Document Type : Original Article
Author
K. N. Toosi University of Technology, P.O. Box 15875-4416, Tehran, Iran
Abstract
This paper discusses various subtleties and problems related to the non-relativistic limit of fermionic quantum field theory to the Schrödinger equation. First, we discuss the concept of the single-particle state and its role in the non-relativistic limit of the field. We extend the non-relativistic limit of the Dirac equation of the action so that the non-relativistic limit of the wave functions of spin 1/2 particles and antiparticles appears simultaneously. We also study the non-relativistic limit using the Foldy–Wouthuysen transformation. Using the least substitution with the electromagnetic field in the Dirac action, we obtain the Schrödinger-Pauli equation for both the particle and the antiparticle.
Keywords
Main Subjects
- M Seul and D Andelman, Science 267 (1995) 476.
- T Padmanabhan, ‟Quantum Field Theory: The Why, What and How”, Heidelberg: Springer (2016).
- D Hooper and T Linden, Rev. D 84, 12 (2011) 123005; I Cholis and D Hooper, Phys. Rev. D 88, 2 (2013) 023013.
- J Jayaraman, Phys. A: Math. Gen. 8, 1 (1975) L1.
- A H Guth, M P Hertzberg, and C Prescod-Weinstein, Rev. D 92, 10 (2015) 103513; E Braaten, A Mohapatra, and H Zhang, Phy. Rev. D 94, 7 (2016) 076004.
- J Jayaraman and R de Lima Rodrigues. "On a generalized Dirac oscillator interaction for the nonrelativistic limit 3 D generalized SUSY model oscillator Hamiltonian of Celka and Hussin", (1994).
- R Banerjee and P Mukherjee, Phys. B 938 (2019) 1.
- H Padmanabhan and T Padmanabhan, Rev. D 84, 8 (2011) 085018.
- D Giulini and A Großardt, Classical Quant. Grav. 29, 21 (2012) 215010.
- C Duval, P A Horváthy, and L Palla, Rev. D 52, 8 (1995) 4700.
)