Analytic continuation of harmonic sums near the integer values

2020 ◽  
Vol 35 (33) ◽  
pp. 2050210
Author(s):  
V. N. Velizhanin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Positive Integer ◽  
Small Parameter ◽  
Analytic Continuation ◽  
Evolution Equations ◽  
Quantum Field ◽  
Simple Method

We present a simple method for analytic continuation of harmonic sums near negative and positive integer numbers. We provide a precomputed database for the exact expansion of harmonic sums over a small parameter near these integer numbers, along with MATHEMATICA code, which shows the application of the database for actual problems. We also provide the FORM code that was used to obtain the database mentioned above. The applications of the obtained database for the study of evolution equations in the quantum field theory are discussed.

scholarly journals Non-Equilibrium Quantum Electrodynamics in Open Systems as a Realizable Representation of Quantum Field Theory of the Brain

Entropy ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 43 ◽  
Author(s):  
Akihiro Nishiyama ◽  
Shigenori Tanaka ◽  
Jack A. Tuszynski
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Time Evolution ◽  
Central Region ◽  
Quantum Electrodynamics ◽  
Quantum Tunneling ◽  
Evolution Equations ◽  
Open Systems ◽  
Quantum Field ◽  
The Brain

We derive time evolution equations, namely the Klein–Gordon equations for coherent fields and the Kadanoff–Baym equations in quantum electrodynamics (QED) for open systems (with a central region and two reservoirs) as a practical model of quantum field theory of the brain. Next, we introduce a kinetic entropy current and show the H-theorem in the Hartree–Fock approximation with the leading-order (LO) tunneling variable expansion in the 1st order approximation for the gradient expansion. Finally, we find the total conserved energy and the potential energy for time evolution equations in a spatially homogeneous system. We derive the Josephson current due to quantum tunneling between neighbouring regions by starting with the two-particle irreducible effective action technique. As an example of potential applications, we can analyze microtubules coupled to a water battery surrounded by a biochemical energy supply. Our approach can be also applied to the information transfer between two coherent regions via microtubules or that in networks (the central region and the N res reservoirs) with the presence of quantum tunneling.

Finite massless quantum field theory

1992 ◽  
Vol 70 (6) ◽  
pp. 463-466
Author(s):  
A. Y. Shiekh
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Analytic Continuation ◽  
Dimensional Regularization ◽  
Quantum Field ◽  
Four Dimensions ◽  
Infrared Divergences ◽  
Massless Quantum

Massless quantum field theory is usually troubled by both ultraviolet and infrared divergences. With the help of analytic continuation, this fact can be exploited to eliminate, or at least reduce the overall number of divergences. This mechanism is investigated within the context of dimensional regularization for the case of massless [Formula: see text] theory in four dimensions.

Zeta-function regularization of quantum field theory

1990 ◽  
Vol 68 (7-8) ◽  
pp. 620-629 ◽  
Author(s):  
A. Y. Shiekh
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Zeta Function ◽  
Analytic Continuation ◽  
Quantum Field ◽  
Four Dimensions ◽  
Group Functions

Analytic continuation leads to the finite renormalization of a quantum field theory. This is illustrated in a determination of the two loop renormalization group functions for [Formula: see text] in four dimensions.

A Review of Conformal Field Theory in 2D

2014 ◽  
Vol 6 (2) ◽  
pp. 1079-1105
Author(s):  
Rahul Nigam
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Statistical Mechanics ◽  
Critical Behavior ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Quantum Field ◽  
Conformal Field ◽  
Insight Into

In this review we study the elementary structure of Conformal Field Theory in which is a recipe for further studies of critical behavior of various systems in statistical mechanics and quantum field theory. We briefly review CFT in dimensions which plays a prominent role for example in the well-known duality AdS/CFT in string theory where the CFT lives on the AdS boundary. We also describe the mapping of the theory from the cylinder to a complex plane which will help us gain an insight into the process of radial quantization and radial ordering. Finally we will develop the representation of the Virasoro algebra which is the well-known "Verma module".  

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