Construction of the light-front QCD Hamiltonian with zero modes modeling the vacuum

We present an attempt to construct a QCD Hamiltonian on the light front (LF), including a semiphenomenological description of vacuum effects. In this approach, we obtain the LF theory via a limit transition from the theory formulated on spacelike planes near the LF. For the zero Fourier modes of fie...

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Bibliographic Details
Published in:Theoretical and mathematical physics 2011-11, Vol.169 (2), p.1600-1610
Main Authors: Malyshev, M. Yu, Prokhvatilov, E. V.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Summary:We present an attempt to construct a QCD Hamiltonian on the light front (LF), including a semiphenomenological description of vacuum effects. In this approach, we obtain the LF theory via a limit transition from the theory formulated on spacelike planes near the LF. For the zero Fourier modes of fields in the coordinate along the light cone to remain independent dynamical variables on the LF, we realize the limit transition differently for zero and nonzero modes. The zero modes then model the vacuum on the LF and allow introducing a semiphenomenological description of vacuum effects. For a gauge-invariant regularization, we introduce a lattice in the space of “transverse” coordinates and a gauge-invariant cutoff of the momentum component along the light cone. We introduce a new description of field variables on the lattice, using unitary matrices related to the lattice links for the gluon zero modes and Hermitian matrices related to the corresponding lattice sites for the nonzero modes.
ISSN:0040-5779
1573-9333
DOI:10.1007/s11232-011-0137-4