arXiv subjects
Publications and source records attributed to A. E. Kaloshin.
We construct a spectral representation of neutrino propagator in matter moving with constant velocity, or in constant homogenious magnetic field. In both cases there exists definite 4-axis $z$ of complete polarization, such that corresponding spin projectos commute with propagator. As a result, all eigenvalues of propagator and dispersion laws are classified accoding to spin projection on this axis.
We discuss diagonalization of propagator for mixing fermions system based on the eigenvalue problem. The similarity transformation converting matrix propagator into diagonal form is obtained. The suggested diagonalization has simple algebraic properties for on-shell fermions and can be used in renormalization of fermion mixing matrix.
We construct a spectral representation of neutrino propagator in moving matter or in external magnetic field. In both cases there exists fixed four-dimensional axis of polarization, such that the corresponding spin projectors commute with propagator. As a result, all eigenvalues of propagator and, consequently, dispersion laws for neutrino in media are classified according to spin projection onto this axis. Use of the found spin projectors simplifies essentially the eigenvalue problem and allows to build spectral representation of propagator in moving matter or external magnetic field in analogy with the vacuum propagator.
A spectral representation for the neutrino propagator in a moving matter with constant density is constructed. It is found that in a matter there exists a 4-dimensional axis of complete polarization, all poles of the propagator are classified according to the values of the spin projection onto this axis.
We show that calculation of a final fermion polarization (for a pure initial state) is equivalent to the problem of looking for complete polarization axis of bispinor. This gives the method for calculation of polarization applicable both for final and intermediate state fermions. We suggest to use fermion propagator (bare or dressed) in form of spectral representation, which gives the orthogonal off-shell energy projectors. This representation leads to covariant separation of particle and antiparticle contributions and gives a natural definition for polarization of intermediate state fermion. The most evident application is related with consistent description of $t$-quark polarization.
We develop the spectral representation of propagator for $n$ mixing fermion fields in the case of $\mathsf{P}$-parity violation. The approach based on the eigenvalue problem for inverse matrix propagator makes possible to build the system of orthogonal projectors and to represent the matrix propagator as a sum of poles with positive and negative energies. The procedure of multiplicative renormalization in terms of spectral representation is investigated and the renormalization matrices are obtained in a closed form without the use of perturbation theory. Since in theory with $\mathsf{P}$-parity violation the standard spin projectors do not commute with the dressed propagator, they should be modified. The developed approach allows us to build the modified (dressed) spin projectors for a single fermion and for a system of fermions.
We develop a variant of $K$-matrix, which includes the effect of opposite parity fermions (OPF) mixing, and apply it for description of $πN$ partial waves $S_{11}$ and $P_{11}$. OPF-mixing leads to appearance of negative energy poles in $K$-matrix and restoration of MacDowell symmetry, relating two partial waves. Joint analysis of PWA results for $S_{11}$ and $P_{11}$ confirms significance of this effect.
We suggest the description of the dressed fermion propagator with parity non-conservation in the form with separated positive and negative energy poles. We found general form of the $γ$-matrix off-shell projectors and corresponding resonance factors. The parity violation leads to deviation of resonance factors from the naive Breit--Wigner form and to appearance of non-trivial spin corrections. However, for top quark with SM vertex the resonance factor returns to the standard one due to $Γ/m\ll1$.
We suggest simple method to solve wave equation for Rarita--Schwinger field without additional constraints. This method based on use of off-shell projection operators allows to diagonalize spin-1/2 sector of the field.
We consider a loop mixing of two fermion fields of opposite parities whereas the parity is conserved in a Lagrangian. Such kind of mixing is specific for fermions and has no analogy in boson case. Possible applications of this effect may be related with physics of baryon resonances. The obtained matrix propagator defines a pair of unitary partial amplitudes which describe the production of resonances of spin $J$ and different parity ${1/2}^{\pm}$ or ${3/2}^{\pm}$. The use of our amplitudes for joint description of $πN$ partial waves $P_{13}$ and $D_{13}$ shows that the discussed effect is clearly seen in these partial waves as the specific form of interference between resonance and background. Another interesting application of this effect may be a pair of partial waves $S_{11}$ and $P_{11}$ where the picture is more complicated due to presence of several resonance states.
We discuss renormalization of propagator of interacting Rarita--Schwinger field. Spin-3/2 contribution after renormalization takes usual resonance form. For non-leading spin-1/2 terms we found procedure, which guarantees absence of poles in energy plane. The obtained renormalized propagator has one free parameter and is a straight generalization of the famous free propagator of Moldauer and Case. Application of this propagator for production of $Δ^{++}(1232)$ in $π^{+}\particle{p}\to π^{+}\particle{p}$ leads to good description of total cross-section and to reasonable agreement with results of partial wave analysis.
We derive accurately the fermion resonance propagator by means of Dyson summation of the self-energy contribution. It turns out that the relativistic fermion resonance differs essentially from its boson analog.
We obtain in analytical form the dressed propagator of the massive Rarita-Schwinger field and discuss its properties. The calculation of the self-energy contributions demonstrates that besides $s=3/2$ component the Rarita-Schwinger field contains also two $s=1/2$ components of opposite parity.
We derive the most general lagrangian of the free massive Rarita--Schwinger field, which generalizes the previously known ones. The special role of the reparameterization transformation is discussed.
We obtain in analytical form the dressed propagator of the massive Rarita-Schwinger field taking into account all spin components. We found that the nearest analogy for dressing the Rarita--Schwinger field in spin--1/2 sector is dressing the two Dirac fermions of opposite parity with presence of mutual transitions. The calculation of the self-energy contributions confirms that besides the leading spin--3/2 component the Rarita--Schwinger field contains also two spin--1/2 components of different parity.
We suggest a simple analytical description of the S-wave isoscalar $ππ$ amplitude, which corresponds to a joint dressing of the bare resonance and background contributions. The amplitude describes well the experimental data on the $δ^0_0$ phase shift in the energy region below 900 MeV and has two poles in the $Re s > 0$ half-plane. Besides the well-known pole of $σ(600)$-meson with $Re s \sim m_π^2$, there exists a more distant pole with $Re s \sim 0.6 GeV^2$. Our analysis indicates for the dynamical origin of the $σ(600)$ pole, while the second pole should be associated with lowest $q\bar{q}$ state.
We obtain in analytical form the dressed propagator of the Rarita-Schwinger field taking into account all spin components and discuss shortly its properties.
We study the effect of unitary mixing of scalar and vector fields in general $ξ$ gauge. This effect takes place for non-conserved vector currents and $ξ$ gauge generates some additional problems with unphysical scalar field. We obtained solutions of Dyson-Schwinger equations and perfomed the renormalization of full propagators. The key feature of renormalization is the usage of Ward identity, which relates some different Green functions. We found that using Ward identity leads to disappearing of $ξ$-dependence in renormalized matrix element.