Mathematical Principles of Theoretical Physics

(Rick Simeone) #1

Chapter 6


Quantum Physics


6.1 Introduction


Quantum physics is the study of the behavior of matter and energy at molecular, atomic,
nuclear, and sub-atomic levels.
Quantum physics was initiated and developed in the first halfof the 20th century, fol-
lowing the pioneering work of (Planck, 1901 ) on blackbody radiation, of (Einstein, 1905 )
on photons and energy quanta, of Niels Bohr on structure of atoms, of (de Broglie, 1924 )
on matter-wave duality. Quantum physics and general relativity have become the two cor-
nerstones of modern physics. We refer interested readers to(Sokolov, Loskutov and Ternov,
1966 ;Greiner, 2000 ;Sakurai, 1994 ), among many others, for the basics and history of quan-
tum physics.
Our recent work on the field theory of the four fundamental interactions and on the weak-
ton model of elementary particles has lead to new insights toa few issues and challenges
in quantum physics, including in particular 1) the basic laws forinteractingmulti-particle
quantum systems, 2) energy levels of sub-atomic particles,and 3) solar neutrino problem.


6.5 Field Theory of Multi-Particle Systems


Based PID and PRI, we know now that the fundamental interactions are due the cor-
responding charges of the particles involved, with the masscharge for gravitational effect,
the electric charge for electromagnetism, the strong and the weak charges for the strong and
weak interactions respectively. The geometric interaction mechanism implies that the dy-
namic matter distribution of the charged particles changesthe geometry of the space-time
manifold as well as the corresponding vector-bundles, leading to the dynamic interaction
laws of the system.
Also, due to PRI, for a multi-particle system consisting of subsystems of different levels,
the coupling can only be achieved through PRI and the principle of symmetry-breaking.
The above new insights from the unified field theory in Chapter 4 give rise to the following
Postulates for interacting multi-particle systems


1) the Lagrangian action for an N-particle system satisfy the SU(N)gauge
invariance;

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