Mathematical Physics

1012 Submissions

[5] viXra:1012.0052 [pdf] replaced on 17 Jan 2011

32 Point Groups of Three Dimensional Crystal Cells Described by 5 Bits

Authors: Giuliano Bettini
Comments: 9 pages, v3 in Italian, v2 in English, corrections to the tables, and a new table added.

There are 32 possible combinations of symmetry operations that define the external symmetry of crystals. These 32 possible combinations result in the 32 crystal classes. But for a radar engineer it is inevitable to associate "32" to "5 bits". I submit a tentative classification of the 32 crystal classes with a 5 bit classification, obviously with a (tentative) physical meaning of each bit. Each bit means a physical property.
Category: Mathematical Physics

[4] viXra:1012.0031 [pdf] replaced on 16 Dec 2010

Further on Non-Cartesian Systems

Authors: Elemér E Rosinger
Comments: 9 pages

A class of non-Cartesian physical systems, [7], are those whose composite state spaces are given by significantly extended tensor products. A more detailed presentation of the way such extended tensor products are constructed is offered, based on a step by step comparison with the construction of usual tensor products. This presentation clarifies the extent to which the extended tensor products are indeed more general than the usual ones.
Category: Mathematical Physics

[3] viXra:1012.0020 [pdf] submitted on 8 Dec 2010

Non-Cartesian Systems : an Open Problem

Authors: Elemer E Rosinger
Comments: 6 pages

The following open problem is presented and motivated : Are there physical systems whose state spaces do not compose according to either the Cartesian product, as classical systems do, or the usual tensor product, as quantum systems do ?
Category: Mathematical Physics

[2] viXra:1012.0014 [pdf] submitted on 4 Dec 2010

Four Departures in Mathematics and Physics

Authors: Elemer E Rosinger
Comments: 28 pages

Much of Mathematics, and therefore Physics as well, have been limited by four rather consequential restrictions. Two of them are ancient taboos, one is an ancient and no longer felt as such bondage, and the fourth is a surprising omission in Algebra. The paper brings to the attention of those interested these four restrictions, as well as the fact that each of them has by now ways, even if hardly yet known ones, to overcome them.
Category: Mathematical Physics

[1] viXra:1012.0002 [pdf] submitted on 1 Dec 2010

Some Comments on Projective Quadrics Subordinate to Pseudo-Hermitian Spaces

Authors: Arkadiusz Jadczyk
Comments: 7 pages, To appear in Advances in Applied Clifford Algebras

We study in some detail the structure of the projective quadric Q' obtained by taking the quotient of the isotropic cone in a standard pseudohermitian space Hp,q with respect to the positive real numbers R+ and, further, by taking the quotient ~Q = Q'/U(1). The case of signature (1. 1) serves as an illustration. ~Q is studied as a compactification of RxHp-1,q-1
Category: Mathematical Physics