Invariant nuclear space of a second quantization operator

M. Bauer, Cesar Augusto Aguillon

Based on Lorentz invariance and Born reciprocity invariance, the canonical quantization of Special Relativity (SR) has been shown to provide a unified origin for the existence of Dirac's Hamiltonian and a self adjoint time operator that circumvents Pauli's objection. As such, this approach restores to Quantum Mechanics (QM) the treatment of space and time on an equivalent footing as that of momentum and energy. Second quantization of the time operator field follows step by step that of the Dirac Hamiltonian field. It introduces the concept of time quanta, in a similar way to the energy quanta in Quantum Field Theory (QFT). An early connection is found allready in Feshbach's unified theory of nuclear reactions. Its possible relevance in current developments such as Feshbach resonances in the fields of cold atom systems, of Bose-Einstein condensates and in the problem of time in Quantum Gravity is noted. .

J. M. Cook

Theodore Garavaglia, Steven Kenneth Kauffmann

The principle of invariance of the c-number symmetric bracket is used to derive both the quantum operator commutator relation $[\hat q, \hat p]=i\hbar$ and the time-dependent Schrödinger equation. A c-number dynamical equation is found which leads to the second quantized field theory of bosons and fermions.

Donald H. Kobe

The representation of an arbitrary operator in second quantization is obtained for both fermion and boson systems by using the isomorphism between second quantization and a graded configuration space.