1,884 research outputs found
Light-front gauge propagator
Gauge fields are special in the sense that they are invariant under gauge
transformations and they lead to problems when we try quantizing them
straightforwardly. To circumvent this problem we need to specify a gauge
condition to fix gauge.Comment: 4 pages. Prepared for Meeting on Hadronic Interactions, Sao Paulo-SP,
Brazil, 28-30 may. 200
Antiparticle Contribution in the Cross Ladder Diagram for Bethe-Salpater Equation in the Light-Front
We construct the homogeneous integral equation for the vertex of the bound
state in the light front with the kernel approximated to order g^4. We will
truncate the hierarchical equations from Green functions to construct dynamical
equations for the two boson bound state exchanging interacting intermediate
bosons and including pair creation process contributing to the crossed ladder
diagram.Comment: 12 pages, 2 figure
Singularity-softening prescription for the Bethe-Salpeter equation
The reduction of the two fermion Bethe-Salpeter equation in the framework of
light-front dynamics is studied for one gauge A+=0. The arising effective
interaction can be perturbatively expanded in powers of the coupling constant
g, allowing a defined number of gauge boson exchanges. The singularity of the
kernel of the integral equation at vanishs plus momentum of the gauge is
canceled exactly in on approuch. We studied the problem using a
singularity-softening prescription for the light-front gauge.Comment: 6 pages, Prepared for 25th Brazilian Meeting of Particles Physics and
Fields, Caxambu, Brazil, 24/27 aug. 2004, Caxambu, Minas Gerais, Brazi
The Light Front Gauge Propagator: The Status Quo
At the classical level, the inverse differential operator for the quadratic
term in the gauge field Lagrangian density fixed in the light front through the
multiplier (nA)^2 yields the standard two term propagator with single
unphysical pole of the type (kn)^-1. Upon canonical quantization on the
light-front, there emerges a third term of the form (kn^(mu)n^(nu))(kn)^-2.
This third term in the propagator has traditionally been dropped on the grounds
that is exactly cancelled by the "instantaneous" term in the interaction
Hamiltonian in the light-front. Our aim in this work is not to discuss which of
the propagators is the correct one, but rather to present at the classical
level, the gauge fixing conditions that can lead to the three-term propagator.Comment: 5 pages. Talk given in Light-Cone Workshop: Hadrons and Beyond, LC03,
Grey College, University of Durham, Durham, 5-9 August, 200
Light-front gauge propagator reexamined-II
Gauge fields are special in the sense that they are invariant under gauge
transformations and \emph{``ipso facto''} they lead to problems when we try
quantizing them straightforwardly. To circumvent this problem we need to
specify a gauge condition to fix the gauge so that the fields that are
connected by gauge invariance are not overcounted in the process of
quantization. The usual way we do this in the light-front is through the
introduction of a Lagrange multiplier, , where is the
external light-like vector, i.e., , and is the vector
potential. This leads to the usual light-front propagator with all the ensuing
characteristics such as the prominent pole which has been the
subject of much research. However, it has been for long recognized that this
procedure is incomplete in that there remains a residual gauge freedom still to
be fixed by some ``ad hoc'' prescription, and this is normally worked out to
remedy some unwieldy aspect that emerges along the way. In this work we propose
\emph{two} Lagrange multipliers with distinct coefficients for the light-front
gauge that leads to the correctly defined propagator with no residual gauge
freedom left. This is accomplished via
terms in the Lagrangian density. These lead to a well-defined and exact though
Lorentz non invariant propagator.Comment: 9 page
Gauge transformations are not canonical transformations
In classical mechanics, we can describe the dynamics of a given system using
either the Lagrangian formalism or the Hamiltonian formalism, the choice of
either one being determined by whether one wants to deal with a second degree
differential equation or a pair of first degree ones. For the former approach,
we know that the Euler-Lagrange equation of motion remains invariant under
additive total derivative with respect to time of any function of coordinates
and time in the Lagrangian function, whereas the latter one is invariant under
canonical transformations. In this short paper we address the question whether
the transformation that leaves the Euler-Lagrange equation of motion invariant
is also a canonical transformation and show that it is not.Comment: 4 page
Antiparticle Contribution in the Cross Ladder Diagram for Two Boson Propagation in the Light-front
In the light-front milieu, there is an implicit assumption that the vacuum is
trivial. By this " triviality " is meant that the Fock space of solutions for
equations of motion is sectorized in two, one of positive energy k- and the
other of negative one corresponding respectively to positive and negative
momentum k+. It is assumed that only one of the Fock space sector is enough to
give a complete description of the solutions, but in this work we consider an
example where we demonstrate that both sectors are necessary.Comment: 10 pages, 5 figure
QED Ward Identity for fermionic field in the light-front
In a covariant gauge we implicitly assume that the Green's function
propagates information from one point of the space-time to another, so that the
Green's function is responsible for the dynamics of the relativistic particle.
In the light front form, which in principle is a change of coordinates, one
would expect that this feature would be preserved. In this manner, the
fermion's field propagator can be split into a propagating piece and a
non-propagating (``contact'') term. Since the latter (``contact'') one does not
propagate information, and therefore, assumedly with no harm to the field
dynamics we wanted to know what would be the impact of dropping it off. To do
that, we investigated its role in the Ward identity in the light front.Comment: 8 pages, no figure
Is the Bohr's quantization hypothesis necessary ?
We deduce the quantization of Bohr's hydrogen's atomic orbit without using
his hypothesis of angular momentum quantization. We show that his hypothesis is
nothing more than a consequence of the Planck's energy quantization.Comment: 5 page
Angular momentum quantization from Planck's energy quantization
We present in this work a pedagogical way of quantizing the atomic orbit for
the hydrogen's atom model proposed by Bohr without using his hypothesis of
angular momentum quantization. In contrast to the usual treatment for the
orbital quantization, we show that using energy conservation, correspondence
principle and Plank's energy quantization Bohr's hypothesis can be deduced from
and is a consequence of the Planck's energy quantization.Comment: 6 page
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