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16
On the analyticity of laguerre series
 Journal of Physics A: Mathematical and Theoretical
, 2008
"... The transformation of a Laguerre series f(z) = ∑ ∞ n=0 λ(α) n L (α) n (z) to a power series f(z) = ∑ ∞ n=0 γnzn is discussed. Since many nonanalytic functions can be expanded in terms of generalized Laguerre polynomials, success is not guaranteed and such a transformation can easily lead to a ..."
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Cited by 10 (2 self)
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The transformation of a Laguerre series f(z) = ∑ ∞ n=0 λ(α) n L (α) n (z) to a power series f(z) = ∑ ∞ n=0 γnzn is discussed. Since many nonanalytic functions can be expanded in terms of generalized Laguerre polynomials, success is not guaranteed and such a transformation can easily lead to a mathematically meaningless expansion containing power series coefficients that are infinite in magnitude. Simple sufficient conditions based on the decay rates and sign patters of the Laguerre series coefficients λ (α) n as n → ∞ can be formulated which guarantee that the resulting power series represents an analytic function. The transformation produces a mathematically meaningful result if the coefficients λ (α) n either decay exponentially or factorially as n → ∞. The situation is much more complicated – but also much more interesting – if the λ (α) n decay only algebraically as n → ∞. If the
Loop Vertex Expansion for Φ2k Theory in Zero Dimension
 Journal of Mathematical Physics
"... In this paper we extend the method of loop vertex expansion to interactions with degree higher than 4. As an example we provide through this expansion an explicit proof that the free energy of φ2k scalar theory in zero dimension is BorelLe Roy summable of order k−1. We detail the computations in t ..."
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Cited by 9 (5 self)
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In this paper we extend the method of loop vertex expansion to interactions with degree higher than 4. As an example we provide through this expansion an explicit proof that the free energy of φ2k scalar theory in zero dimension is BorelLe Roy summable of order k−1. We detail the computations in the case of a φ6 interaction.
Construction of 2dimensional GrosseWulkenhaar model
, 2011
"... In this paper we construct the noncommutative GrosseWulkenhaar model on 2dimensional Moyal plane with the method of loop vertex expansion. We treat renormalization with this new tool, adapt Nelson’s argument and prove Borel summability of the perturbation series. This is the first noncommutative ..."
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Cited by 6 (0 self)
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In this paper we construct the noncommutative GrosseWulkenhaar model on 2dimensional Moyal plane with the method of loop vertex expansion. We treat renormalization with this new tool, adapt Nelson’s argument and prove Borel summability of the perturbation series. This is the first noncommutative quantum field theory model to be built in a nonperturbative sense.
How are Feynman graphs resummed by the Loop Vertex Expansion, arXiv 1006
"... The purpose of this short letter is to clarify which set of pieces of Feynman graphs are resummed in a Loop Vertex Expansion, and to formulate a conjecture on the φ4 theory in noninteger dimension. LPT20XXxx ..."
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Cited by 4 (4 self)
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The purpose of this short letter is to clarify which set of pieces of Feynman graphs are resummed in a Loop Vertex Expansion, and to formulate a conjecture on the φ4 theory in noninteger dimension. LPT20XXxx
Multiinstantons and exact results. III: Unification of even and odd anharmonic oscillators, Annals Phys
, 2010
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Available online at www.eap.ee On the acceleration of convergence by regular matrix methods
, 2007
"... Abstract. Regular matrix methods that improve and accelerate the convergence of sequences and series are studied. Some problems related to the speed of convergence of sequences and series with respect to matrix methods are discussed. Several theorems on the improvement and acceleration of the conver ..."
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Abstract. Regular matrix methods that improve and accelerate the convergence of sequences and series are studied. Some problems related to the speed of convergence of sequences and series with respect to matrix methods are discussed. Several theorems on the improvement and acceleration of the convergence are proved. The results obtained are used to increase the order of approximation of Fourier expansions and Zygmund means of Fourier expansions in certain Banach spaces. Key words: convergence acceleration, matrix methods, Fourier expansions, order of approximation. 1.
1 The Feynman Diagrams and Virtual Quanta
"... 2 The received view in philosophical studies of quantum field theory is that the Feynman diagrams are simply calculational tools. Alongside with this view we have the one that takes the virtual quanta to be also simply formal tools. This received view was developed and consolidated in philosophy of ..."
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2 The received view in philosophical studies of quantum field theory is that the Feynman diagrams are simply calculational tools. Alongside with this view we have the one that takes the virtual quanta to be also simply formal tools. This received view was developed and consolidated in philosophy of physics works by Mario Bunge, Paul Teller, Michael Redhead, Robert Weingard, Brigitte Falkenburg, and others. In this paper I will present an alternative to the received view. 1.
interactions in quantum electrodynamics
"... The Dirac equation, the concept of quanta, and the description of ..."