On the Non-Existence of Unbounded Discrete Space-Time

Research Article

Year 2018, Volume: 1 Issue: 2, 52 - 55, 10.11.2018

n-scales introduce a generalization of time-scales that has been put forward

to unify continuous and discrete analyses in higher dimensions. In this paper we

investigate massive scalar field theory on a regular n-Scale. We have given the

modified field equation that is appropriate to this space-time structure and gave the

mode solutions. If the space-time is discrete and unbounded, we have found that

no massive scalar field can exist. Hence, we concluded that unbounded discrete

space-time cannot exist. If discrete space-time exists, it has to be bounded in each

dimension.

B. Aulbach and S. Hilger. Linear dynamic processes with inhomogeneous time scale. Non-Linear Dynamics and Quantum Dynamical Systems, 59:9--20, 1990.
M. Bohner and A. Peterson. Dynamic Equations on Time Scales An Introduction With Applications. Birkhauser, 2001.
M. Bohner and A. Peterson. Advances in Dynamic Equations on Time Scales. Birkhauser, 2003.
Martin Bohner and GS Guseino. Multiple integration on time scales. Dynamic systems and applications, 14(3/4):579, 2005.
Furkan Semih Dündar. The theory of n-scales. AIP Conference Proceedings, 1926(1):020014, 2018.
Bülent Oğur. Qualitative analysis of dynamical systems on time scales with initial time difference. Master's thesis, Gebze Institute of Technology, 2013.

Year 2018, Volume: 1 Issue: 2, 52 - 55, 10.11.2018

B. Aulbach and S. Hilger. Linear dynamic processes with inhomogeneous time scale. Non-Linear Dynamics and Quantum Dynamical Systems, 59:9--20, 1990.
M. Bohner and A. Peterson. Dynamic Equations on Time Scales An Introduction With Applications. Birkhauser, 2001.
M. Bohner and A. Peterson. Advances in Dynamic Equations on Time Scales. Birkhauser, 2003.
Martin Bohner and GS Guseino. Multiple integration on time scales. Dynamic systems and applications, 14(3/4):579, 2005.
Furkan Semih Dündar. The theory of n-scales. AIP Conference Proceedings, 1926(1):020014, 2018.
Bülent Oğur. Qualitative analysis of dynamical systems on time scales with initial time difference. Master's thesis, Gebze Institute of Technology, 2013.

There are 6 citations in total.

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Research Article
Authors	Furkan Semih Dündar Metin Arık
Publication Date	November 10, 2018
Published in Issue	Year 2018 Volume: 1 Issue: 2

APA	Dündar, F. S., & Arık, M. (2018). On the Non-Existence of Unbounded Discrete Space-Time. Mathematical Advances in Pure and Applied Sciences, 1(2), 52-55.
AMA	Dündar FS, Arık M. On the Non-Existence of Unbounded Discrete Space-Time. MAPAS. November 2018;1(2):52-55.
Chicago	Dündar, Furkan Semih, and Metin Arık. “On the Non-Existence of Unbounded Discrete Space-Time”. Mathematical Advances in Pure and Applied Sciences 1, no. 2 (November 2018): 52-55.
EndNote	Dündar FS, Arık M (November 1, 2018) On the Non-Existence of Unbounded Discrete Space-Time. Mathematical Advances in Pure and Applied Sciences 1 2 52–55.
IEEE	F. S. Dündar and M. Arık, “On the Non-Existence of Unbounded Discrete Space-Time”, MAPAS, vol. 1, no. 2, pp. 52–55, 2018.
ISNAD	Dündar, Furkan Semih - Arık, Metin. “On the Non-Existence of Unbounded Discrete Space-Time”. Mathematical Advances in Pure and Applied Sciences 1/2 (November2018), 52-55.
JAMA	Dündar FS, Arık M. On the Non-Existence of Unbounded Discrete Space-Time. MAPAS. 2018;1:52–55.
MLA	Dündar, Furkan Semih and Metin Arık. “On the Non-Existence of Unbounded Discrete Space-Time”. Mathematical Advances in Pure and Applied Sciences, vol. 1, no. 2, 2018, pp. 52-55.
Vancouver	Dündar FS, Arık M. On the Non-Existence of Unbounded Discrete Space-Time. MAPAS. 2018;1(2):52-5.