## Book Volume 1

#### Maxwell and Dirac Equations

Page: 3-19 (17)

Author: Takehisa Fujita and Naohiro Kanda

PDF Price: $15

##### Abstract

This chapter discusses the basic equations in quantum field theory. First, we clarify some important properties of Maxwell equation so that the main part of the electromagnetisms can be easily understood. Then, we present some useful properties of the Dirac equation and its free wave solution. These two equations are the basic ingredients in understanding quantum field theory. We also give the exact energy spectrum of Dirac equation with Coulomb plus gravity potential in hydrogenlike atom

##### Abstract

In this chapter, we discuss the S-matrix theory in quantum field theory. Here, we first treat the non-relativistic scattering theory and its relation to the Tmatrix. In particular, we discuss the scattering problem in terms of the Lippmann- Schwinger equation. Then we discuss the S-matrix theory in quantum field theory. This is based on the perturbation theory and we present the example of the S-matrix evaluation. In particular, we discuss some basic problems in the Feynman propagator of photon and show a possible physical difference between Feynman and correct propagators of photon.

##### Abstract

Here, we present the calculations of the self-energy of photon and electron. First the renormalization scheme of photon is discussed in connection with the triangle diagrams which have no divergence at all, and therefore the self-energy of photon is not related to any physical observables. Then, we discuss the renormalization scheme of fermion self-energy term which is still connected with the vertex correction in QED. Also, we discuss briefly the physics of Lamb shifts which should be treated in detail in chapter 7. Then, we present the calculation of the photonphoton scattering cross section and some possible experiments on the photon-photon cross section. Finally, the problem of the chiral anomaly equation is discussed, and we see that there are neither anomaly equation nor the violation of the axial current conservation in physical world.

#### Quantum Chromodynamics and Related Topics

Page: 72-85 (14)

Author: Takehisa Fujita and Naohiro Kanda

PDF Price: $15

##### Abstract

Quantum chromodynamics is the theoretical frame work in which one can treat the physics of the strong interactions. This is the non-abelian gauge field theory, and it cannot be solved in the perturbation theory since the free Lagrangian densities of quarks and gluons are not gauge invariant. In the perturbation theory, we describe all the physical observables in terms of the properties of quarks and gluons, and if they are not related to physical observables, then there is no point of employing the perturbation theory. Here, we also discuss the nucleon-nucleon interactions based on the meson exchange processes and present the calculation of the two pion exchange potential. Further, we discuss some physical observables in connection with quarks, that is, the magnetic moments of nucleons in terms of quark model and the total cross section ratio between σe+e-→ hadrons and σe+e-→μ+μ-. These physical quantities are related to the quark degrees of freedom.

##### Abstract

In this chapter, we first present a brief review of the weak interaction theory. In particular, we discuss why the conserved vector current model had to be modified to a new theory. After that, we clarify the physics of the spontaneous symmetry breaking and then discuss the intrinsic problem of the Higgs mechanism in the Weinberg-Salam model. In addition, we present the calculation of the vertex correction due to the weak vector bosons and show that there is no logarithmic divergence in this vertex corrections. Therefore, there is no need of the renormalization procedure in the weak interaction models with massive vector bosons.

##### Abstract

In this chapter, we present the new model of the quantum field theory
of gravitation which is, by now, properly included into the Lagrangian density of
quantum electrodynamics. In this model of QED plus gravity, Dirac fields couple to
the electromagnetic field A^{μ} as well as the gravitational field G. The gravity appears
in the mass term as m(1 + gG)ψψ with the coupling constant of g, thus keeping the
local gauge invariance of the total Lagrangian of QED plus gravity. Here, after a
brief review of the new gravity model, we present the discussion of applying the new
gravity model to the time shifts of various kinds of planet motions.

##### Abstract

In this chapter, we discuss some of the problems which are not yet
fully understood in the calculations of quantum field theory. First, we discuss the
neutron EDM in terms of the vertex corrections from the W^{±} bosons. Then, we
present the calculation of the weak charge which may arise from the parity violating
interaction. Also, we discuss the Lamb shifts in muonic hydrogen as well as in
muonium, and present the calculation of the center of mass corrections in these exotic
atoms. It is shown that the effect of the center of mass corrections destroys the
close agreement between theory and experiment in muonic hydrogen. In addition,
the effect in muonium is so large that it destroys the excellent agreement between
Bethe’s calculation and experiment of the Lamb shifts, and this may well affect on
the understanding of the fundamental mechanism of the Lamb shifts.

## Introduction

Quantum physics is based on four fundamental interactions of electromagnetic, weak, gravitational and strong forces. All the interactions are expressed in terms of fermion and boson fields which can describe the quantum states of electrons, nucleons and photons in atoms or nuclei. Correct behaviors of these particles can now be described by the basic field theory terminology, and this textbook explains, for the first time, quantum field theory in a unifying method. At present, modern quantum theory is at a critical junction between different theories, and this textbook presents a clear description of fundamental quantum fields with a sound theoretical framework. No exotic theoretical concepts such as general relativity nor spontaneous symmetry breaking nor quantum anomaly are adopted in this textbook, and indeed all the observed physical quantities can be well understood within the standard field theory framework without introducing any non-physical particles or fields. From this textbook, readers will be guided through a concrete future direction of quantum field theory and will learn how the motion of electrons in any kind of material can be understood in terms of fields or state vectors. Readers will also learn about application of basic field theory in quantum chemistry, quantum biology and so on. Fundamental Problems in Quantum Field Theory is a handy resource for undergraduate and graduate students as well as supervisors involved in advanced courses in quantum physics.