66,946 research outputs found
Closed-loop control of stochastic nonlinear systems
Technique resolves problems in complex control systems, such as those used for space vehicle guidance and control. Main disadvantage of procedure is that it is only appropriate in situations where trajectory concept is valid
Relativistic particle motion in nonuniform electromagnetic waves
A charged particle moving in a strong nonuniform electromagnetic wave which suffers a net acceleration in the direction of the negative intensity gradient of the wave was investigated. Electrons will be expelled perpendicularly from narrow laser beams and various instabilities result
The light-cone gauge without prescriptions
Feynman integrals in the physical light-cone gauge are harder to solve than
their covariant counterparts. The difficulty is associated with the presence of
unphysical singularities due to the inherent residual gauge freedom in the
intermediate boson propagators constrained within this gauge choice. In order
to circumvent these non-physical singularities, the headlong approach has
always been to call for mathematical devices --- prescriptions --- some
successful ones and others not so much so. A more elegant approach is to
consider the propagator from its physical point of view, that is, an object
obeying basic principles such as causality. Once this fact is realized and
carefully taken into account, the crutch of prescriptions can be avoided
altogether. An alternative third approach, which for practical computations
could dispense with prescriptions as well as prescinding the necessity of
careful stepwise watching out of causality would be of great advantage. And
this third option is realizable within the context of negative dimensions, or
as it has been coined, negative dimensional integration method, NDIM for short.Comment: 9 pages, PTPTeX (included
Feynman integrals with tensorial structure in the negative dimensional integration scheme
Negative dimensional integration method (NDIM) is revealing itself as a very
useful technique for computing Feynman integrals, massless and/or massive,
covariant and non-covariant alike. Up to now, however, the illustrative
calculations done using such method are mostly covariant scalar integrals,
without numerator factors. Here we show how those integrals with tensorial
structures can also be handled with easiness and in a straightforward manner.
However, contrary to the absence of significant features in the usual approach,
here the NDIM also allows us to come across surprising unsuspected bonuses. In
this line, we present two alternative ways of working out the integrals and
illustrate them by taking the easiest Feynman integrals in this category that
emerges in the computation of a standard one-loop self-energy diagram. One of
the novel and as yet unsuspected bonus is that there are degeneracies in the
way one can express the final result for the referred Feynman integral.Comment: 9 pages, revtex, no figure
Negative dimensional approach for scalar two-loop three-point and three-loop two-point integrals
The well-known -dimensional Feynman integrals were shown, by Halliday and
Ricotta, to be capable of undergoing analytic continuation into the domain of
negative values for the dimension of space-time. Furthermore, this could be
identified with Grassmannian integration in positive dimensions. From this
possibility follows the concept of negative dimensional integration for loop
integrals in field theories. Using this technique, we evaluate three two-loop
three-point scalar integrals, with five and six massless propagators, with
specific external kinematic configurations (two legs on-shell), and four
three-loop two-point scalar integrals. These results are given for arbitrary
exponents of propagators and dimension, in Euclidean space, and the particular
cases compared to results published in the literature.Comment: 6 pages, 7 figures, Revte
Two-loop self-energy diagrams worked out with NDIM
In this work we calculate two two-loop massless Feynman integrals pertaining
to self-energy diagrams using NDIM (Negative Dimensional Integration Method).
We show that the answer we get is 36-fold degenerate. We then consider special
cases of exponents for propagators and the outcoming results compared with
known ones obtained via traditional methods.Comment: LaTeX, 10 pages, 2 figures, styles include
- …