Unified field theory

In physics, a unified field theory (UFT) is a type of field theory that allows all that is usually thought of as fundamental forces and elementary particles to be written in terms of a pair of physical and virtual fields. According to the modern discoveries in physics, forces are not transmitted directly between interacting objects but instead are described and interpreted by intermediary entities called fields. Classically, however, a duality of the fields is combined into a single physical field. For over a century, unified field theory has remained an open line of research. The term was coined by Albert Einstein, who attempted to unify his general theory of relativity with electromagnetism. The "Theory of Everything" and Grand Unified Theory are closely related to unified field theory, but differ by not requiring the basis of nature to be fields, and often by attempting to explain physical constants of nature. Earlier attempts based on classical physics are described in the arti

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Simulated annealing study of the disordered quantum magnet LiHoxEryY1-x-yF4

Thermal and quantum phase transitions of some rare earth compounds (LiErF4, LiYbF4, LiGdF4 and LiTmF4) are established using the mean field theory. These preliminary calculations allowed evidencing the existence of a novel high-field antiferromagnetic phase in LiErF4, and a still unexplained symmetry breaking in LiGdF4. But the discrepancies with experimental results impel a more sophisticated method. We then present analytical and numerical evidence for the validity of an effective approach to the description of the dipolar coupled antiferromagnet LiErF4. We show that the approach, when implemented in mean field calculations, is able to capture both the qualitative and quantitative aspects of the physics of LiErF4 at small external field and low temperature, yielding results that agree with those obtained in the full Hilbert space using mean field theory. This model nevertheless still fails to describe the LiHoF4 system and needs to be improved. We finally use this toy model as a basis for classical Monte Carlo simulations of LiErF4, which allows the calculation of thermodynamical quantities of the system, as well as the evolution of the order parameters as a function of field H and temperature T. These calculations yield results that are much closer to the experiments than those based on the mean field approximation. Although the theoretical critical temperature is still overestimated by 34%, the critical exponents computed from this effective model correspond to those found experimentally.

2012

Harmonic analysis and mean field theory

Denis Karateev

We review some aspects of harmonic analysis for the Euclidean conformal group, including conformally-invariant pairings, the Plancherel measure, and the shadow transform. We introduce two efficient methods for computing these quantities: one based on weight-shifting operators, and another based on Fourier space. As an application, we give a general formula for OPE coefficients in Mean Field Theory (MFT) for arbitrary spinning operators. We apply this formula to several examples, including MFT for fermions and "seed" operators in 4d, and MFT for currents and stress-tensors in 3d.

Springer2019

Aspects of Gauge Theories Vacua

Adrien Florio

This thesis is concerned with gauge theories, their complicated vacuum and resulting effects. After an introduction to the subject, it is divided into four parts. Firstly, we treat the problem of chiral charge dynamics at finite temperature. Quantum field theory predicts a possibility for massless fermions to be transferred into electromagnetic fields with non-zero helicity and vice-versa. This phenomenon has applications ranging from cosmology to heavy-ions physics. We present a numerical investigation from first principles of the resulting complex dynamics and find a qualitative agreement with previous studies based on hydrodynamical approaches but measure rates that differ by up to an order of magnitude. We interpret this effect as contributions coming from small scales not previously taken into account. Secondly, we present a study of open-boundary conditions in lattice QCD at finite temperature. They were designed to ease up the problem of "topological freezing", which plagues numerical simulations close to the continuum limit. In particular, we determine the length of the "boundary zone" for two different temperatures. We also use the boundary effects to extract screening masses. Thirdly, we move on to present a compendium of lattice techniques, including some new algorithms, to perform real-time classical simulations of bosonic matter, Abelian and non-Abelian gauge fields in an expanding universe. We also briefly introduce CosmoLattice, a numerical software designed to perform such simulations, which are particularly interesting to study the reheating phase of our universe. Finally, we study yet another technique to probe non-perturbative sectors of field theories. Namely, we show that one can reconstruct the Schwinger pair production rate, which is the rate of production of particles due to the presence of a strong electric field, using only a few terms of the weak magnetic field expansion. This surprising result is obtained by using techniques coming from the field of resurgence and the analysis of asymptotic expansions. We conclude this work by presenting some general outlooks, sharing aspects of all these different yet related topics.

EPFL2020

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