from Bose-Einstein condensation (BEC) to BCS-type superfluidity shows universal features in terms of a concentration parameter for the ratio between scattering length and average interatomic distance. We discuss the relevance of the Yukawa coupling between atoms and molecules, establish an exact narrow resonance limit and show that renormalized quantities are independent of the Yukawa coupling for the broad resonance, BCS and BEC limits. Within our functional integral formalism we compute the atom scattering in vacuum and the molecular binding energy. This connects the universal concentration parameter to the magnetic field of a given experiment. Beyond mean field theory we include the fluctuations of the molecule field and the renormalization effects for the atom-molecule coupling. We find excellent agreement with the observed fraction of bare molecules in 6 Li and qualitative agreement with the condensate fraction in 6 Li and 40 K. In addition to the phase diagram and condensate fraction we compute the correlation length for molecules, the in-medium scattering length for molecules and atoms and the sound velocity.

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Section: Appendix A: Renormalization Of Feshbach Couplingmentioning

confidence: 99%

Universality in phase transitions for ultracold fermionic atoms

2006

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“…Then, the generator of gauge transformationsÎ g in (7.48) receives a further contribution and readŝ 78) and with (3.8b) in the presence of the regulator term we arrive at…”

Section: Chiral Symmetry and Anomaliesmentioning

confidence: 99%

“…This includes the bosonisation of fermionic degrees of freedom [72,73,78,80], e.g. in low-energy QCD, where the relevant degrees of freedom are mesons and baryons instead of quarks.…”

Section: A Field Reparameterisationsmentioning

confidence: 99%

“…In theories with a complicated phase structure this might necessitate introducing a large number of vertices to the effective action in terms of the fundamental fields. A way to avoid such a drawback is to reparameterise the theory in terms of the relevant degrees of freedom [41,[72][73][74][75][76][78][79][80][81][82].…”

Section: Truncation Schemes and Optimisationmentioning

confidence: 99%

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Aspects of the functional renormalisation group

2007

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We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A simple equation for the flow of these relations is provided. The setting includes general flows in the presence of composite operators and their relation to standard flows, an important example being N PI quantities. We discuss optimisation and derive a functional optimisation criterion.Applications deal with the interrelation between functional flows and the quantum equations of motion, general Dyson-Schwinger equations. We discuss the combined use of these functional equations as well as outlining the construction of practical renormalisation schemes, also valid in the presence of composite operators. Furthermore, the formalism is used to derive various representations of modified symmetry relations in gauge theories, as well as to discuss gauge-invariant flows. We close with the construction and analysis of truncation schemes in view of practical optimisation.

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“…This is a known ambiguity in the context of mean field theory, and only the non-perturbative physics can settle the value of the four-fermion terms [26]. Thus we may extend the definition of the torsion four-fermion interaction terms to include such ambiguities and write:…”

Section: Dynamical Breaking Ofmentioning

confidence: 99%

Supersymmetry, Cosmological Constant and Inflation: Towards a fundamental cosmic picture via “running vacuum”

Mavromatos

2016

EPJ Web Conf.

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Abstract. On the occasion of a century from the proposal of General relativity by Einstein, I attempt to tackle some open issues in modern cosmology, via a toy but non-trivial model. Specifically, I would like to link together: (i) the smallness of the cosmological constant today, (ii) the evolution of the universe from an inflationary era after the bigbang till now, and (iii) local supersymmetry in the gravitational sector (supergravity) with a broken spectrum at early eras, by making use of the concept of the "running vacuum" in the context of a simple toy model of four-dimensional N=1 supergravity. The model is characterised by dynamically broken local supersymmetry, induced by the formation of gravitino condensates in the early universe. As I will argue, there is a Starobinsky-type inflationary era characterising the broken supersymmetry phase in this model, which is compatible with the current cosmological data, provided a given constraint is satisfied among some tree-level parameters of the model and the renormalised cosmological constant of the de Sitter background used in the analysis. Applying the "running vacuum" concept, then, to the effective field theory at the exit of inflation, makes a smooth connection (in cosmic time) with the radiation dominance epoch and subsequently with the current era of the Universe, characterised by a small (but dominant) cosmological-constant contribution to the cosmic energy density. In this approach, the smallness of the cosmological constant today is attributed to the failure (due to quantum gravity non-perturbative effects) of the aforementioned constraint.

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Flow equations without mean field ambiguity

Cited by 78 publications

References 41 publications

Universality in phase transitions for ultracold fermionic atoms

Universality in phase transitions for ultracold fermionic atoms

Aspects of the functional renormalisation group

Supersymmetry, Cosmological Constant and Inflation: Towards a fundamental cosmic picture via “running vacuum”

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