Clifford algebras

A set of matrices satisfying Eq. (9-254), together with all their products and linear combinations with complex coefficient is called a Clifford algebra. The basic facts concerning such algebras are the following 11... 

Clebsch-Gordon coefficients, 404 Clifford algebra, 520 Closed trajectory, 328 Closest approach, distance of, 6 Code... 

The relations 04,0 1 + 0.104- = 2Ski, Dirac representation. In a phase space language, employing Weyl quantisation, this Hamiltonian can be written as (see, e.g., (Dimassi and Sjostrand, 1999))... 

First we have a brief review on Heisenberg algebra and Clifford algebra and their representations. The general reference is [43, 9.13]... 

Remark 8.5. In the literature, the defining relation (8.3) for the Clifford algebra is... 

Next theorem asserts that 0 o H X ) becomes a representation space of the Heisen-berg/Clifford algebra by Pa[i] and P/ [—z]. 

On the 0(3) level, vacuum gauge theory is defined by a Clifford algebra... 

PR. Holland, A. Kyprianidis, and J. P. Vigier, Causal phase space approach to fermion theories understood through Clifford algebras, Lett. Math. Phys. 12(2), 101-110 (1986). 

Spin is typically treated as a quantum phenomenon an easily accesible and readable account is given by Ohanian [107]. However, the possibility that spin may be a phenomenon with classical overtones has been a recurrent one [79,107-111,122-124], The connection between the classical polarization of light and quantum mechanics was noted long ago by Fano [125], while the connection between polarization and Clifford algebra for spinors was noted more recently [126], Finally, some philosophers have suggested that spin is a mere property of space [127],... 

We overview our valence bond (VB) approach to the ir-electron Pariser-Parr-Pople (PPP) model Hamiltonians referred to sis the PPP-VB method. It is based on the concept of overlap enhanced atomic orbitals (OEAOs) that characterizes modern ab initio VB methods and employs the techniques afforded by the Clifford algebra unitary group approach (CAUGA) to carry out actual computations. We present a sample of previous results, sis well sis some new ones, to illustrate the ability of the PPP-VB method to provide a highly correlated description of the ir-electron PPP model systems, while relying on conceptusilly very simple wave functions that involve only a few covalent structures. 

D. Hestenes and G. Sobczyk, Clifford Algebra to Geometric Calculus, Reidel, Dordrecht, 1984. 

P. Lounesto, Clifford Algebras and Spinors, Cambridge University Press, Cambridge, England, 2001. 

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