scholarly journals An exact solution of the Dirac equation for a time-dependent Hamiltonian in 1-1 dimension space-time

2010 ◽  
Vol 88 (2) ◽  
pp. 137-138 ◽  
Author(s):  
Dan Solomon
Keyword(s):  
Exact Solution ◽  
Dirac Equation ◽  
Space Time ◽  
Time Dependent ◽  
Dependent Potential ◽  
Dimension Space

We find an exact solution to the Dirac equation in 1–1 dimension space-time in the presence of a time-dependent potential that consists of a combination of electric, scalar, and pseudoscalar terms.

De la combinatoire du modèle de l'échiquier de Feynman et des fonctions spéciales

1984 ◽  
Vol 62 (7) ◽  
pp. 632-638
Author(s):  
J. G. Williams
Keyword(s):  
Exact Solution ◽  
Dirac Equation ◽  
Hypergeometric Series ◽  
Jacobi Polynomials ◽  
Dimensional Space ◽  
Space Time ◽  
Continuous Limit ◽  
Two Dimensional ◽  
Dimensional Space Time

The exact solution of the Feynman checkerboard model is given both in terms of the hypergeometric series and in terms of Jacobi polynomials. It is shown how this leads, in the continuous limit, to the Dirac equation in two-dimensional space-time.

Exact solution Dirac equation for an energy-dependent potential

2012 ◽  
Vol 127 (10) ◽  
Author(s):  
H. Hassanabadi ◽  
E. Maghsoodi ◽  
R. Oudi ◽  
S. Zarrinkamar ◽  
H. Rahimov
Keyword(s):  
Exact Solution ◽  
Dirac Equation ◽  
Dependent Potential ◽  
Energy Dependent

scholarly journals Some differences between Dirac's hole theory and quantum field theory

2005 ◽  
Vol 83 (3) ◽  
pp. 257-271 ◽  
Author(s):  
Dan Solomon
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Exact Solution ◽  
Dirac Equation ◽  
Vacuum Energy ◽  
Time Dependent ◽  
Quantum Field ◽  
Hole Theory

Dirac's hole theory (HT) and quantum field theory (QFT) are generally considered equivalent. However, it was recently shown by several investigators that this is not necessarily the case because when the change in the vacuum energy was calculated for a time-independent perturbation, HT and QFT yielded different results. In this paper, we extend this discussion to include a time-dependent perturbation for which the exact solution to the Dirac equation is known. We show that for this case also, HT and QFT yield different results. In addition, we offer some discussion of the problem of anomalies in QFT. PACS Nos.: 03.65–w, 11.10–z

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