Quantum Field Theory on Noncommutative Curved Space-times and Noncommutative Gravity

Subhamoy Singha Roy

doi:doi:10.11648/j.ajset.20210604.11

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Quantum Field Theory on Noncommutative Curved Space-times and Noncommutative Gravity

Subhamoy Singha Roy

Published in American Journal of Science, Engineering and Technology (Volume 6, Issue 4)

Received: 13 August 2021 Accepted: 27 August 2021 Published: 5 October 2021

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Abstract

In the noncommutative gauge-theoretical formulation of Langman and Szabo, apparently it appears that the torsion generated there is a generalized one i.e. it may containvector, axial vector and tensor components. However, when we transcribe the noncommutative gauge theory in terms of the Maxwell gauge theory using the Seiberg-Wittencorrespondence, we have noted that upto the first order in the noncommutative parameter, this effectively can be taken to induce a change in chiral anomaly and hence theassociated torsion should be an axial vector one. The noncommutative gauge symmetriesgive a very natural and explicit realizations of the mixing of space-time and internal symmetries which is a characteristic feature of the conventional gauge theory of gravity. Thegauge fields of the dimensionally reduced noncommutative Yang-Mills theory map ontoaWeitzenbӧck space time and a teleparallel theory of gravity arises as the zero curvature reduction of a Poincare gauge theory which induces an Einstein-Cartan space-timecharacterized by connections with both nonvanishing torsion and curvature. However, theteleparallelism equivalent of general relativity involves all the components of torsion. Thechiral anomaly in the Einstein-Cartan space U₄ is characterized by the topological invariants like Pontryagin density as well as the Nieh-Yan density when the latter term involvesthe length scale governed by the measure of noncommutativity of space points. It is shownthat we have discussed the equivalence of this formalism with noncommutative U(1) Yang Mills theory.

Published in	American Journal of Science, Engineering and Technology (Volume 6, Issue 4)
DOI	10.11648/j.ajset.20210604.11
Page(s)	89-93
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Noncommutative Space-Time, Teleparallel Gravity, Berry Phase

References

[1]	E. Langmann and R. Y. Szabo: Phys. Rev. D. 64, 104019 (2001).
[2]	R. Jackiw: Phys. Rev. Lett. 54, 109 (1985).
[3]	D. Banerjee and P. Bandyopadhyay: J. Math. Phys. 33, 990 (1992).
[4]	Y. S. Wu and A. Zee: Nucl. Phys. B 258, 157 (1985).
[5]	K. Sen and P. Bandyopadhyay: J. Math. Phys. 35, 2270 (1994).
[6]	N. Seiberg and E. Witten: J. High Energy Physics, 09, 032 (1999).
[7]	P. Bandyopadhyay: Geometry, Topology and Quantum Field Theory (Kluwer Academic, Dordrecht, (2003)).
[8]	E. W. Mielke: Ann. Phys. 219, 78 (1992).
[9]	P. Bandyopadhyay: Int. J. Mod. Phys. A 15, 1415 (2000).
[10]	S. Singha Roy and P. Bandyopadhyay: Europhysics Lett. 109, 48002 (2015).
[11]	S. Singha Roy: Theoretical Physics. 2, 141 (2017).
[12]	S. Singha Roy and P. Bandyopadhyay: Phys. Lett. A. 382, 1973 (2018).
[13]	P. Bandyopadhyay: Int. J. Mod. Phys. A 15, 4107 (2000).
[14]	S. Singha Roy: Phys. Astron. Int. J. 4, 30 (2020).
[15]	J. Fr¨ohlich, O. Grandjean and A. Recknagel: Supersymmetry and Noncommutative Geometry in Quantum Fields and Quantum Space Time, p 93, (Plenum Press, NewYork, (1996))
[16]	S. Singha Roy and P. Bandyopadhyay: Phys. Lett. A. 377, 2884 (2013).

