Casimir energy in a curved background with a spherical boundary and arbitrary radius: An exact solution via the point splitting method

1994 ◽  
Vol 49 (10) ◽  
pp. 5313-5318 ◽  
Author(s):  
Selçuk Ş. Bayin ◽  
M. Özcan
Keyword(s):  
Exact Solution ◽  
Splitting Method ◽  
Casimir Energy ◽  
Spherical Boundary ◽  
Point Splitting

scholarly journals Assessment of Hydrometeor Collection Rates from Exact and Approximate Equations. Part II: Numerical Bounding

2007 ◽  
Vol 46 (1) ◽  
pp. 82-96
Author(s):  
Brian J. Gaudet ◽  
Jerome M. Schmidt
Keyword(s):  
Mass Transfer ◽  
Exact Solution ◽  
Splitting Method ◽  
Time Discretization ◽  
Large Mass ◽  
Time Step ◽  
Transfer Rates ◽  
Mass Moment ◽  
Time Splitting ◽  
Approximate Equations

Abstract Past microphysical investigations, including Part I of this study, have noted that the collection equation, when applied to the interaction between different hydrometeor species, can predict large mass transfer rates, even when an exact solution is used. The fractional depletion in a time step can even exceed unity for the collected species with plausible microphysical conditions and time steps, requiring “normalization” by a microphysical scheme. Although some of this problem can be alleviated through the use of more moment predictions and hydrometeor categories, the question as to why such “overdepletion” can be predicted in the first place remains insufficiently addressed. It is shown through both physical and conceptual arguments that the explicit time discretization of the bulk collection equation for any moment is not consistent with a quasi-stochastic view of collection. The result, under certain reasonable conditions, is a systematic overprediction of collection, which can become a serious error in the prediction of higher-order moments in a bulk scheme. The term numerical bounding is used to refer to the use of a quasi-stochastically consistent formula that prevents fractional collections exceeding unity for any moments. Through examples and analysis it is found that numerical bounding is typically important in mass moment prediction for time steps exceeding approximately 10 s. The Poisson-based numerical bounding scheme is shown to be simple in application and conceptualization; within a straightforward idealization it completely corrects overdepletion while even being immune to the rediagnosis error of the time-splitting method. The scheme’s range of applicability and utility are discussed.

The constraint equation of the vertex function of quantum anomaly and Dyson–Schwinger equations in massless QED2 theory

2020 ◽  
Vol 35 (18) ◽  
pp. 2050146
Author(s):  
Yang Yu ◽  
Jian-Feng Li
Keyword(s):  
Vertex Function ◽  
Axial Vector ◽  
Splitting Method ◽  
Vector Current ◽  
Constraint Equation ◽  
Axial Vector Current ◽  
Fermion Propagator ◽  
Schwinger Model ◽  
Quantum Anomaly ◽  
Point Splitting

In this paper, we calculate the quantum anomaly for the longitudinal and the transverse Ward–Takahashi (WT) identities for vector and axial-vector currents in QED2 theory by means of the point-splitting method. It is found that the longitudinal WT identity for vector current and transverse WT identity for axial-vector current have no anomaly while the longitudinal WT identity for axial-vector current and the transverse WT identity for vector current have anomaly in QED2 theory. Moreover, we study the four WT identities in massless QED2 theory and get the result that the four WT identities together give the constraint equation of the vertex function of quantum anomaly. At last, we discuss the Dyson–Schwinger equations in massless QED2 theory. It is found that the vertex function of the quantum anomaly has corrections for the fermion propagator and Schwinger model.

scholarly journals SCALAR CASIMIR EFFECT BETWEEN TWO CONCENTRIC SPHERES

2012 ◽  
Vol 27 (16) ◽  
pp. 1250082 ◽  
Author(s):  
MUSTAFA ÖZCAN
Keyword(s):  
Scalar Field ◽  
Casimir Effect ◽  
Casimir Energy ◽  
Outer Radius ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Parallel Plates ◽  
New Approach ◽  
Concentric Spheres ◽  
Spherical Boundary

The Casimir effect giving rise to an attractive force between the closely spaced two concentric spheres that confine the massless scalar field is calculated by using a direct mode summation with contour integration in the complex plane of eigenfrequencies. We developed a new approach appropriate for the calculation of the Casimir energy for spherical boundary conditions. The Casimir energy for a massless scalar field between the closely spaced two concentric spheres coincides with the Casimir energy of the parallel plates for a massless scalar field in the limit when the dimensionless parameter η, ([Formula: see text] where a(b) is inner (outer) radius of sphere), goes to zero. The efficiency of new approach is demonstrated by calculation of the Casimir energy for a massless scalar field between the closely spaced two concentric half spheres.

POINT-SPLITTING REGULARIZATION IN N=2 SUPERCONFORMAL FIELD THEORY

1999 ◽  
Vol 14 (20) ◽  
pp. 3207-3237
Author(s):  
BELAL E. BAAQUIE ◽  
KOK KEAN YIM
Keyword(s):  
Field Theory ◽  
Complex Structure ◽  
Splitting Method ◽  
Superconformal Algebra ◽  
Operator Product ◽  
Central Extensions ◽  
Superconformal Field Theory ◽  
Conformal Field ◽  
Coset Model ◽  
Point Splitting

In this paper, the method of point-splitting regularization is applied on the N=2 superconformal field theory, specifically the superconformal coset model formulated by Kazama and Suzuki. We obtain the correct central extensions for the N=2 superconformal algebra after many nontrivial cancellations among the various singular expressions. This shows the consistency of the point-splitting method in an N=2 superconformal system. In the process, we arrive at the Kazama–Suzuki conditions which govern the existence of an N=2 superconformal coset model in the N=1 coset model. In addition, we obtain a number of mathematical relations between the structure constants and the complex structure of the model, which allow us to simplify the U(1) current of the N=2 superconformal algebra. In the course of our analysis, we found that, at least in a two dimension conformal field theory, the operator product expansion of a composite current must be written in a way which conveys all the information of the commutator equations.

scholarly journals Point-splitting method of the commutator anomaly of Gauss law operators

1997 ◽  
Vol 56 (4) ◽  
pp. 2236-2241 ◽  
Author(s):  
R. A. Bertlmann ◽  
Tomáš Sýkora
Keyword(s):  
Splitting Method ◽  
Point Splitting
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