Ghost condensation in nonlinear gauges: Euclidean space, Minkowski space, and high temperature

2003 ◽  
Vol 67 (4) ◽  
Author(s):  
H. Sawayanagi
Keyword(s):  
High Temperature ◽  
Euclidean Space ◽  
Minkowski Space

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 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 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.

scholarly journals QCD Factorization and PDFs from Lattice QCD Calculation

2015 ◽  
Vol 37 ◽  
pp. 1560041 ◽  
Author(s):  
Yan-Qing Ma ◽  
Jian-Wei Qiu
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Lattice Qcd ◽  
Correlation Functions ◽  
Parton Distribution ◽  
Distribution Functions ◽  
Matrix Elements ◽  
Parton Distribution Functions ◽  
Qcd Factorization ◽  
The Matrix

In this talk, we review a QCD factorization based approach to extract parton distribution and correlation functions from lattice QCD calculation of single hadron matrix elements of quark-gluon operators. We argue that although the lattice QCD calculations are done in the Euclidean space, the nonperturbative collinear behavior of the matrix elements are the same as that in the Minkowski space, and could be systematically factorized into parton distribution functions with infrared safe matching coefficients. The matching coefficients can be calculated perturbatively by applying the factorization formalism on to asymptotic partonic states.

scholarly journals Thermal Casimir effect for rectangular cavities inside (D+1)-dimensional Minkowski space–time revisited

2014 ◽  
Vol 29 (08) ◽  
pp. 1450043 ◽  
Author(s):  
Rui-Hui Lin ◽  
Xiang-Hua Zhai
Keyword(s):  
Free Energy ◽  
High Temperature ◽  
Boundary Conditions ◽  
Minkowski Space ◽  
Casimir Effect ◽  
Side Length ◽  
Temperature Dependent ◽  
Dependent Part ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space

We reconsider the thermal scalar Casimir effect for p-dimensional rectangular cavity inside (D+1)-dimensional Minkowski space–time and clarify the ambiguity in the regularization of the temperature-dependent part of the free energy. We derive rigorously the regularization of the temperature-dependent part of the free energy by making use of the Abel–Plana formula repeatedly and get the explicit expression of the terms to be subtracted. In the cases of D = 3, p = 1 and D = 3, p = 3, we precisely recover the results of parallel plates and three-dimensional box in the literature. Furthermore, for D>p and D = p cases with periodic, Dirichlet and Neumann boundary conditions, we give the explicit expressions of the Casimir free energy in both low temperature (small separations) and high temperature (large separations) regimes, through which the asymptotic behavior of the free energy changing with temperature and the side length is easy to see. We find that for D>p, with the side length going to infinity, the Casimir free energy tends to positive or negative constants or zero, depending on the boundary conditions. But for D = p, the leading term of the Casimir free energy for all three boundary conditions is a logarithmic function of the side length. We also discuss the thermal Casimir force changing with temperature and the side length in different cases and find that when the side length goes to infinity, the force always tends to be zero for different boundary conditions regardless of D>p or D = p. The Casimir free energy and force at high temperature limit behave asymptotically alike that they are proportional to the temperature, be they positive (repulsive) or negative (attractive) in different cases. Our study may be helpful in providing a comprehensive and complete understanding of this old problem.

scholarly journals ANALYSIS ON q-DEFORMED QUANTUM SPACES

2007 ◽  
Vol 22 (01) ◽  
pp. 95-164 ◽  
Author(s):  
HARTMUT WACHTER
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Tensor Products ◽  
Main Concern ◽  
Star Products ◽  
Classical Analysis ◽  
Four Dimensions ◽  
Deformed Minkowski Space ◽  
Physical Importance ◽  
The Subject

A q-deformed version of classical analysis is given to quantum spaces of physical importance, i.e. Manin plane, q-deformed Euclidean space in three or four dimensions, and q-deformed Minkowski space. The subject is presented in a rather complete and self-contained way. All relevant notions are introduced and explained in detail. The different possibilities to realize the objects of q-deformed analysis are discussed and their elementary properties are studied. In this manner attention is focused on star products, q-deformed tensor products, q-deformed translations, q-deformed partial derivatives, dual pairings, q-deformed exponentials, and q-deformed integration. The main concern of this work is to show that these objects fit together in a consistent framework, which is suitable to formulate physical theories on quantum spaces.

scholarly journals Study of the Homogeneous Bethe-Salpeter Equation in the 2+1 Minkowski Space

2017 ◽  
Vol 45 ◽  
pp. 1760055
Author(s):  
Vitor Gigante ◽  
Jorge H. Alvarenga Nogueira ◽  
Emanuel Ydrefors ◽  
Cristian Gutierrez
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Bound State ◽  
Coupling Constants ◽  
Good Representation ◽  
Interaction Kernel ◽  
Relativistic Approach ◽  
Important Challenge ◽  
Near Future ◽  
Good Agreement

The problem of a relativistic bound-state system consisting of two scalar bosons interacting through the exchange of another scalar boson, in 2+1 space-time dimensions, has been studied. The Bethe-Salpeter equation (BSE) was solved by adopting the Nakanishi integral representation (NIR) and the Light-Front projection. The NIR allows us to solve the BSE in Minkowski space, which is a big and important challenge, since most of non-perturbative calculations are done in Euclidean space, e.g. Lattice and Schwinger-Dyson calculations. We have in this work adopted an interaction kernel containing the ladder and cross-ladder exchanges. In order to check that the NIR is also a good representation in 2+1, the coupling constants and Wick-rotated amplitudes have been computed and compared with calculations performed in Euclidean space. Very good agreement between the calculations performed in the Minkowski and Euclidean spaces has been found. This is an important consistence test that allows Minkowski calculations with the Nakanishi representation in 2+1 dimensions. This relativistic approach will allow us to perform applications in condensed matter problems in a near future.

scholarly journals HIGHER DIMENSIONAL OPERATORS AND THEIR EFFECTS IN (NON)SUPERSYMMETRIC MODELS

2008 ◽  
Vol 23 (10) ◽  
pp. 711-720 ◽  
Author(s):  
D. M. GHILENCEA
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Space Time ◽  
Analytical Continuation ◽  
Power Counting ◽  
Higher Derivative ◽  
Minkowski Space Time ◽  
Higher Dimensional ◽  
Supersymmetric Models ◽  
Higher Derivatives

It is shown that a 4D N = 1 softly broken supersymmetric theory with higher derivative operators in the Kahler or the superpotential part of the Lagrangian and with an otherwise arbitrary superpotential, can be re-formulated as a theory without higher derivatives but with additional (ghost) superfields and modified interactions. The importance of the analytical continuation Minkowski–Euclidean space–time for the UV behaviour of such theories is discussed in detail. In particular it is shown that power counting for divergences in Minkowski space–time does not always work in models with higher dimensional (derivative) operators.

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