scholarly journals Solving the Bethe - Salpeter Equation in Minkowski Space: Scalar Theories and Beyond

1997 ◽  
Vol 50 (1) ◽  
pp. 147 ◽  
Author(s):  
K. Kusaka ◽  
A. G. Williams ◽  
K. M. Simpson
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Vertex Function ◽  
Bound States ◽  
Spectral Representation ◽  
Ladder Approximation ◽  
Wick Rotation ◽  
Space Solution ◽  
Scalar Theories ◽  
Scattering Kernel

The Bethe–Salpeter equation (BSE) for bound states in scalar theories is reformulated and solved in terms of a generalized spectral representation directly in Minkowski space. This differs from the conventional approach, where the BSE is solved in Euclidean space after a Wick rotation. For all but the lowest-order (i.e. ladder) approximation to the scattering kernel, the naive Wick rotation is invalid. Our approach generates the vertex function and Bethe–Salpeter amplitude for the entire allowed range of momenta, whereas these cannot be directly obtained from the Euclidean space solution. Our method is quite general and can be applied even in cases where the Wick rotation is not possible.

scholarly journals Preface: Quarks, hadrons and nuclei

1997 ◽  
Vol 50 (1) ◽  
pp. I
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Vertex Function ◽  
Bound States ◽  
Spectral Representation ◽  
Ladder Approximation ◽  
Wick Rotation ◽  
Space Solution ◽  
Scalar Theories ◽  
Scattering Kernel

The Bethe–Salpeter equation (BSE) for bound states in scalar theories is reformulated and solved in terms of a generalized spectral representation directly in Minkowski space. This differs from the conventional approach, where the BSE is solved in Euclidean space after a Wick rotation. For all but the lowest-order (i.e. ladder) approximation to the scattering kernel, the naive Wick rotation is invalid. Our approach generates the vertex function and Bethe–Salpeter amplitude for the entire allowed range of momenta, whereas these cannot be directly obtained from the Euclidean space solution. Our method is quite general and can be applied even in cases where the Wick rotation is not possible.

scholarly journals Solving the Bethe-Salpeter equation for bound states of scalar theories in Minkowski space

1997 ◽  
Vol 56 (8) ◽  
pp. 5071-5085 ◽  
Author(s):  
Kensuke Kusaka ◽  
Ken Simpson ◽  
Anthony G. Williams
Keyword(s):  
Minkowski Space ◽  
Bound States ◽  
Scalar Theories

scholarly journals Pseudo-scalar mesons at finite temperatures from a Dyson-Schwinger-Bethe-Salpeter approach

2019 ◽  
Vol 204 ◽  
pp. 08005
Author(s):  
Sergey Dorkin ◽  
Leonid Kaptari ◽  
Burkhard Kämpfer
Keyword(s):  
Low Temperatures ◽  
Vertex Function ◽  
Bound States ◽  
Quark Propagator ◽  
Ladder Approximation ◽  
Zero Temperature ◽  
Interaction Kernel ◽  
Gap Equation ◽  
Scalar Mesons ◽  
Pseudo Scalar

The truncated Dyson-Schwinger–Bethe-Salpeter equations are employed at non-zero temperature. The truncations refer to a rainbow-ladder approximation augmented with an interaction kernel which facilitates a special temperature dependence. At low temperatures, T → 0, we recover a quark propagator from the Dyson-Schwinger (gap) equation smoothly interpolating to the T = 0 results. Utilizing that quark propagator we evaluate the Bethe-Salpeter vertex function in the pseudo-scalar qq̅ channel for the lowest boson Matsubara frequencies and find a competition of qq̅ bound states and quasi-free two-quark states at T = O (100 MeV).

scholarly journals Three-boson bound states in Minkowski space with contact interactions

2020 ◽  
Vol 101 (9) ◽  
Author(s):  
E. Ydrefors ◽  
J. H. Alvarenga Nogueira ◽  
V. A. Karmanov ◽  
T. Frederico
Keyword(s):  
Minkowski Space ◽  
Bound States ◽  
Contact Interactions

scholarly journals A Spectral Calculus for Lorentz Invariant Measures on Minkowski Space

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1696
Author(s):  
John Mashford
Keyword(s):  
Minkowski Space ◽  
Wide Class ◽  
Invariant Measures ◽  
Spectral Representation ◽  
Scalar Particles ◽  
Lebesque Measure

This paper presents a spectral calculus for computing the spectra of causal Lorentz invariant Borel complex measures on Minkowski space, thereby enabling one to compute their densities with respect to Lebesque measure. The spectra of certain elementary convolutions involving Feynman propagators of scalar particles are computed. It is proved that the convolution of arbitrary causal Lorentz invariant Borel complex measures exists and the product of such measures exists in a wide class of cases. Techniques for their computation in terms of their spectral representation are presented.

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).

Relativistic bound states in three space-time dimensions in Minkowski space

2016 ◽  
Author(s):  
C. Gutierrez ◽  
V. Gigante ◽  
T. Frederico ◽  
Lauro Tomio
Keyword(s):  
Minkowski Space ◽  
Bound States ◽  
Space Time ◽  
Relativistic Bound States ◽  
Three Space

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.

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