558 research outputs found
Quantization of bosonic fields with two mass and spin states
We investigate bosonic fields possessing two mass and spin states. The
density matrix in the first order formalism is obtained. The quantization of
fields in the first order formulation is performed and propagators are found.Comment: 9 page
Field theory of massive and massless vector particles in the Duffin - Kemmer - Petiau formalism
Field theory of massive and massless vector particles is considered in the
first-order formalism. The Hamiltonian form of equations is obtained after the
exclusion of non-dynamical components. We obtain the canonical and symmetrical
Belinfante energy-momentum tensors and their nonzero traces. We note that the
dilatation symmetry is broken in the massive case but in the massless case the
modified dilatation current is conserved. The canonical quantization is
performed and the propagator of the massive fields is found in the Duffin -
Kemmer - Petiau formalism.Comment: 20 pages, typos corrected, a reference added, journal version,
accepted in Int.J.Mod.Phys.
"Square Root" of the Proca Equation: Spin-3/2 Field Equation
New equations describing particles with spin 3/2 are derived. The non-local
equation with the unique mass can be considered as "square root" of the Proca
equation in the same sense as the Dirac equation is related to the
Klein-Gordon-Fock equation. The local equation describes spin 3/2 particles
with three mass states. The equations considered involve fields with spin-3/2
and spin-1/2, i.e. multi-spin 1/2, 3/2. The projection operators extracting
states with definite energy, spin, and spin projections are obtained. All
independent solutions of the local equation are expressed through projection
matrices. The first order relativistic wave equation in the 20-dimensional
matrix form, the relativistically invariant bilinear form and the corresponding
Lagrangian are given. Two parameters characterizing non-minimal electromagnetic
interactions of fermions are introduced, and the quantum-mechanical Hamiltonian
is found. It is proved that there is only causal propagation of waves in the
approach considered.Comment: 17 pages, corrections in Eqs. (50), (51
Solutions of Podolsky's Electrodynamics Equation in the First-Order Formalism
The Podolsky generalized electrodynamics with higher derivatives is
formulated in the first-order formalism. The first-order relativistic wave
equation in the 20-dimensional matrix form is derived. We prove that the
matrices of the equation obey the Petiau-Duffin-Kemmer algebra. The
Hermitianizing matrix and Lagrangian in the first-order formalism are given.
The projection operators extracting solutions of field equations for states
with definite energy-momentum and spin projections are obtained, and we find
the density matrix for the massive state. The -matrix Schrodinger
form of the equation is derived, and the Hamiltonian is obtained. Projection
operators extracting the physical eigenvalues of the Hamiltonian are found.Comment: 17 pages, minor corrections, published versio
On superluminal fermions within the second derivative equation
We postulate the second-order derivative equation with four parameters for
spin-1/2 fermions possessing two mass states. For some choice of parameters
fermions propagate with the superluminal speed. Thus, the novel tachyonic
equation is suggested. The relativistic 20-component first-order wave equation
is formulated and projection operators extracting states with definite energy
and spin projections are obtained. The Lagrangian formulation of the
first-order equation is presented and the electric current and energy-momentum
tensor are found. The minimal and non-minimal electromagnetic interactions of
fermions are considered and Schr\"{o}dinger's form of the equation and the
quantum-mechanical Hamiltonian are obtained. The canonical quantization of the
field in the first-order formalism is performed and we find the vacuum
expectation of chronological pairing of operators.Comment: 21 pages, minor corrections, journal version, accepted in IJMP
Kalb-Ramond fields in the Petiau-Duffin-Kemmer formalism and scale invariance
Kalb-Ramond equations for massive and massless particles are considered in
the framework of the Petiau-Duffin-Kemmer formalism. We obtain
matrices of the relativistic wave equation of the first-order and solutions in
the form of density matrix. The canonical and Belinfante energy-momentum
tensors are found. We investigate the scale invariance and obtain the conserved
dilatation current. It was demonstrated that the conformal symmetry is broken
even for massless fields.Comment: 9 pages, no figure
Effective Lagrangian and Dynamical Symmetry Breaking in the SU(2)XU(1) NJL Model
Dynamical symmetry breaking and the formation of scalar condensates in the
SU(2)XU(1) Nambu-Jona-Lasinio model with two coupling constants has been
studied in the framework of the mean field approximation. The bosonization
procedures of the model are performed using the functional integration method.
The possibility of the spontaneous CP symmetry breaking in the model under
consideration has been shown. The mass spectrum of the bound states of
fermions, as well as the effective Lagrangian of interacting scalar and
pseudoscalar mesons are obtained.Comment: 7 pages, LaTeX. Minor correction
The multiplicity and the spectra of secondaries correlated with the leading particle energy
The spectra of leading particles of different nature in pp-collisions at E sub 0 = 33 GeV are obtained. The multiplicities and the spectra of secondaries, mesons, gamma-quanta, lambda and lambda-hyperons and protons for different leading particle energy ranges are determined
Phase diagram of Nambu-Jona-Lasinio model with dimensional regularization
We investigate the phase diagram on temperature-chemical potential plane in
the Nambu-Jona-Lasinio model with the dimensional regularization. While the
structure of the resulting diagram shows resemblance to the one in the
frequently used cutoff regularization, some results of our study indicate
striking difference between these regularizations. The diagram in the
dimensional regularization exhibits strong tendency of the first order phase
transition.Comment: 9 pages, 9 figure
Charge Radii and Magnetic Polarizabilities of the Rho and K* Mesons in QCD String Theory
The effective action for light mesons in the external uniform static
electromagnetic fields was obtained on the basis of QCD string theory. We imply
that in the presence of light quarks the area law of the Wilson loop integral
is valid. The approximation of the Nambu-Goto straight-line string is used to
simplify the problem. The Coulomb-like short-range contribution which goes from
one-gluon exchange is also neglected. We do not take into account spin-orbital
and spin-spin interactions of quarks and observe the and mesons.
The wave function of the meson ground state is the Airy function. Using the
virial theorem we estimate the mean charge radii of mesons in terms of the
string tension and the Airy function zero. On the basis of the perturbative
theory, in the small external magnetic field we find the diamagnetic
polarizabilities of and mesons: , Comment: 22 pages, no figures, in LaTeX 2.09, typos correcte
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