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Possible generalizations of quantum theory permitting to describe in a unique way the development of the quantum system and the measurement process are discussed. The approach to the problem based on the Lindblad's equation for the statistical operator is reviewed. The Tomonaga-Schwinger like equation of this type is introduced to establish Lorentz invariance. The application of tachyonic field to overcome divergences arising in this equation is analyzed. Other approaches to the problem are shortly discussed., The paper was written based on the materials of the lecture on the 15th International V.A. Fock School for Advances of Physics 2005, 21-27 November 2005, St. Petersburg. Published in the Proceedings of the School, ed. by V. Novozhilov, Publishing house of Saint Petersburg State University, St. Petersburg, 2006

A possibility of semiphenomenological description of vacuum effects in QCD quantized on the Light Front (LF) is discussed. A modification of the canonical LF Hamiltonian for QCD is proposed, basing on the detailed study of the exact description of vacuum condensate in QED(1+1) that uses correct form of LF Hamiltonian., Comment: LaTeX 2e, 9 pages, 2 figures. Proceedings of "Quarks-2006", St-Petersburg 2006

Canonical formulation of quantum field theory on the Light Front (LF) is reviewed. The problem of constructing the LF Hamiltonian which gives the theory equivalent to original Lorentz and gauge invariant one is considered. We describe possible ways of solving this problem: (a) the limiting transition from the equal-time Hamiltonian in a fast moving Lorentz frame to LF Hamiltonian, (b) the direct comparison of LF perturbation theory in coupling constant and usual Lorentz-covariant Feynman perturbation theory. The results of the application of method (b) to QED-1+1 and QCD-3+1 are given. Gauge invariant regularization of LF Hamiltonian via introducing a lattice in transverse coordinates and imposing periodic boundary conditions in LF coordinate x^- for gauge fields on the interval |x^-| smaller than L is also considered., Comment: LaTeX 2.09, 48 pages. The paper is written for editorial collection "Progress in Field Theory Research", Nova Science Publishers, New York. New improved expression for the effective LF Hamiltonian of QED(1+1) was added

A light-front Hamiltonian reproducing the results of two-dimensional quantum electrodynamics in the Lorentz coordinates is constructed using the bosonization procedure and an analysis of the bosonic perturbation theory in all orders in the fermion mass. The resulting Hamiltonian involves a supplementary counterterm in addition to the usual terms appearing in the naive light-front quantization. This term is proportional to a linear combination of zeroth fermion modes (which are multiplied by a factor compensating the charge and fermion number). The coefficient of the counterterm has no ultraviolet divergence, depends on the value of the fermion condensate in the \theta-vacuum, and is linear in this value for a small fermion mass., Comment: LaTeX 2.09, 17 pages, Proceedings of "11th V.Fock School of Physics", St-Petersburg 2001

We consider the perturbation theory in the fermion mass (chiral perturbation theory) for the two-dimensional quantum electrodynamics. With this aim, we rewrite the theory in the equivalent bosonic form in which the interaction is exponential and the fermion mass becomes the coupling constant. We reformulate the bosonic perturbation theory in the superpropagator language and analyze its ultraviolet behavior. We show that the boson Green's functions without vacuum loops remain finite in all orders of the perturbation theory in the fermion mass., Comment: LaTeX 2.09, 9 pages

The counterterms, which must be included into Light-Front Hamiltonian of $QED_2$ to get the equivalence with conventional Lorentz-covariant formulation, are found. This is done to all orders of perturbation theory in fermion mass, using the bosonization at intermediate steps and comparing Light-Front and Lorentz-covariant perturbation theories for bosonized model. The obtained Light-Front Hamiltonian contains all terms, present in the $QED_2$ theory, canonically (naively) quantized on the Light-Front (in the Light-Front gauge) and an unusual counterterm. This counterterm is proportional to linear combination of fermion zero modes (which are multiplied by some operator factors neutralizing their charge and fermionic number). The coefficients before these zero mode operators are UV finite and depend on condensate parameter in the $\theta$-vacuum. These coefficients are proportional to fermion mass, when this mass goes to zero., Comment: LaTex 2.09, 49 pages

Light-Front (LF) Hamiltonian for QED in (1+1)-dimensions is constructed using the boson form of this model with additional Pauli-Villars type ultraviolet regularization. Perturbation theory, generated by this LF Hamiltonian, is proved to be equivalent to usual covariant chiral perturbation theory. The obtained LF Hamiltonian depends explicitly on chiral condensate parameters which enter in a form of some coupling constants., LaTex, 15 pages, 3 figures

Canonical formulation of quantum field theory on the Light Front (LF) is reviewed. The problem of constructing the LF Hamiltonian which gives the theory equivalent to original Lorentz and gauge invariant one is considered. We describe possible ways of solving this problem: (a) the limiting transition from the equal-time Hamiltonian in a fastly moving Lorentz frame to LF Hamiltonian, (b) the direct comparison of LF perturbation theory in coupling constant and usual Lorentz-covariant Feynman perturbation theory. Gauge invariant regularization of LF Hamiltonian via introducing a lattice in transverse coordinates and imposing periodic boundary conditions in LF coordinate $x^-$ for gauge fields on the interval $|x^-|< L$ is considered. We find that LF canonical formalism for this regularization avoid usual most complicated constraints connecting zero and nonzero modes of gauge fields., LaTeX2.09, 45 pages, 7 figures, Published in the book: "Quantum Theory in honour of Vladimir A. Fock", Part 1. Unesco, St. Petersburg University, Euro-Asian Physical Society, 1998

A lattice gauge theory with an action polynomial in independent field variables is considered. The link variables are described by unconstrained complex matrices instead of unitary ones. A mechanism which permits to switch off in the continuous limit the arising extra fields is discussed. The Euclidean version of the theory with an 4-dimensional lattice is described. The canonical form of this theory in Lorentz coordinates with continuous time is given. The canonical formulation in the light-front coordinates is investigated for the lattice in 2-dimensional transverse space and for the 3-dimensional lattice including one of the light-like coordinates. The light-front zero mode problem is considered in the framework of this canonical formulation., Comment: 17 pages, LaTex

Quantum theory of Lorentz invariant local scalar fields without restrictions on 4-momentum spectrum is considered. The mass spectrum may be both discrete and continues and the square of mass as well as the energy may be positive or negative. Such fields can exist as part of a hidden matter in the Universe if they interact with ordinary fields very weakly. Generalization of Kallen-Lehmann representation for propagators of these fields is found. The considered generalized fields may violate CPT- invariance. Restrictions on mass-spectrum of CPT-violating fields are found. Local fields that annihilate vacuum state and violate CPT- invariance are constructed in this scope. Correct local relativistic generalization of Lindblad equation for density matrix is written for such fields. This generalization is particulary needed to describe the evolution of quantum system and measurement process in a unique way. Difficulties arising when the field annihilating the vacuum interacts with ordinary fields are discussed., Comment: Latex 23 pages, sent to "Foundations of Physics"