scholarly journals Testing the surrogate zeta-function method

1986 ◽  
Vol 64 (5) ◽  
pp. 633-636 ◽  
Author(s):  
Alan Chodos ◽  
Eric Myers
Keyword(s):  
Euclidean Space ◽  
Zeta Function ◽  
Minkowski Space ◽  
Function Method ◽  
Casimir Energy ◽  
Kaluza Klein

Use of the surrogate zeta-function method was crucial in calculating the Casimir energy in non-Abelian Kaluza–Klein theories. We establish the validity of this method for the case where the background metric is (Euclidean space) × (N sphere). Our techniques do not apply to the case where the background is (Minkowski space) × (N sphere).

scholarly journals Equivalence of zeta function technique and Abel–Plana formula in regularizing the Casimir energy of hyper-rectangular cavities

2014 ◽  
Vol 29 (35) ◽  
pp. 1450181
Author(s):  
Rui-Hui Lin ◽  
Xiang-Hua Zhai
Keyword(s):  
Zeta Function ◽  
Regularization Method ◽  
Function Method ◽  
Casimir Energy ◽  
Function Technique ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Epstein Zeta Function ◽  
Formula Method ◽  
Reflection Formula

Zeta function regularization is an effective method to extract physical significant quantities from infinite ones. It is regarded as mathematically simple and elegant but the isolation of the physical divergency is hidden in its analytic continuation. By contrast, Abel–Plana formula method permits explicit separation of divergent terms. In regularizing the Casimir energy for a massless scalar field in a D-dimensional rectangular box, we give the rigorous proof of the equivalence of the two methods by deriving the reflection formula of Epstein zeta function from repeatedly application of Abel–Plana formula and giving the physical interpretation of the infinite integrals. Our study may help with the confidence of choosing any regularization method at convenience among the frequently used ones, especially the zeta function method, without the doubts of physical meanings or mathematical consistency.

Renormalization In Quantum Gauge Theory Using Zeta-Function Method

2009 ◽  
Author(s):  
Viorel Chiritoiu ◽  
Gheorghe Zet ◽  
Madalin Bunoiu ◽  
Iosif Malaescu
Keyword(s):  
Gauge Theory ◽  
Zeta Function ◽  
Function Method ◽  
Quantum Gauge Theory

scholarly journals BOUNDARY CONDITIONS IN THE DIRAC APPROACH TO GRAPHENE DEVICES

2012 ◽  
Vol 14 ◽  
pp. 240-249 ◽  
Author(s):  
C.G. BENEVENTANO ◽  
E.M. SANTANGELO
Keyword(s):  
Boundary Conditions ◽  
Zeta Function ◽  
Continuum Limit ◽  
Casimir Energy ◽  
Local Boundary ◽  
Graphene Devices ◽  
The Continuum

We study a family of local boundary conditions for the Dirac problem corresponding to the continuum limit of graphene, both for nanoribbons and nanodots. We show that, among the members of such family, MIT bag boundary conditions are the ones which are in closest agreement with available experiments. For nanotubes of arbitrary chirality satisfying these last boundary conditions, we evaluate the Casimir energy via zeta function regularization, in such a way that the limit of nanoribbons is clearly determined.

Gravitational Casimir energy in non-Abelian Kaluza-Klein theories

1985 ◽  
Vol 31 (12) ◽  
pp. 3064-3072 ◽  
Author(s):  
Alan Chodos ◽  
Eric Myers
Keyword(s):  
Casimir Energy ◽  
Kaluza Klein

scholarly journals A NOTE ON THE CASIMIR ENERGY OF A MASSIVE SCALAR FIELD IN POSITIVE CURVATURE SPACE

2004 ◽  
Vol 19 (02) ◽  
pp. 111-116 ◽  
Author(s):  
E. ELIZALDE ◽  
A. C. TORT
Keyword(s):  
High Temperature ◽  
Scalar Field ◽  
Zeta Function ◽  
Vacuum Energy ◽  
Positive Curvature ◽  
Zero Point ◽  
Casimir Energy ◽  
Massive Scalar ◽  
Zero Temperature ◽  
Massive Scalar Field

We re-evaluate the zero point Casimir energy for the case of a massive scalar field in R1×S3 space, allowing also for deviations from the standard conformal value ξ=1/6, by means of zero temperature zeta function techniques. We show that for the problem at hand this approach is equivalent to the high temperature regularization of the vacuum energy, as conjectured in a previous publication. The analytic continuation can be performed in two ways, which are seen to be equivalent.

