Fourier expansion associated with the Lorentz group in the space of functions with support outisde the light cone

1978 ◽  
Vol 36 (3) ◽  
pp. 752-759
Author(s):  
Yu. G. Shondin
Keyword(s):  
Lorentz Group ◽  
Light Cone ◽  
Fourier Expansion

scholarly journals On Analog of Fourier Transform in Interior of the Light Cone

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Tatyana Shtepina
Keyword(s):  
Fourier Transform ◽  
Lorentz Group ◽  
Light Cone ◽  
Inverse Transform ◽  
Irreducible Components ◽  
One To One

We introduce an analog of Fourier transformFhρin interior of light cone that commutes with the action of the Lorentz group. We describe some properties ofFhρ, namely, its action on pseudoradial functions and functions being products of pseudoradial function and space hyperbolic harmonics. We prove thatFhρ-transform gives a one-to-one correspondence on each of the irreducible components of quasiregular representation. We calculate the inverse transform too.

Spectral Analysis on Upper Light Cone in R3 and the Radon Transform

1988 ◽  
Vol 40 (6) ◽  
pp. 1458-1481 ◽  
Author(s):  
Antoni Wawrzyñczyk
Keyword(s):  
Spectral Analysis ◽  
Symmetric Space ◽  
Lorentz Group ◽  
Radon Transform ◽  
Light Cone ◽  
General Procedure ◽  
Natural Action ◽  
3 Dimensional ◽  
Generalized Radon Transform ◽  
Image Position

The upper light cone L in R3 is a homogeneous space of the 3-dimensional Lorentz group G. It may be identified with the space of horocycles in the upper hyperboloide H which is the symmetric space associated to G. There exists a duality between H and L (see [5] p. 144) and a general procedure leads to a generalized Radon transform:and the dual Radon transformThese operations commute with the natural action of the group G.

From the Galilei to the Lorentz group in a general light-cone frame

1977 ◽  
Vol 122 (3) ◽  
pp. 535-544 ◽  
Author(s):  
E. Elizalde ◽  
J. Gomis
Keyword(s):  
Lorentz Group ◽  
Light Cone

Light-cone QCD on the lattice

2000 ◽  
Vol 83-84 (1-3) ◽  
pp. 116-120 ◽  
Author(s):  
S Dalley
Keyword(s):  
Light Cone

scholarly journals The Topological Origin of Quantum Randomness

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 581
Author(s):  
Stefan Heusler ◽  
Paul Schlummer ◽  
Malte S. Ubben
Keyword(s):  
High School ◽  
Hilbert Space ◽  
Group Theory ◽  
Lorentz Group ◽  
Quantum Physics ◽  
Time Development ◽  
Mathematical Structures ◽  
Stochastic Nature ◽  
Quantum Randomness ◽  
And Topology

What is the origin of quantum randomness? Why does the deterministic, unitary time development in Hilbert space (the ‘4π-realm’) lead to a probabilistic behaviour of observables in space-time (the ‘2π-realm’)? We propose a simple topological model for quantum randomness. Following Kauffmann, we elaborate the mathematical structures that follow from a distinction(A,B) using group theory and topology. Crucially, the 2:1-mapping from SL(2,C) to the Lorentz group SO(3,1) turns out to be responsible for the stochastic nature of observables in quantum physics, as this 2:1-mapping breaks down during interactions. Entanglement leads to a change of topology, such that a distinction between A and B becomes impossible. In this sense, entanglement is the counterpart of a distinction (A,B). While the mathematical formalism involved in our argument based on virtual Dehn twists and torus splitting is non-trivial, the resulting haptic model is so simple that we think it might be suitable for undergraduate courses and maybe even for High school classes.

scholarly journals Light-cone sum rules for proton decay

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ulrich Haisch ◽  
Amando Hala
Keyword(s):  
Lattice Qcd ◽  
Light Cone ◽  
Sum Rules ◽  
State Of The Art ◽  
Form Factors ◽  
Baryon Number ◽  
Proton Decay ◽  
Matrix Elements ◽  
Decay Channels ◽  
Systematic Uncertainties

Abstract We estimate the form factors that parametrise the hadronic matrix elements of proton-to-pion transitions with the help of light-cone sum rules. These form factors are relevant for semi-leptonic proton decay channels induced by baryon-number violating dimension-six operators, as typically studied in the context of grand unified theories. We calculate the form factors in a kinematical regime where the momentum transfer from the proton to the pion is space-like and extrapolate our final results to the regime that is relevant for proton decay. In this way, we obtain estimates for the form factors that show agreement with the state-of-the-art calculations in lattice QCD, if systematic uncertainties are taken into account. Our work is a first step towards calculating more involved proton decay channels where lattice QCD results are not available at present.

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