125 research outputs found
Nonperturbative calculation of the anomalous magnetic moment in the Yukawa model within truncated Fock space
Within the covariant formulation of light-front dynamics, we calculate the
state vector of a physical fermion in the Yukawa model. The state vector is
decomposed in Fock sectors and we consider the first three ones: the single
constituent fermion, the constituent fermion coupled to one scalar boson, and
the constituent fermion coupled to two scalar bosons. This last three-body
sector generates nontrivial and nonperturbative contributions to the state
vector, which are calculated numerically. Field-theoretical divergences are
regularized using Pauli-Villars fermion and boson fields. Physical observables
can be unambiguously deduced using a systematic renormalization scheme we have
developed previously. As a first application, we consider the anomalous
magnetic moment of the physical fermion.Comment: 24 pages, 16 figure
Towards a Geometric Approach to the Formulation of the Standard Model
A geometric interpretation of the spontaneous symmetry breaking effect, which
plays a key role in the Standard Model, is developed. The advocated approach is
related to the effective use of the momentum 4-spaces of the constant
curvature, de Sitter and anti de Sitter, in the apparatus of quantum field
theory.Comment: 8 pages, LaTe
Hamiltonian structures of fermionic two-dimensional Toda lattice hierarchies
By exhibiting the corresponding Lax pair representations we propose a wide
class of integrable two-dimensional (2D) fermionic Toda lattice (TL)
hierarchies which includes the 2D N=(2|2) and N=(0|2) supersymmetric TL
hierarchies as particular cases. We develop the generalized graded R-matrix
formalism using the generalized graded bracket on the space of graded operators
with involution generalizing the graded commutator in superalgebras, which
allows one to describe these hierarchies in the framework of the Hamiltonian
formalism and construct their first two Hamiltonian structures. The first
Hamiltonian structure is obtained for both bosonic and fermionic Lax operators
while the second Hamiltonian structure is established for bosonic Lax operators
only.Comment: 12 pages, LaTeX, the talks delivered at the International Workshop on
Classical and Quantum Integrable Systems (Dubna, January 24 - 28, 2005) and
International Conference on Theoretical Physics (Moscow, April 11 - 16, 2005
Towards a Maximal Mass Model
We investigate the possibility to construct a generalization of the Standard
Model, which we call the Maximal Mass Model because it contains a limiting mass
for its fundamental constituents. The parameter is considered as a new
universal physical constant of Nature and therefore is called the fundamental
mass. It is introduced in a purely geometrical way, like the velocity of light
as a maximal velocity in the special relativity. If one chooses the Euclidean
formulation of quantum field theory, the adequate realization of the limiting
mass hypothesis is reduced to the choice of the de Sitter geometry as the
geometry of the 4-momentum space. All fields, defined in de Sitter p-space in
configurational space obey five dimensional Klein-Gordon type equation with
fundamental mass as a mass parameter. The role of dynamical field variables
is played by the Cauchy initial conditions given at , guarantying the
locality and gauge invariance principles. The corresponding to the geometrical
requirements formulation of the theory of scalar, vector and spinor fields is
considered in some detail. On a simple example it is demonstrated that the
spontaneously symmetry breaking mechanism leads to renormalization of the
fundamental mass . A new geometrical concept of the chirality of the fermion
fields is introduced. It would be responsible for new measurable effects at
high energies . Interaction terms of a new type, due to the existence
of the Higgs boson are revealed. The most intriguing prediction of the new
approach is the possible existence of exotic fermions with no analogues in the
SM, which may be candidate for dark matter constituents.Comment: 28 page
The Relativistic Linear Singular Oscillator
Exactly-solvable model of the linear singular oscillator in the relativistic
configurational space is considered. We have found wavefunctions and energy
spectrum for the model under study. It is shown that they have correct
non-relativistic limits.Comment: 14 pages, 12 figures in eps format, IOP style LaTeX file (revised
taking into account referees suggestions
Two-fermion relativistic bound states in Light-Front Dynamics
In the Light-Front Dynamics, the wave function equations and their numerical
solutions, for two fermion bound systems, are presented. Analytical expressions
for the ladder one-boson exchange interaction kernels corresponding to scalar,
pseudoscalar, pseudovector and vector exchanges are given. Different couplings
are analyzed separately and each of them is found to exhibit special features.
The results are compared with the non relativistic solutions.Comment: 40 pages, to be published in Phys. Rev. C, .tar.gz fil
A relativistic model of the -dimensional singular oscillator
Exactly solvable -dimensional model of the quantum isotropic singular
oscillator in the relativistic configurational -space is proposed. It
is shown that through the simple substitutions the finite-difference equation
for the -dimensional singular oscillator can be reduced to the similar
finite-difference equation for the relativistic isotropic three-dimensional
singular oscillator. We have found the radial wavefunctions and energy spectrum
of the problem and constructed a dynamical symmetry algebra.Comment: 8 pages, accepted for publication in J. Phys.
Pion-Nucleon Scattering in Kadyshevsky Formalism: I Meson Exchange Sector
In a series of two papers we present the theoretical results of /meson-baryon scattering in the Kadyshevsky formalism. In this paper the
results are given for meson exchange diagrams. On the formal side we show, by
means of an example, how general couplings, i.e. couplings containing multiple
derivatives and/or higher spin fields, should be treated. We do this by
introducing and applying the Takahashi-Umezawa and the Gross-Jackiw method. For
practical purposes we introduce the method. We also show how the
Takashashi-Umezawa method can be derived using the theory of Bogoliubov and
collaborators and the Gross-Jackiw method is also used to study the
-dependence of the Kadyshevsky integral equation. Last but not least we
present the second quantization procedure of the quasi particle in Kadyshevsky
formalism.Comment: 29 page
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