Speaker
Dr
Jan Żochowski
(University of Białystok)
Description
A novel quantization procedure with the explicit Lorentz symmetry is applied for a fermion field in $D=3+1$ dimensions. The Wightman function for a free fermion field is evaluated in terms of the covariant singular function $\Delta_{+}(x)$. The singularities at the LF hypersurface $x^{+}=0$ appear whenever the "bad" component $\psi_{-}$ is considered. Accordingly the anti-commutator function cannot follow from the canonical Dirac method for constrained systems. The chronological ordering in $x^{+}$ temporal variable leads to the Feynman propagator with a well-known addition of non-covariant term. The Yukawa model in $D=3+1$ dimensions is considered for the Gaussian effective potential with the
point-splitting regularization with a space-like separation.
Primary author
Dr
Jan Żochowski
(University of Białystok)
Co-author
Prof.
Jerzy A. Przeszowski
(University of Białystok)
