Planar factors of proper homogeneous Lorentz transformations

Journal Article · Fri Feb 01 00:00:00 EST 1985 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.526667· OSTI ID:6147511

Fahnline, D E

This article discusses two constructions factoring proper homogeneous Lorentz transformations H into the product of two planar transformations. A planar transformation is a proper homogeneous Lorentz transformation changing vectors in a two-flat through the origin, called the transformation two-flat, into new vectors in the same two-flat and which leaves unchanged vectors in the orthogonal two-flat, called the pointwise invariant two-flat. The first construction provides two planar factors such that a given timelike vector lies in the transformation two-flat of one and in the pointwise invariant two-flat of the other; it leads to several basic conditions on the trace of H and to necessary and sufficient conditions for H to be planar. The second construction yields explicit formulas for the orthogonal factors of H when they exist and are unique, where two planar transformations are orthogonal if the transformation two-flat of one is the pointwise invariant two-flat of the other.

• Research Organization: The Pennsylvania State University, Altoona, Pennsylvania 16603
• OSTI ID: 6147511
• Journal Information: J. Math. Phys. (N.Y.); (United States), Vol. 26:2
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
LORENTZ TRANSFORMATIONS
FACTORIZATION
INVARIANCE PRINCIPLES
ORTHOGONAL TRANSFORMATIONS
ROTATION
SYMMETRY
VECTORS
MOTION
TENSORS
TRANSFORMATIONS
645301* - High Energy Physics- Particle Invariance Principles & Symmetries- General- (-1987)