scholarly journals Continuous spin representations from group contraction

2005 ◽  
Vol 46 (5) ◽  
pp. 053515 ◽  
Author(s):  
Abu M. Khan ◽  
Pierre Ramond
Keyword(s):  
Continuous Spin ◽  
Group Contraction ◽  
Spin Representations

Realizations of generators of complex angular momentum

1990 ◽  
Vol 68 (7-8) ◽  
pp. 599-603
Author(s):  
Shuchi Bora ◽  
H. C. Chandola ◽  
B. S. Rajput
Keyword(s):  
Angular Momentum ◽  
Lorentz Group ◽  
Continuous Spin ◽  
Zero Mass ◽  
Complex Angular Momentum ◽  
General Manner ◽  
Homogeneous Lorentz Group ◽  
Real Mass ◽  
Spin Representations ◽  
Spin Contribution

We use the generators of complex angular momentum in complex c3 space and derive the realizations of the homogeneous Lorentz group for nonzero real mass, zero mass, and imaginary mass systems. We use the appropriate little group for different systems to calculate the modifications in the spin contribution to angular momentum and the unphysical continuous spin representations are shown to be eliminated. We diagonalize the helicity operator in c3 space and obtain the generators of complex angular-momentum operators, which are shown to lead, in a general manner, to the standard helicity representations of the Poincare group for timelike and spacelike systems.

scholarly journals Continuous spin representations of the Poincaré and super-Poincaré groups

2002 ◽  
Vol 43 (12) ◽  
pp. 6279-6295 ◽  
Author(s):  
Lars Brink ◽  
Abu M. Khan ◽  
Pierre Ramond ◽  
Xiaozhen Xiong
Keyword(s):  
Continuous Spin ◽  
Spin Representations

scholarly journals Massless finite and infinite spin representations of Poincaré group in six dimensions

2021 ◽  
pp. 136064
Author(s):  
I.L. Buchbinder ◽  
S.A. Fedoruk ◽  
A.P. Isaev ◽  
M.A. Podoinitsyn
Keyword(s):  
Poincaré Group ◽  
Poincare Group ◽  
Six Dimensions ◽  
Spin Representations

scholarly journals Polaritonic XY-Ising machine

Nanophotonics ◽  
2020 ◽  
Vol 9 (13) ◽  
pp. 4127-4138 ◽  
Author(s):  
Kirill P. Kalinin ◽  
Alberto Amo ◽  
Jacqueline Bloch ◽  
Natalia G. Berloff
Keyword(s):  
Dissipative Systems ◽  
Phase Information ◽  
Physical Origin ◽  
Continuous Spin ◽  
Network Nodes ◽  
Computing Platform ◽  
Ability To Act ◽  
Spin Hamiltonians ◽  
Long Range Interactions ◽  
Accuracy And Stability

AbstractGain-dissipative systems of various physical origin have recently shown the ability to act as analogue minimisers of hard combinatorial optimisation problems. Whether or not these proposals will lead to any advantage in performance over the classical computations depends on the ability to establish controllable couplings for sufficiently dense short- and long-range interactions between the spins. Here, we propose a polaritonic XY-Ising machine based on a network of geometrically isolated polariton condensates capable of minimising discrete and continuous spin Hamiltonians. We elucidate the performance of the proposed computing platform for two types of couplings: relative and absolute. The interactions between the network nodes might be controlled by redirecting the emission between the condensates or by sending the phase information between nodes using resonant excitation. We discuss the conditions under which the proposed machine leads to a pure polariton simulator with pre-programmed couplings or results in a hybrid classical polariton simulator. We argue that the proposed architecture for the remote coupling control offers an improvement over geometrically coupled condensates in both accuracy and stability as well as increases versatility, range, and connectivity of spin Hamiltonians that can be simulated with polariton networks.

“Fuzzy” calculus: The link between quantum mechanics and discrete fractional operators

2020 ◽  
Vol 23 (3) ◽  
pp. 764-786
Author(s):  
Raoul R. Nigmatullin ◽  
Paolo Lino ◽  
Guido Maione
Keyword(s):  
Fractional Integral ◽  
Continuous Spin ◽  
First Order ◽  
Discrete Signals ◽  
Resonance Frequencies ◽  
Fuzzy Calculus ◽  
New Form ◽  
Hidden States ◽  
Extended Interpretation ◽  
Continuous Range

AbstractIn this paper, based on the “fuzzy” calculus covering the continuous range of operations between two couples of arithmetic operations (+, –) and (×, :), a new form of the fractional integral is proposed occupying an intermediate position between the integral and derivative of the first order. This new form of the fractional integral satisfies the C1 criterion according to the Ross classification. The new calculus is tightly related to the continuous values of the continuous spin S = 1 and can generalize the expression for the fractional values of the shifting discrete index. This calculus can be interpreted as the appearance of the hidden states corresponding to unobservable values of S = 1. Many well-known formulas can be generalized and receive a new extended interpretation. In particular, one can factorize any rectangle matrix and receive the “perfect” filtering formula that allows transforming any (deterministic or random) function to another arbitrary function and vice versa. This transformation can find unexpected applications in data transmission, cryptography and calibration of different gadgets and devices. One can also receive the hybrid (”centaur”) formula for the Fourier (F-) transformation unifying both expressions for the direct and inverse F-transformations in one mathematical unit. The generalized Dirichlet formula, which is obtained in the frame of the new calculus to allow selecting the desired resonance frequencies, will be useful in discrete signals processing, too. The basic formulas are tested numerically on mimic data.

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