Undergraduate Course

•  Department of Physics

  Mechanics C and D

  The main theme of these lectures is the langrangian and hamiltonian formalisms of classical mechanics. First of all, generalized coordinate and its conjugate momentum are introduced, and then equations of motion (EOM) for a system of point particles are written in terms of these variables. The EOM are re-formulated as a variational problem, which requires the action (= time integral of lagrangian) to be stationary for the real trajectory.
  We see that relation between a symmetry and a conserved quantities is clarified in terms of lagrangians.
  These pictures are carried into the phase space. Then the time-evolution of the variables are determined by hamiltonian. Poisson brackets are introduced and the EOM can be expressed rather simply in terms of them. Canonical transformations are transformations of the canonical varialbels which do not change the Poisson brackets. A generator of canonical transformations is conserved. The hamiltonian formalism and the canonical transformation will play an important role in quantum mechanics.

  
  
  

  Theory of Relativity

  The theory of special relativity is presented, starting from the two principles. The Lorentz transformation is introduced as the coordinate transformation between two inertial frames that does not change the light speed. The transformation naturally induces the Lorentz contraction, changes the concepts of time and introduces the new causality.
  After reviewing vectors and tensors in the Minkowski spacetime, how to construct a relativistic theory is outlined. Classical Mechanics and Electromagnetism are reformulated in the relativistc forms, from which the relation between energy and momentum is reduced.

  
  
  

•  For students who do not belong to scientific departments

  Quantum Physics

  Qunatum theory was first introduced to describe microphysics, and now are developed to study a system with many degrees of freedom, such as condensed matter and the early universe. The logic of quantum theory is different from that of classical theory.
  In this lecture, we explain why quantum theory is necessary and how it is constructed. After introduction of some basic concepts about states and observables, we formulate them by use of wave functions and hermitian operators acting on them. Then a few examples, which are exactly soluble, are employed to show peculiar features of quantum theory.

  
  
  

Graduate Course

•  Master course

  Elementary Particle Physics

  The laws of elementary particles are described in terms of Quantum Field Theory. After a brief review of it, introduced are various symmetries, such as Poincare symmetry, isospin and chiral symmetry, gauge symmetry and CPT symmetries. Next the relations between the continuous symmetries and the conserved currents are discussed. Based on the gauge symmetries, we construct the standard model of elementary particles.