We present certain classical continuum long wave-length limits of prototype integrable quantum spin chains, and define the corresponding construction of classical continuum Lax operators. We also provide two specific examples, i.e. the isotropic and anisotropic Heisenberg models. ∗Proceedings contribution to the Corfu Summer Institute on Elementary Particle Physics and Gravity Workshop on Non C...

Since the particles such as molecules, atoms and nuclei are composite particles, it is important to recognize that physics must be invariant for the composite particles and their constituent particles, this requirement is called particle invariance in this paper. But difficulties arise immediately because for fermion we use Dirac equation, for meson we use Klein-Gordon equation and for classica...

We present a new probabilistic model of compact commutative Lie groups that produces invariantequivariant and disentangled representations of data. To define the notion of disentangling, we borrow a fundamental principle from physics that is used to derive the elementary particles of a system from its symmetries. Our model employs a newfound Bayesian conjugacy relation that enables fully tracta...

Since particles such as molecules, atoms and nuclei are composite particles, it is important to recognize that physics must be invariant for the composite particles and their constituent particles, this requirement is called particle invariance in this paper. But difficulties arise immediately because for fermion we use the Dirac equation, for meson we use the Klein-Gordon equation and for clas...

Since particles such as molecules, atoms and nuclei are composite particles, it is important to recognize that physics must be invariant for the composite particles and their constituent particles, this requirement is called particle invariance in this paper. But difficulties arise immediately because for fermion we use the Dirac equation, for meson we use the Klein-Gordon equation and for clas...

The “Standard Model” of elementary particle physics encompasses the progress that has been made in the past half-century in understanding the weak, electromagnetic, and strong interactions. The name was apparently bestowed by my Ph. D. thesis advisor, Sam B. Treiman, whose dedication to particle physics kindled the light for so many of his students during those times of experimental and theoret...

The “Standard Model” of elementary particle physics encompasses the progress that has been made in the past half-century in understanding the weak, electromagnetic, and strong interactions. The name was apparently bestowed by my Ph. D. thesis advisor, Sam B. Treiman, whose dedication to particle physics kindled the light for so many of his students during those times of experimental and theoret...

Neutrino masses are zero in the minimal supersymmetric standard model. I discuss how they may become nonzero with new interactions which may or may not violate R-parity conservation. ———————– Talk presented at the 6th Corfu Summer Institute on Elementary Particle Physics, 1998.

Inspired by the concept of complementarity, we present a illustrative model for the weak interactions with unbroken gauge symmetry and unbroken supersymmetry. The observable particles are bound states of some more fundamental particles. Supersymmetry is broken at the macroscopic scale of the observable particles by a discrete symmetry but remains exact at the scale of the fundamental particle a...