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Subhamoy Singha Roy. (2021). Quantum Field Theory on Noncommutative Curved Space-times and Noncommutative Gravity. American Journal of Science, Engineering and Technology, 6(4), 89-93. https://doi.org/10.11648/j.ajset.20210604.11

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Subhamoy Singha Roy. Quantum Field Theory on Noncommutative Curved Space-times and Noncommutative Gravity. Am. J. Sci. Eng. Technol. 2021, 6(4), 89-93. doi: 10.11648/j.ajset.20210604.11

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AMA Style

Subhamoy Singha Roy. Quantum Field Theory on Noncommutative Curved Space-times and Noncommutative Gravity. Am J Sci Eng Technol. 2021;6(4):89-93. doi: 10.11648/j.ajset.20210604.11

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@article{10.11648/j.ajset.20210604.11,
  author = {Subhamoy Singha Roy},
  title = {Quantum Field Theory on Noncommutative Curved Space-times and Noncommutative Gravity},
  journal = {American Journal of Science, Engineering and Technology},
  volume = {6},
  number = {4},
  pages = {89-93},
  doi = {10.11648/j.ajset.20210604.11},
  url = {https://doi.org/10.11648/j.ajset.20210604.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajset.20210604.11},
  abstract = {In the noncommutative gauge-theoretical formulation of Langman and Szabo, apparently it appears that the torsion generated there is a generalized one i.e. it may containvector, axial vector and tensor components. However, when we transcribe the noncommutative gauge theory in terms of the Maxwell gauge theory using the Seiberg-Wittencorrespondence, we have noted that upto the first order in the noncommutative parameter, this effectively can be taken to induce a change in chiral anomaly and hence theassociated torsion should be an axial vector one. The noncommutative gauge symmetriesgive a very natural and explicit realizations of the mixing of space-time and internal symmetries which is a characteristic feature of the conventional gauge theory of gravity. Thegauge fields of the dimensionally reduced noncommutative Yang-Mills theory map ontoaWeitzenbӧck space time and a teleparallel theory of gravity arises as the zero curvature reduction of a Poincare gauge theory which induces an Einstein-Cartan space-timecharacterized by connections with both nonvanishing torsion and curvature. However, theteleparallelism equivalent of general relativity involves all the components of torsion. Thechiral anomaly in the Einstein-Cartan space U4 is characterized by the topological invariants like Pontryagin density as well as the Nieh-Yan density when the latter term involvesthe length scale governed by the measure of noncommutativity of space points. It is shownthat we have discussed the equivalence of this formalism with noncommutative U(1) Yang Mills theory.},
 year = {2021}
}

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TY  - JOUR
T1  - Quantum Field Theory on Noncommutative Curved Space-times and Noncommutative Gravity
AU  - Subhamoy Singha Roy
Y1  - 2021/10/05
PY  - 2021
N1  - https://doi.org/10.11648/j.ajset.20210604.11
DO  - 10.11648/j.ajset.20210604.11
T2  - American Journal of Science, Engineering and Technology
JF  - American Journal of Science, Engineering and Technology
JO  - American Journal of Science, Engineering and Technology
SP  - 89
EP  - 93
PB  - Science Publishing Group
SN  - 2578-8353
UR  - https://doi.org/10.11648/j.ajset.20210604.11
AB  - In the noncommutative gauge-theoretical formulation of Langman and Szabo, apparently it appears that the torsion generated there is a generalized one i.e. it may containvector, axial vector and tensor components. However, when we transcribe the noncommutative gauge theory in terms of the Maxwell gauge theory using the Seiberg-Wittencorrespondence, we have noted that upto the first order in the noncommutative parameter, this effectively can be taken to induce a change in chiral anomaly and hence theassociated torsion should be an axial vector one. The noncommutative gauge symmetriesgive a very natural and explicit realizations of the mixing of space-time and internal symmetries which is a characteristic feature of the conventional gauge theory of gravity. Thegauge fields of the dimensionally reduced noncommutative Yang-Mills theory map ontoaWeitzenbӧck space time and a teleparallel theory of gravity arises as the zero curvature reduction of a Poincare gauge theory which induces an Einstein-Cartan space-timecharacterized by connections with both nonvanishing torsion and curvature. However, theteleparallelism equivalent of general relativity involves all the components of torsion. Thechiral anomaly in the Einstein-Cartan space U4 is characterized by the topological invariants like Pontryagin density as well as the Nieh-Yan density when the latter term involvesthe length scale governed by the measure of noncommutativity of space points. It is shownthat we have discussed the equivalence of this formalism with noncommutative U(1) Yang Mills theory.
VL  - 6
IS  - 4
ER  -

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Author Information

Subhamoy Singha Roy

Department of Physics, JIS College of Engineering, Kalyani, Nadia, India

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Subhamoy Singha Roy. (2021). Quantum Field Theory on Noncommutative Curved Space-times and Noncommutative Gravity. American Journal of Science, Engineering and Technology, 6(4), 89-93. https://doi.org/10.11648/j.ajset.20210604.11

