Physical equivalence on non-standard space and symmetries on infinitesimal- lattice spaces

Details Physical equivalence on non-standard space and symmetries on infinitesimal- lattice spaces Physical equivalence on non-standard space and symmetries on infinitesimal- lattice spaces

1999-10-19

arxiv.org/abs/hep-th/9910152v1

Nuovo Cim.B116:403-426,2001

Physics

High Energy Physics

High Energy Physics - Theory

35pages,Latex

Scientific paper

Equivalence in physics is discussed on the basis of experimental data accompanied by experimental errors. The introduction of the equivalence being consistent with the mathematical definition is possible only in theories constructed on non-standard number spaces by taking the experimental errors as infinitesimal numbers of the non-standard spaces. Following the idea for the equivalence (the physical equivalence), a new description of space-time in terms of infinitesimal-lattice points on non-standard real number space $\SR$ is proposed. The infinitesimal-lattice space, $^*{\cal L}$, is represented by the set of points on $\SR$ which are written by $l_n=n\SE$, where the infinitesimal lattice-spacing $\SE$ is determined by a non-standard natural number $^*N$ such that $\SE\equiv ^*N^{-1}$. By using infinitesimal neighborhoos ($\MON$) of real number $r$ on $\SL$ we can make a space $\SM$ which is isomorphic to $\RE$ as additive group. Therefore, every point on $(\SM)^N$ automatically has the internal confined-subspace $\MON$. A field theory on $\SL$ is proposed. To determine a projection from $\SL$ to $\SM$, a fundamental principle based on the physical equivalence is introduced. The physical equivalence is expressed by the totally equal treatment for indistinguishable quantities in our observations. Following the principle, we show that U(1) and SU(N) symmetries on the space $(\SM)^N$ are induced from the internal substructure $(\MON)^N$. Quantized state describing configuration space is constructed on $(\SM)^N$. We see that Lorentz and general relativistic transformations are also represented by operators which involve the U(1) and SU(N) internal symmetries.

Affiliated with

Also associated with

No associations

Rating

Physical equivalence on non-standard space and symmetries on infinitesimal- lattice spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Physical equivalence on non-standard space and symmetries on infinitesimal- lattice spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Physical equivalence on non-standard space and symmetries on infinitesimal- lattice spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-361817