Abstract
In this chapter, many-fermion spaces are discussed with emphasis on the role of independent particle motion. A determinantal measure is presented in the chapter and its mathematical properties are analyzed. The relation to Hartree-Fock theory is discussed in this chapter Possible extensions are described and their significance pointed out. It has been observed that it takes a drastically lower number of states to approximate the ground state of a Hamiltonian, with sufficiently small two-body to one-body ratio, as compared to the large number of determinantal states required to describe an “average”, randomly selected state of S(N, k) . The many-body theory transcends the boundaries of any specific field of theoretical physics. Its concepts, methods and nomenclature appear in atomic physics, nuclear physics, and solid state physics among others. The theories that utilize the concept of independent motion of many identical fermions in a fundamental way are of prime significance in physics. Their initial development in the quantum-mechanical era dates back to the earliest days of atomic spectroscopy.
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