Levi-Civita

During my undergraduate years, 1935-1939, in Honors Mathematics and Physics at the University of Toronto, increasingly, I became interested in mathematical physics, picking up some elementary quantum mechanics and relativity. My first encounter with Einstein s general relativity theory (GRT) was in the substantial treatise of Levi-Civita on differential geometry, which ends with a 150-page introduction to GRT. This is a beautiful theory, which I presented in lectures from 1950 in Toronto because it had become the dominant orthodoxy everyone should know ... 

Ordinary Raman scattering is determined by derivatives of the electric dipole-electric dipole tensor ae, and ROA by derivatives of cross-products of this tensor with the imaginary part G,e of the electric dipole-magnetic dipole tensor (the optical activity tensor) and the tensor Ae which results from the double contraction of the third rank electric dipole-electric quadrupole tensor Ae with the third rank antisymmetric unit tensor s of Levi-Civita. The electronic property tensors have the form ... 

In the case of a scalar field, the irreducible matrix D is a unit matrix, and drops out of. I1. For rotation through an angle S9t about the Cartesian axis ek, the rotational submatrix of the Lorentz matrix is given by Xkx = ()Hkekl]x], where el]k is the totally antisymmetric Levi-Civita tensor. For the one-electron Schrodinger field f, Noether s theorem defines three conserved components of a spatial axial vector,... 

Obviously the zero values of the angular variables define the unity matrix of the 50(4) group ea is the complete antisymmetric - Levi-Civita - tensor. The commutation properties of the infinitesimal operators defined in this manner are... 

THE ABSOLUTE DIFFERENTIAL CALCULUSfCALCULUS OFTENSORS), Tullio Levi-Civita. Great 20th-century mathematician s classic work on material necessary for mathematical grasp of theory of relativity. 452pp. 5X x 8Vt... 

The Levi-Civita symbol is denoted by iJk and is antisymmetric in all three indices. It is defined by... 

Its primary use in our applications is for expressing various commutation relations in compact form and performing calculations involving them. The Levi-Civita symbol also arises naturally in vector analysis. Thus, if et, i = 1, 2, 3, are three mutually perpendicular unit vectors defining a right-handed coordinate system, then... 

Levi-Civita symbol 85 Lewis number 66 light gathering power 31 light second 110 light year 110 line width 31... 

Tullio Levi-Civita, Professor of Rational Mechanics in the University of Rome, Fellow of R. Accademia Nazionale dei Lincei. Edited by Dr. Enrico Persico. Authorized translation by Miss M. Long, late Scholar of Girton College, Cambridge. 21s. net. 

By Tullio Levi-Civita. Authorized translation by John Dougall M.A., D.Sc. 2s. net. 

---