Light Cone 2015

Light Front Fermion Field Quantization with Explicit Lorentz Symmetry

21 Sept 2015, 18:10

Hall Aula Bruno Touschek (Laboratori Nazionali di Frascati)

Poster Session POSTER SESSION

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 ${\mathrm{\Delta }}_{+}(x)$. 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.