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A four-fermion interaction which includes right singlets of both up and down fermions is included in the initial locally SU(2)⊗S(1)-invariant model. In the suitable approximation, the propagators are constructed and the mass spectrum is found of fermi and gauge vector fields as well as of the collective scalar fields due to the dynamical symmetry breakdown.

We consider a P-odd variant of a spin-3/2 particle theory in the matrix formulation. We determine a matrix algebra of a first-order equation. We find solutions of the free equation for a massive particle in the form of projection matrices-dyads. We obtain exact solutions of the equation in the case of an external plane wave field with linear polarization and in the case of an axially symmetric magnetic field.

We study dynamical symmetry breaking and mass generation in a U(5) four-fermion model with two coupling constants. We show that the consistency conditions result in a connection between the dynamical masses of the fermion quintuplet. The masses of fermions and of collective states are expressed through two independent quantities only. We find the propagator of the collective fields, from which it follows that there are goldstone fields as well as fields of massive particles. The mass formulas are obtained on the basis of dimensional regularization of divergent integrals.

Instanton-induced four-quark interactions of u and d-quarks is studied. It is shown that there is a possibility of scalar and pseudoscalar condensates formation, leading to a spontaneous breakdown of the CP-parity. Using self-consistency conditions, relationships are found between current masses of the quarks and their dynamical masses and parameters reflecting the degree of CP-violation. The mass matrix of scalar and pseudoscalar mesons, which are bound states of quarks, is computed.

The model of a scalar structured particle is considered, which possesses polarizability in an external electromagnetic field. The expression for the 4-dimensional current density is found. The exact solution of the equations describing a scalar particle with polarizability in a uniform external magnetic field is obtained. Up to the terms of order O(H2), the energy spectrum can be formally obtained by the substitution of the particle mass in the expression for a pointlike scalar particle: m?m-?H2/2, where? is the magnetic polarizability of the particle. It is shown that the rms radius of a trajectory can be obtained by the substitution of the charge in the well-known formula for a structureless scalar particle: e?e(1{-aH2/m)1/2 (wherea is the electric polarizability).

It is shown that dynamic symmetry breaking in the locally SU(2) ? U(1)-invariant model with mixed inclusion of fermions in a four-fermion interaction leads to a situation in which one collective scalar field, representing the sum of all generations of fermion-antifermion pairs, acts as the total (one-loop) effective Lagrangian. Mass formulas are found for the scalar field and gauge vector fields. The effective Lagrangian obtained coincides in form with the standard Lagrangian in the Glashow-Weinberg-Salam theory of electroweak interactions.

Expressions for the total cross sections of elementary interaction processes between the primary fermion scalar fields and the scalar fields generated by dynamical symmetry breaking are derived within the framework of the globalSU (2)L⊗U (1)-invariant four-fermion model by means of lowest-approximation loop expansions of the propagators for the indicated fields.

Using the Dyson-Schwinger equation, the four-fermion Green functions in one-loop approximation to the SU(2)L ? U(1) four-fermion model are found, as well as corrections to them. An expression is obtained for the collective field propagator in the one-loop approximation, and its regularization is performed. In the model under consideration, collective excitations are identified with a massless Goldstone field and a massive scalar field. It is shown that as a result of the reconstruction of the vacuum, one fermion (the analog of the neutrino) is massless, while the other (the analog of the electron), massive.

Exact solutions are obtained for the wave equations for a scalar particle that possesses polarizability in the field of a plane electromagnetic wave of arbitrary polarization and in a constant electric field.

It is shown that a system of quaternion equations equivalent to the Dirac-Kähler equation is invariant with respect to transformations of field functions inducible by translations in quaternion coordinate space.

A CP-odd, chirally noninvariant four-fermion model with three coupling constants is studied by an effective-potential method. The mass spectrum of the fermion and of the collective scalar and pseudoscalar fields is found. In the particular case of a chirally invariant model, the pseudoscalar field becomes a massless Goldstone field. The complete effective action, which has the form of a s-model, is calculated in the single-loop approximation. The Gell-Mann-Levy method is used to find the axial current. Partial conservation of axial current is demonstrated. It is thus shown that the original model reproduces the basic features of non-perturbative quantum chromodynamics: a breaking of chiral symmetry and of CP parity.

A study is made of a six-parameter internal-symmetry group of the classical theory of a vector field of general type (and its nonlinear generalizations). This group, which is not related to a change of the space-time coordinates, is interpreted physically.

For the particular case of multispin particles (here, with a maximum spin of 1), it is shown that in field theory it is possible to analyze transformation groups with tensor and spinor parameters without including coordinate transformations at the same time.

A system of tensorial equations is suggested as a bipotential generalization of the Stückelberg equations written for spin-tensors. These equations describe particles having two spin states: 1/2 and 3/2 (particles with the multispin 1/2, 3/2). The Lagrangian of the theory is invariant under the transformations of the field variables forming a group U(1) ?SO (4, 2) ?SO (4, 2). Localization of the transformation parameters of this group of internal symmetry leads to introduction of a non-Abelian gauge field carrying the maximal spin 2. A possible physical interpretation of a multispin particle theory is discussed.

The process π → μ + ν in the field of a plane electromagnetic wave is investigated with allowance for the complex structure of the pion. Exact values are obtained for the probability of pion decay in circularly and elliptically polarized fields. Pion structure effects become observable for χ ∼ 5, where .