C-symmetry | EPFL Graph Search

In physics, charge conjugation is a transformation that switches all particles with their corresponding antiparticles, thus changing the sign of all charges: not only electric charge but also the charges relevant to other forces. The term C-symmetry is an abbreviation of the phrase "charge conjugation symmetry", and is used in discussions of the symmetry of physical laws under charge-conjugation. Other important discrete symmetries are P-symmetry (parity) and T-symmetry (time reversal). These discrete symmetries, C, P and T, are symmetries of the equations that describe the known fundamental forces of nature: electromagnetism, gravity, the strong and the weak interactions. Verifying whether some given mathematical equation correctly models nature requires giving physical interpretation not only to continuous symmetries, such as motion in time, but also to its discrete symmetries, and then determining whether nature adheres to these symmetries. Unlike the continuous symmetries, the interpretation of the discrete symmetries is a bit more intellectually demanding and confusing. An early surprise appeared in the 1950s, when Chien Shiung Wu demonstrated that the weak interaction violated P-symmetry. For several decades, it appeared that the combined symmetry CP was preserved, until CP-violating interactions were discovered. Both discoveries lead to Nobel prizes. The C-symmetry is particularly troublesome, physically, as the universe is primarily filled with matter, not anti-matter, whereas the naive C-symmetry of the physical laws suggests that there should be equal amounts of both. It is currently believed that CP-violation during the early universe can account for the "excess" matter, although the debate is not settled. Earlier textbooks on cosmology, predating the 1970s, routinely suggested that perhaps distant galaxies were made entirely of anti-matter, thus maintaining a net balance of zero in the universe. This article focuses on exposing and articulating the C-symmetry of various important equations and theoretical systems, including the Dirac equation and the structure of quantum field theory.

Numerical investigations of 3D CFTs using conformal bootstrap methods

Marten Jan Reehorst

Conformal field theories (CFTs) play a very significant role in modern physics, appearing in such diverse fields as particle physics, condensed matter and statistical physics and in quantum gravity both as the string worldsheet theory and through the AdS/CFT correspondence. In recent years major breakthroughs have been made in solving these CFTs through a method called numerical conformal bootstrap. This method uses consistency conditions on the CFT data in order to find and constrain conformal field theories and obtain precise measurements of physical observables. In this thesis we apply the conformal bootstrap to study among others the O(2)- and the ARP^3- models in 3D. In the first chapter we extend the conventional scalar numerical conformal bootstrap to a mixed system of correlators involving a scalar field charged under a global U(1) symmetry and the associated conserved spin-1 current J. The inclusion of a conserved spinning operator is an important advance in the numerical bootstrap program. Using numerical bootstrap techniques we obtain bounds on new observables not accessible in the usual scalar bootstrap. Concentrating on the O(2) model we extract rigorous bounds on the three-point function coefficient of two currents and the unique relevant scalar singlet, as well as those of two currents and the stress tensor. Using these results, and comparing with a quantum Monte Carlo simulation of the O(2) model conductivity, we give estimates of the thermal one-point function of the relevant singlet and the stress tensor. We also obtain new bounds on operators in various sectors. In the second chapter we investigate the existence of a second-order phase transition in the ARP^3 model. This model has a global O(4) symmetry and a discrete Z_2 gauge symmetry. It was shown by a perturbative renormalization group analysis that its Landau-Ginzburg-Wilson effective description does not have any stable fixed point, thus disallowing a second-order phase transition. However, it was also shown that lattice simulations contradict this, finding strong evidence for the existence of a second-order phase transition. In this chapter we apply conformal bootstrap methods to the correlator of four scalars t transforming in the traceless symmetric representation of O(4) in order to investigate the existence of this second order phase transition. We find various features that stand out in the region predicted by the lattice data. Moreover, under reasonable assumptions a candidate island can be isolated. We also apply a mixed t-s bootstrap setup in which this island persists. In addition we study the kink-landscape for all representations appearing in the t times t OPE for general N. Among others, we find a new family of kinks in the upper-bound on the dimension of the first scalar operator in the "Box" and "Hook" representations.

EPFL2020

Complexes luminescents de lanthanides avec des dérivés du cyclène comme briques pour l'ingénierie de sondes analytiques biomédicales

This work deals with the engineering of a new luminescent complex of lanthanide, able to be specifically grafted onto biological materials and to emit a characteristic light useful in quantifying the concentration of the target molecules. We have based our molecular design on TbL1, wich possesses a significant quantum yield in water pointing to an efficient intramolecular energy transfer. We have elaborated the synthesis of a ligand derived from L1 and named L3, by functionalizing one of the chromophoric groups into a moiety able to couple the luminescent sensor to biological materials. The synthesis of the complexes was then realized. The thermodynamic study of the ligands L1 and L3, and their terbium complexes in water was made to establish the distribution diagrams and to compare their behaviour, especially at neutral pH. In addition, EuL1 was also investigated and the complexation constants of TbL1, EuL1 and TbL3 in water showed that these molecules are thermodynamically stable in aqueous media. Characterization of EuL3 in the solid state by high resolution luminescence allowed us to determine the geometry of the coordination sphere of the Eu(III) ion, which possesses a distorded C4 symmetry. The detailed study of the Eu(III) ion transitions evidenced two different sites, possibly arising from an equilibrium induced by the competition between a water molecule and the carboxylate function. This interpretation is in line with the measured lifetimes of the Tb(III) and Eu(III) excited states and the calculation of the hydration number of the complexes in aqueous solution. The determination of the energy of the singlet state and triplet states of the ligand, as well as of the emitting levels of the Ln(III) ions in solution showed that their relative values are favorable for a good intramolecular energy transfer. The quantum yields of TbL3 and EuL3, which amount to 2.6 % and 1.4 %, respectively, are lower than those of the complexes with L1, denoting that the presence of the acid function increases losses in the energy transfer. However, these values remain sizeable enough for potential biomedical applications. The study of the intermolecular energy transfer from EuL1, EuL3 and TbL3 to the acceptor Cy5 has proved promising, and the resulting yields were 90 % for EuL1 and 80 % for the complexes with L3.

EPFL2004

Complexes luminescents de lanthanides avec des dérivés du cyclène comme briques pour l'ingénierie de sondes analytiques biomédicales

EPFL2004

Numerical investigations of 3D CFTs using conformal bootstrap methods

Marten Jan Reehorst

EPFL2020