Covariant Isotropic Constitutive Relations in Clifford's Geometric Algebra - Abstract

2001 ◽  
Vol 15 (3) ◽  
pp. 409-410
Author(s):  
P. Puska
Keyword(s):  
Geometric Algebra ◽  
Constitutive Relations ◽  
Clifford’S Geometric Algebra

Constitutive relations in classical optics in terms of geometric algebra

2015 ◽  
Vol 55 (2) ◽  
Author(s):  
Adolfas Dargys
Keyword(s):  
Wave Propagation ◽  
Electromagnetic Wave ◽  
Vector Space ◽  
Closed System ◽  
Geometric Algebra ◽  
Electromagnetic Wave Propagation ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Basis Vectors

To have a closed system, the Maxwell electromagnetic equations should be supplemented by constitutive relations which describe medium properties and connect primary fields (E, B) with secondary ones (D, H). J.W. Gibbs and O. Heaviside introduced the basis vectors {i, j, k} to represent the fields and constitutive relations in the three-dimensional vectorial space. In this paper the constitutive relations are presented in a form of Cl3,0 algebra which describes the vector space by three basis vectors {σ1, σ2, σ3} that satisfy Pauli commutation relations. It is shown that the classification of electromagnetic wave propagation phenomena with the help of constitutive relations in this case comes from the structure of Cl3,0 itself. Concrete expressions for classical constitutive relations are presented including electromagnetic wave propagation in a moving dielectric.

scholarly journals The double-padlock problem: Is secure classical information transmission possible without key exchange?

2014 ◽  
Vol 33 ◽  
pp. 1460355
Author(s):  
James M. Chappell ◽  
Lachlan J. Gunn ◽  
Derek Abbott
Keyword(s):  
Open Problem ◽  
Geometric Algebra ◽  
Mathematical Description ◽  
The Other ◽  
Mathematical Representation ◽  
Information Channel ◽  
Physical Realization ◽  
Classical Information ◽  
Reduced Complexity ◽  
Clifford’S Geometric Algebra

The idealized Kish-Sethuraman (KS) cipher is theoretically known to offer perfect security through a classical information channel. However, realization of the protocol is hitherto an open problem, as the required mathematical operators have not been identified in the previous literature. A mechanical analogy of this protocol can be seen as sending a message in a box using two padlocks; one locked by the Sender and the other locked by the Receiver, so that theoretically the message remains secure at all times. We seek a mathematical representation of this process, considering that it would be very unusual if there was a physical process with no mathematical description. We select Clifford's geometric algebra for this task as it is a natural formalism to handle rotations in spaces of various dimension. The significance of finding a mathematical description that describes the protocol, is that it is a possible step toward a physical realization having benefits in increased security with reduced complexity.

scholarly journals Analysis of Two-Player Quantum Games in an EPR Setting Using Clifford's Geometric Algebra

PLoS ONE ◽  
2012 ◽  
Vol 7 (1) ◽  
pp. e29015 ◽  
Author(s):  
James M. Chappell ◽  
Azhar Iqbal ◽  
Derek Abbott
Keyword(s):  
Geometric Algebra ◽  
Quantum Games ◽  
Clifford’S Geometric Algebra

scholarly journals Applications of Clifford’s Geometric Algebra

2013 ◽  
Vol 23 (2) ◽  
pp. 377-404 ◽  
Author(s):  
Eckhard Hitzer ◽  
Tohru Nitta ◽  
Yasuaki Kuroe
Keyword(s):  
Geometric Algebra ◽  
Clifford’S Geometric Algebra
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