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.

Markov chains and generalized continued fractions

1992 ◽  
Vol 29 (04) ◽  
pp. 838-849 ◽  
Author(s):  
Thomas Hanschke
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Wide Class ◽  
Stochastic Models ◽  
Continuous Time ◽  
Continued Fractions ◽  
Invariant Measures ◽  
Continuous Time Markov Chains ◽  
Generalized Continued Fractions

This paper deals with a class of discrete-time Markov chains for which the invariant measures can be expressed in terms of generalized continued fractions. The representation covers a wide class of stochastic models and is well suited for numerical applications. The results obtained can easily be extended to continuous-time Markov chains.

THE ANALYTIC PROPERTIES OF THE QUARK PROPAGATOR IN THE INSTANTON DILUTE-GAS APPROXIMATION

1993 ◽  
Vol 08 (06) ◽  
pp. 503-511
Author(s):  
N.J. DOWRICK ◽  
N.A. McDOUGALL
Keyword(s):  
Minkowski Space ◽  
Wide Class ◽  
Quark Propagator ◽  
Gauge Transformations ◽  
Dilute Gas

The quark propagator when calculated in the instanton dilute-gas approximation is found to have no pole when continued to Minkowski space. We argue that this result is stable under a wide class of gauge transformations, but conclude that it is probably an artifact of the dilute-gas approximation.

Markov chains and generalized continued fractions

1992 ◽  
Vol 29 (4) ◽  
pp. 838-849 ◽  
Author(s):  
Thomas Hanschke
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Wide Class ◽  
Stochastic Models ◽  
Continuous Time ◽  
Continued Fractions ◽  
Invariant Measures ◽  
Continuous Time Markov Chains ◽  
Generalized Continued Fractions

This paper deals with a class of discrete-time Markov chains for which the invariant measures can be expressed in terms of generalized continued fractions. The representation covers a wide class of stochastic models and is well suited for numerical applications. The results obtained can easily be extended to continuous-time Markov chains.

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.

On generalized partially null Mannheim curves in Minkowski space-time

2016 ◽  
Vol 46 (1) ◽  
pp. 159-170 ◽  
Author(s):  
Emilija Nešović ◽  
Milica Grbović
Keyword(s):  
Minkowski Space ◽  
Space Time ◽  
Minkowski Space Time

scholarly journals Quantum volume and length fluctuations in a midi-superspace model of Minkowski space

2015 ◽  
Vol 32 (5) ◽  
pp. 055009
Author(s):  
Jeremy Adelman ◽  
Franz Hinterleitner ◽  
Seth Major
Keyword(s):  
Minkowski Space ◽  
Quantum Volume
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