A Quantum Field Theory Approach to Simple Liquids: The Elementary Excitations of Helium 4

In the framework of Quantum Field Theory we propose a novel approach to the theory of bosonic simple liquids, formulated in terms of a scalar, complex quantum field, the wave-field Ψ(x,t). The problem is treated in a mean-field approximation, diagonalizing the quadratic part of the Hamiltonian à la Bogoliubov and calculating in a perturbative scheme the one-loop correction to the self-energy function. We derive the dispersion relation and the dynamic and static structure factors of the liquid 4 He , obtaining results that are successfully compared with experimental data.

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Dynamical mean field approximation applied to quantum field theory

Physical Review D ◽

10.1103/physrevd.88.125006 ◽

2013 ◽

Vol 88 (12) ◽

Cited By ~ 8

Author(s):

Oscar Akerlund ◽

Philippe de Forcrand ◽

Antoine Georges ◽

Philipp Werner

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Mean Field ◽

Field Approximation ◽

Mean Field Approximation ◽

Quantum Field

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Kinetic field theory: Non-linear cosmic power spectra in the mean-field approximation

SciPost Physics ◽

10.21468/scipostphys.10.6.153 ◽

2021 ◽

Vol 10 (6) ◽

Author(s):

Matthias Bartelmann ◽

Johannes Dombrowski ◽

Sara Konrad ◽

Elena Kozlikin ◽

Robert Lilow ◽

...

Keyword(s):

Field Theory ◽

Power Spectrum ◽

Mean Field ◽

Power Spectra ◽

Field Approximation ◽

Density Fluctuations ◽

Mean Field Approximation ◽

Non Linear ◽

Two Parameters ◽

Kinetic Field

We use the recently developed Kinetic Field Theory (KFT) for cosmic structure formation to show how non-linear power spectra for cosmic density fluctuations can be calculated in a mean-field approximation to the particle interactions. Our main result is a simple, closed and analytic, approximate expression for this power spectrum. This expression has two parameters characterising non-linear structure growth which can be calibrated within KFT itself. Using this self-calibration, the non-linear power spectrum agrees with results obtained from numerical simulations to within typically \lesssim10\,\%≲10% up to wave numbers k\lesssim10\,h\,\mathrm{Mpc}^{-1}k≲10hMpc−1 at redshift z = 0z=0. Adjusting the two parameters to optimise agreement with numerical simulations, the relative difference to numerical results shrinks to typically \lesssim 5\,\%≲5%. As part of the derivation of our mean-field approximation, we show that the effective interaction potential between dark-matter particles relative to Zel’dovich trajectories is sourced by non-linear cosmic density fluctuations only, and is approximately of Yukawa rather than Newtonian shape.

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