arXiv subjects
Publications and source records attributed to V. P. Lomov.
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 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 obtain in analytical form the dressed propagator of the Rarita-Schwinger field taking into account all spin components and discuss shortly its properties.