Probabilities in Quantum Mechanics

This chapter examines the role played by probabilities on each of the major approaches to understanding quantum mechanics. It is argued that the sorts of considerations brought up in previous chapters, having to do with limitations on precise knowledge of physical states, and the result of applying dynamical evolution to agents’ degrees of belief about those states, have a part to play on each of those approaches. The chapter includes an introduction to the basic formalism of quantum mechanics.

Quantum solutions in relativistic classical mechanics

Quantum solutions of the classical equation of relativistic mechanics are found. The synthesis of classical and quantum physics can become the basic formalism for the second quantum revolution, since the existence of quantum solutions to all equations of classical physics means that macroscopic bodies of both inanimate and living matter, under certain conditions, can be quantum objects. This new direction of physics can find application in the development of nature-like technologies.

Review of accelerator-based searches for Neutral Long-Lived Particles

In this paper we present the current status of searches for neutral long-lived particles. The basic formalism that allows the determination of the number of expected long-lived particles is presented. Heavy neutral leptons can be a type of long-lived particles. The main observational motivations for the existence of heavy neutral lepton is covered as well. A summary of the main results from both collider searches and fixed target/beam dump experiments is presented. The outlook for next generation experiments and their impact on the parameter space of coupling strength and mass of heavy neutral leptons is also discussed.

A guide to two-dimensional conformal field theory

This is a review of two-dimensional conformal field theory including the Virasoro algebra, the bootstrap, and some of the relations to integrable models. An effort is made to develop the basic formalism in a way which is both elementary but also as flexible as possible at the same time. Some advanced topics such as conformal field theory on higher genus surfaces and relations to the isomonodromic deformation problem are discussed; for other topics we offer a first guide to the literature.

Feynman rules for Weyl spinors with mixed Dirac and Majorana mass terms

We present a basic formalism for using the Weyl spinor notation in Feynman rules. We focus on Weyl spinors with mixed Dirac and Majorana mass terms. To clarify the definitions we derive the Feynman rules from the path integral and present two examples: loop corrections for a fermion propagator and a tree level analysis of a seesaw toy model.