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Full-Text Articles in Physics
On Levi-Civita’S Alternating Symbol, Schouten’S Alternating Unit Tensors, Cpt, And Quantization, Evert Jan Post, Stan Sholar, Hooman Rahimizadeh, Michael Berg
On Levi-Civita’S Alternating Symbol, Schouten’S Alternating Unit Tensors, Cpt, And Quantization, Evert Jan Post, Stan Sholar, Hooman Rahimizadeh, Michael Berg
Mathematics Faculty Works
The purpose of the present article is to demonstrate that by adopting a unifying differential geometric perspective on certain themes in physics one reaps remarkable new dividends in both microscopic and macroscopic domains. By replacing algebraic objects by tensor-transforming objects and introducing methods from the theory of differentiable manifolds at a very fundamental level we obtain a Kottler-Cartan metric-independent general invariance of the Maxwell field, which in turn makes for a global quantum superstructure for Gauss-Amp`ere and Aharonov-Bohm “quantum integrals.” Beyond this, our approach shows that postulating a Riemannian metric at the quantum level is an unnecessary concept and our …
Exotic Statistics For Strings In 4d Bf Theory, John C. Baez, Derek K. Wise, Alissa S. Crans
Exotic Statistics For Strings In 4d Bf Theory, John C. Baez, Derek K. Wise, Alissa S. Crans
Mathematics Faculty Works
After a review of exotic statistics for point particles in 3d BF theory, and especially 3d quantum gravity, we show that string-like defects in 4d BF theory obey exotic statistics governed by the 'loop braid group'. This group has a set of generators that switch two strings just as one would normally switch point particles, but also a set of generators that switch two strings by passing one through the other. The first set generates a copy of the symmetric group, while the second generates a copy of the braid group. Thanks to recent work of Xiao-Song Lin, we can …
Mach’S Principle In A Mixed Newton-Einstein Context, Evert Jan Post, Michael Berg
Mach’S Principle In A Mixed Newton-Einstein Context, Evert Jan Post, Michael Berg
Mathematics Faculty Works
A closed physical space, in conjunction with scalar versus pseudo scalar distinctions, and an accordingly adapted Gauss theorem, reveal unexpected perspectives on Mach's principle, the mass-energy theorem, and a bonus insight into the nature of the solutions of the Einstein field equations of gravity.