Search results for "Feynman diagram"

The response field and the saddle points of quantum mechanical path integrals

2021

In quantum statistical mechanics, Moyal's equation governs the time evolution of Wigner functions and of more general Weyl symbols that represent the density matrix of arbitrary mixed states. A formal solution to Moyal's equation is given by Marinov's path integral. In this paper we demonstrate that this path integral can be regarded as the natural link between several conceptual, geometric, and dynamical issues in quantum mechanics. A unifying perspective is achieved by highlighting the pivotal role which the response field, one of the integration variables in Marinov's integral, plays for pure states even. The discussion focuses on how the integral's semiclassical approximation relates to…

Radiative kaon capture on nuclei.

1990

Hypernuclear formation through the radiative capture of in-flight ${\mathit{K}}^{\mathrm{\ensuremath{-}}}$ is studied in a distorted wave impluse approximation approach. The elementary operator is obtained from first-order Feynman diagrams and is constrained by the reactions ${\mathit{K}}^{\mathrm{\ensuremath{-}}}$p\ensuremath{\rightarrow}\ensuremath{\Lambda}\ensuremath{\gamma} and, via crossing, by \ensuremath{\gamma}p\ensuremath{\rightarrow}${\mathit{K}}^{+}$\ensuremath{\Lambda}. The ${\mathit{K}}^{\mathrm{\ensuremath{-}}}$ distortion has been included via a simple optical potential which is in agreement with ${\mathit{K}}^{\mathrm{\ensuremath{-}}}$ elastic scattering on nuclei. Using the…

MBPT for the Green's function

2013

Threshold expansion of Feynman diagrams within a configuration space technique

2000

The near threshold expansion of generalized sunset-type (water melon) diagrams with arbitrary masses is constructed by using a configuration space technique. We present analytical expressions for the expansion of the spectral density near threshold and compare it with the exact expression obtained earlier using the method of the Hankel transform. We formulate a generalized threshold expansion with partial resummation of the small mass corrections for the strongly asymmetric case where one particle in the intermediate state is much lighter than the others.

Feynman diagrams as a weight system: four-loop test of a four-term relation

1996

At four loops there first occurs a test of the four-term relation derived by the second author in the course of investigating whether counterterms from subdivergence-free diagrams form a weight system. This test relates counterterms in a four-dimensional field theory with Yukawa and $\phi^4$ interactions, where no such relation was previously suspected. Using integration by parts, we reduce each counterterm to massless two-loop two-point integrals. The four-term relation is verified, with $ = 0 - 3\zeta_3 + 6\zeta_3 - 3\zeta_3 = 0$, demonstrating non-trivial cancellation of the trefoil knot and thus supporting the emerging connection between knots and counterterms, via transcendental number…

Computing the full two-loop gluon Regge trajectory within Lipatov's high energy effective action

2013

We discuss computational details of our recent result, namely, the first derivation of the two-loop gluon Regge trajectory within the framework of Lipatov's high energy effective action. In particular, we elaborate on the direct evaluation of Feynman two-loop diagrams by using the Mellin-Barnes representations technique. Our result is in precise agreement with previous computations in the literature, providing this way a highly non-trivial test of the effective action and the proposed subtraction and renormalization scheme combined with our approach for the treatment of the loop diagrams.

Appell Functions and the Scalar One-Loop Three-point Integrals in Feynman Diagrams

2002

The scalar three-point function appearing in one-loop Feynman diagrams is compactly expressed in terms of a generalized hypergeometric function of two variables. Use is made of the connection between such Appell function and dilogarithms coming from a previous investigation. Special cases are obtained for particular values of internal masses and external momenta.

Symmetries and Effective Vertices

2015

When facing the computation of more realistic processes, the calculations can become lengthy very fast as the number of Feynman diagrams grows. Before starting the calculation process the problem should be reduced to its minimal form. Here we will present an example of how to reduce the number of calculated diagrams for a given process (which in this case will be a Higgs-like scalar decay to two photons through a charged scalar loop) using gauge symmetry.

Electrong-factor determinations in Penning traps

2013

The magnetic moment of the electron, expressed by the g-factor in units of the Bohr magneton, is a key quantity in the theory of quantum electrodynamics (QED). Experiments using single particles confined in Penning traps have provided very precise values of the g-factor for the free electron as well as the electron bound in hydrogen-like ions. In this paper the status of these experiments is reviewed. The results allow testing calculations of higher order Feynman diagrams. Comparison of experimental and theoretical results for free and bound particles show no discrepancy within the limits of error, thus representing to date the most sensitive test of QED. Moreover, the g-factor provides a u…

Longitudinal and Transverse Correlation Functions in the  4 Model below and near the Critical Point

2010

We have extended our method of grouping Feynman diagrams (GFD theory) to study the transverse and longitudinal correlation functions G⊥(k) and G‖(k) in φ model below the critical point (T < Tc) in the presence of an infinitesimal external field. Our method allows a qualitative analysis without cutting the perturbation series. The long-wave limit k → 0 has been studied at T < Tc, showing that G⊥(k) a k−λ⊥ and G‖(k) b k−λ‖ with exponents d/2 < λ⊥ < 2 and λ‖ = 2λ⊥−d are the physical solutions of our equations at the spatial dimensionality 2 < d < 4, which coincides with the asymptotic solution at T → Tc as well as with a nonperturbative renormalization group (RG) analysis provided in our paper…