62,826 research outputs found
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
Prescriptionless light-cone integrals
Perturbative quantum gauge field theory seen within the perspective of
physical gauge choices such as the light-cone entails the emergence of
troublesome poles of the type in the Feynman integrals,
and these come from the boson field propagator, where and
is the external arbitrary four-vector that defines the gauge proper.
This becomes an additional hurdle to overcome in the computation of Feynman
diagrams, since any graph containing internal boson lines will inevitably
produce integrands with denominators bearing the characteristic gauge-fixing
factor. How one deals with them has been the subject of research for over
decades, and several prescriptions have been suggested and tried in the course
of time, with failures and successes.
However, a more recent development in this front which applies the negative
dimensional technique to compute light-cone Feynman integrals shows that we can
altogether dispense with prescriptions to perform the calculations. An
additional bonus comes attached to this new technique in that not only it
renders the light-cone prescriptionless, but by the very nature of it, can also
dispense with decomposition formulas or partial fractioning tricks used in the
standard approach to separate pole products of the type , .
In this work we demonstrate how all this can be done.Comment: 6 pages, no figures, Revtex style, reference [2] correcte
Negative Dimensional Integration: "Lab Testing" at Two Loops
Negative dimensional integration method (NDIM) is a technique to deal with
D-dimensional Feynman loop integrals. Since most of the physical quantities in
perturbative Quantum Field Theory (pQFT) require the ability of solving them,
the quicker and easier the method to evaluate them the better. The NDIM is a
novel and promising technique, ipso facto requiring that we put it to test in
different contexts and situations and compare the results it yields with those
that we already know by other well-established methods. It is in this
perspective that we consider here the calculation of an on-shell two-loop three
point function in a massless theory. Surprisingly this approach provides twelve
non-trivial results in terms of double power series. More astonishing than this
is the fact that we can show these twelve solutions to be different
representations for the same well-known single result obtained via other
methods. It really comes to us as a surprise that the solution for the
particular integral we are dealing with is twelvefold degenerate.Comment: 10 pages, LaTeX2e, uses style jhep.cls (included
Non-planar double-box, massive and massless pentabox Feynman integrals in negative dimensional approach
Negative dimensional integration method (NDIM) is a technique which can be
applied, with success, in usual covariant gauge calculations. We consider three
two-loop diagrams: the scalar massless non-planar double-box with six
propagators and the scalar pentabox in two cases, where six virtual particles
have the same mass and in the case where all of them are massless. Our results
are given in terms hypergeometric functions of Mandelstam variables and for
arbitrary exponents of propagators and dimension as well.Comment: Latex, 12 pages, 2 figures, uses axodraw (included
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