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ACS Style

Subhamoy Singha Roy. Quantum Field Theory on Noncommutative Curved Space-times and Noncommutative Gravity. Am. J. Sci. Eng. Technol. 2021, 6(4), 89-93. doi: 10.11648/j.ajset.20210604.11

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AMA Style

Subhamoy Singha Roy. Quantum Field Theory on Noncommutative Curved Space-times and Noncommutative Gravity. Am J Sci Eng Technol. 2021;6(4):89-93. doi: 10.11648/j.ajset.20210604.11

Copy | Download

@article{10.11648/j.ajset.20210604.11,
  author = {Subhamoy Singha Roy},
  title = {Quantum Field Theory on Noncommutative Curved Space-times and Noncommutative Gravity},
  journal = {American Journal of Science, Engineering and Technology},
  volume = {6},
  number = {4},
  pages = {89-93},
  doi = {10.11648/j.ajset.20210604.11},
  url = {https://doi.org/10.11648/j.ajset.20210604.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajset.20210604.11},
  abstract = {In the noncommutative gauge-theoretical formulation of Langman and Szabo, apparently it appears that the torsion generated there is a generalized one i.e. it may containvector, axial vector and tensor components. However, when we transcribe the noncommutative gauge theory in terms of the Maxwell gauge theory using the Seiberg-Wittencorrespondence, we have noted that upto the first order in the noncommutative parameter, this effectively can be taken to induce a change in chiral anomaly and hence theassociated torsion should be an axial vector one. The noncommutative gauge symmetriesgive a very natural and explicit realizations of the mixing of space-time and internal symmetries which is a characteristic feature of the conventional gauge theory of gravity. Thegauge fields of the dimensionally reduced noncommutative Yang-Mills theory map ontoaWeitzenbӧck space time and a teleparallel theory of gravity arises as the zero curvature reduction of a Poincare gauge theory which induces an Einstein-Cartan space-timecharacterized by connections with both nonvanishing torsion and curvature. However, theteleparallelism equivalent of general relativity involves all the components of torsion. Thechiral anomaly in the Einstein-Cartan space U4 is characterized by the topological invariants like Pontryagin density as well as the Nieh-Yan density when the latter term involvesthe length scale governed by the measure of noncommutativity of space points. It is shownthat we have discussed the equivalence of this formalism with noncommutative U(1) Yang Mills theory.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Quantum Field Theory on Noncommutative Curved Space-times and Noncommutative Gravity
AU  - Subhamoy Singha Roy
Y1  - 2021/10/05
PY  - 2021
N1  - https://doi.org/10.11648/j.ajset.20210604.11
DO  - 10.11648/j.ajset.20210604.11
T2  - American Journal of Science, Engineering and Technology
JF  - American Journal of Science, Engineering and Technology
JO  - American Journal of Science, Engineering and Technology
SP  - 89
EP  - 93
PB  - Science Publishing Group
SN  - 2578-8353
UR  - https://doi.org/10.11648/j.ajset.20210604.11
AB  - In the noncommutative gauge-theoretical formulation of Langman and Szabo, apparently it appears that the torsion generated there is a generalized one i.e. it may containvector, axial vector and tensor components. However, when we transcribe the noncommutative gauge theory in terms of the Maxwell gauge theory using the Seiberg-Wittencorrespondence, we have noted that upto the first order in the noncommutative parameter, this effectively can be taken to induce a change in chiral anomaly and hence theassociated torsion should be an axial vector one. The noncommutative gauge symmetriesgive a very natural and explicit realizations of the mixing of space-time and internal symmetries which is a characteristic feature of the conventional gauge theory of gravity. Thegauge fields of the dimensionally reduced noncommutative Yang-Mills theory map ontoaWeitzenbӧck space time and a teleparallel theory of gravity arises as the zero curvature reduction of a Poincare gauge theory which induces an Einstein-Cartan space-timecharacterized by connections with both nonvanishing torsion and curvature. However, theteleparallelism equivalent of general relativity involves all the components of torsion. Thechiral anomaly in the Einstein-Cartan space U4 is characterized by the topological invariants like Pontryagin density as well as the Nieh-Yan density when the latter term involvesthe length scale governed by the measure of noncommutativity of space points. It is shownthat we have discussed the equivalence of this formalism with noncommutative U(1) Yang Mills theory.
VL  - 6
IS  - 4
ER  -

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