Harmonic evolutes of B-scrolls with constant mean curvature in Lorentz–Minkowski space

2019 ◽  
Vol 16 (05) ◽  
pp. 1950076 ◽  
Author(s):  
Rafael López ◽  
Željka Milin Šipuš ◽  
Ljiljana Primorac Gajčić ◽  
Ivana Protrka
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Ruled Surfaces ◽  
Null Curve ◽  
Base Curve

In this paper, we study harmonic evolutes of [Formula: see text]-scrolls, that is, of ruled surfaces in Lorentz–Minkowski space having no Euclidean counterparts. Contrary to Euclidean space where harmonic evolutes of surfaces are surfaces again, harmonic evolutes of [Formula: see text]-scrolls turn out to be curves. In particular, we show that the harmonic evolute of a [Formula: see text]-scroll of constant mean curvature together with its base curve forms a null Bertrand pair. This allows us to characterize [Formula: see text]-scrolls of constant mean curvature and reconstruct them from a given null curve which is their harmonic evolute.

Harmonic curvatures of the strip in Minkowski space

2018 ◽  
Vol 11 (04) ◽  
pp. 1850061
Author(s):  
Filiz Ertem Kaya ◽  
Ayşe Yavuz
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Strip Theory ◽  
First Time ◽  
Cylindrical Helix

This study aimed to give definitions and relations between strip theory and harmonic curvatures of the strip in Minkowski space. Previously, the same was done in Euclidean Space (see [F. Ertem Kaya, Y. Yayli and H. H. Hacısalihoglu, A characterization of cylindrical helix strip, Commun. Fac. Sci. Univ. Ank. Ser. A1 59(2) (2010) 37–51]). The present paper gives for the first time a generic characterization of the harmonic curvatures of the strip, helix strip and inclined strip in Minkowski space.

scholarly journals COSMOLOGICAL CONSTANT PROBING SHAPE MODULI THROUGH LARGE EXTRA DIMENSIONS

2006 ◽  
Vol 21 (15) ◽  
pp. 3095-3109 ◽  
Author(s):  
SATOSHI MATSUDA ◽  
SHIGENORI SEKI
Keyword(s):  
Cosmological Constant ◽  
Extra Dimensions ◽  
Vacuum Energy ◽  
Large Extra Dimensions ◽  
Casimir Energy ◽  
Wilkinson Microwave Anisotropy Probe ◽  
Extra Space ◽  
Kaluza Klein

We consider a compactification of extra dimensions and numerically calculate Casimir energy which is provided by the mass of Kaluza–Klein modes. For the extra space we consider a torus with shape moduli and show that the corresponding vacuum energy is represented as a function of the moduli parameter of the extra dimensions. By assuming that the Casimir energy may be identified with cosmological constant, we evaluate the size of extra dimensions in terms of the recent data given by the Wilkinson Microwave Anisotropy Probe (WMAP) measurement and the supernovae observations. We suggest that the observed cosmological constant may probe the shape moduli of the extra space by the study of the Casimir energy of the compactified extra dimensions.

scholarly journals A New Angular Measurement in Minkowski 3-Space

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 56 ◽  
Author(s):  
Jinhua Qian ◽  
Xueqian Tian ◽  
Jie Liu ◽  
Young Ho Kim
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Angular Measurement ◽  
Frenet Frame ◽  
Measuring Methods ◽  
Null Curve

In Lorentz–Minkowski space, the angles between any two non-null vectors have been defined in the sense of the angles in Euclidean space. In this work, the angles relating to lightlike vectors are characterized by the Frenet frame of a pseudo null curve and the angles between any two non-null vectors in Minkowski 3-space. Meanwhile, the explicit measuring methods are demonstrated through several examples.

scholarly journals The Dirichlet Problem of the Constant Mean Curvature in Equation in Lorentz-Minkowski Space and in Euclidean Space

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1211 ◽  
Author(s):  
Rafael López
Keyword(s):  
Dirichlet Problem ◽  
Euclidean Space ◽  
Minkowski Space ◽  
Mean Curvature ◽  
Elliptic Equations ◽  
Constant Mean Curvature ◽  
Euclidean Case ◽  
Curvature Equation ◽  
Mean Curvature Equation ◽  
The Mean

We investigate the differences and similarities of the Dirichlet problem of the mean curvature equation in the Euclidean space and in the Lorentz-Minkowski space. Although the solvability of the Dirichlet problem follows standards techniques of elliptic equations, we focus in showing how the spacelike condition in the Lorentz-Minkowski space allows dropping the hypothesis on the mean convexity, which is required in the Euclidean case.

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