7 research outputs found
Non perturbative renormalization group and momentum dependence of n-point functions (II)
In a companion paper (hep-th/0512317), we have presented an approximation
scheme to solve the Non Perturbative Renormalization Group equations that
allows the calculation of the -point functions for arbitrary values of the
external momenta. The method was applied in its leading order to the
calculation of the self-energy of the O() model in the critical regime. The
purpose of the present paper is to extend this study to the next-to-leading
order of the approximation scheme. This involves the calculation of the 4-point
function at leading order, where new features arise, related to the occurrence
of exceptional configurations of momenta in the flow equations. These require a
special treatment, inviting us to improve the straightforward iteration scheme
that we originally proposed. The final result for the self-energy at
next-to-leading order exhibits a remarkable improvement as compared to the
leading order calculation. This is demonstrated by the calculation of the shift
, caused by weak interactions, in the temperature of Bose-Einstein
condensation. This quantity depends on the self-energy at all momentum scales
and can be used as a benchmark of the approximation. The improved
next-to-leading order calculation of the self-energy presented in this paper
leads to excellent agreement with lattice data and is within 4% of the exact
large result.Comment: 35 pages, 11 figure
Non perturbative renormalisation group and momentum dependence of -point functions (I)
We present an approximation scheme to solve the Non Perturbative
Renormalization Group equations and obtain the full momentum dependence of the
-point functions. It is based on an iterative procedure where, in a first
step, an initial ansatz for the -point functions is constructed by solving
approximate flow equations derived from well motivated approximations. These
approximations exploit the derivative expansion and the decoupling of high
momentum modes. The method is applied to the O() model. In leading order,
the self energy is already accurate both in the perturbative and the scaling
regimes. A stringent test is provided by the calculation of the shift in the transition temperature of the weakly repulsive Bose gas, a quantity
which is particularly sensitive to all momentum scales. The leading order
result is in agreement with lattice calculations, albeit with a theoretical
uncertainty of about 25%.Comment: 48 pages, 15 figures A few minor corrections. A reference adde
On the 2-point function of the O(N) model
The self-energy of the critical 3-dimensional O(N) model is calculated. The
analysis is performed in the context of the Non-Perturbative Renormalization
Group, by exploiting an approximation which takes into account contributions of
an infinite number of vertices. A very simple calculation yields the 2-point
function in the whole range of momenta, from the UV Gaussian regime to the
scaling one. Results are in good agreement with best estimates in the
literature for any value of N in all momenta regimes. This encourages the use
of this simple approximation procedure to calculate correlation functions at
finite momenta in other physical situations
A new method to solve the Non Perturbative Renormalization Group equations
We propose a method to solve the Non Perturbative Renormalization Group
equations for the -point functions. In leading order, it consists in solving
the equations obtained by closing the infinite hierarchy of equations for the
-point functions. This is achieved: i) by exploiting the decoupling of modes
and the analyticity of the -point functions at small momenta: this allows us
to neglect some momentum dependence of the vertices entering the flow
equations; ii) by relating vertices at zero momenta to derivatives of lower
order vertices with respect to a constant background field. Although the
approximation is not controlled by a small parameter, its accuracy can be
systematically improved. When it is applied to the O(N) model, its leading
order is exact in the large limit; in this case, one recovers known results
in a simple and direct way, i.e., without introducing an auxiliary field.Comment: Minor changes. Version to be publishe
Perturbation theory and non-perturbative renormalization flow in scalar field theory at finite temperature
We use the non-perturbative renormalization group to clarify some features of
perturbation theory in thermal field theory. For the specific case of the
scalar field theory with O(N) symmetry, we solve the flow equations within the
local potential approximation. This approximation reproduces the perturbative
results for the screening mass and the pressure up to order g^3, and starts to
differ at order g^4. The method allows a smooth extrapolation to the regime
where the coupling is not small, very similar to that obtained from a simple
self-consistent approximation.Comment: 42 pages, 19 figures; v2: typos corrected and references added,
version accepted for publication in Nucl. Phys.
La diferencia de masa neutrón-protón
Facultad de Ciencias Exacta
La diferencia de masa neutrón-protón
Facultad de Ciencias Exacta