The present article reviews the multiple applications of group theory to symmetry problems in physics. In classical physics, this concerns primarily relativity: Euclidean, Galilean, and Einsteinian (special). Going over quantum mechanics, we first note that basic principles imply state space a system has an intrinsic structure pre-Hilbert one completes into genuine Hilbert space. framework, des...

We review some approaches to the quark-lepton mass problem. The ideas of mass-protection and approximate chiral flavour symmetries as a framework for resolving the mass hierarchy problem are presented. Dy-namical calculations of the top quark and Higgs particle masses, based on infra-red fixed points and the so-called multiple point principle respectively, are discussed. We also consider mass m...

I begin these lectures by examining the transformation properties of quantum elds under the discrete symmetries of Parity, P, Charge Conjugation, C, and Time Reversal, T. With these results in hand, I then show how the structure of the Standard Model helps explain the conservation/violation of these symmetries in various sectors of the theory. This discussion is also used to give a qualitative ...

We consider models for physics beyond the standard model in which supersymmetry is broken spontaneously near the weak scale by fields that are charged under electroweak symmetry. We show that this is possible if some or all of the light quarks and leptons are composite near the weak scale. Flavor-changing neutral currents can be naturally suppressed by a GIM mechanism or by approximate flavor s...

We consider lifted importance sampling (LIS), a previously proposed approximate inference algorithm for statistical relational learning (SRL) models. LIS achieves substantial variance reduction over conventional by using various lifting rules that take advantage of the symmetry in representation. However, it suffers from two drawbacks. First, does not some important symmetries representation an...

Lifted probabilistic inference algorithms have been successfully applied to a large number of symmetric graphical models. Unfortunately, the majority of realworld graphical models is asymmetric. This is even the case for relational representations when evidence is given. Therefore, more recent work in the community moved to making the models symmetric and then applying existing lifted inference...

We use modular invariance and crossing symmetry of conformal field theory to reveal approximate reflection symmetries in the spectral decompositions of the partition function in two dimensions in the limit of large central charge and of the four-point function in any dimension in the limit of large scaling dimensions ∆0 of external operators. We use these symmetries to motivate universal upper ...

We consider lifted importance sampling (LIS), a previously proposed approximate inference algorithm for statistical relational learning (SRL) models. LIS achieves substantial variance reduction over conventional importance sampling by using various lifting rules that take advantage of the symmetry in the relational representation. However, it suffers from two drawbacks. First, it does not take ...

We study the supersymmetric spontaneous symmetry breaking of SO(10) into SU (3)⊗ SU (2) ⊗ U (1) for the most physically interesting cases of SU (5) or flipped SU (5) ⊗ U (1) intermediate symmetries. The first case is more easily realized while the second one requires a fine-tuning condition on the parameters of the superpotential. This is because in the case of SU (5) symmetry there is at most ...