Chiral Symmetry Breaking and Quark Mass Generation of Fermions

Subhamoy Singha Roy

doi:doi:10.11648/j.ep.20220601.11

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Chiral Symmetry Breaking and Quark Mass Generation of Fermions

Subhamoy Singha Roy

Published in Engineering Physics (Volume 6, Issue 1)

Received: 30 December 2021 Accepted: 18 January 2022 Published: 11 March 2022

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Abstract

It has been shown earlier that the measure of entanglement between two nearest neighbor spins ina spin system given by concurrence is related to the Berry phase acquired by the ground state whenit evolves in a closed path. The significant aspect of this quantization procedure is that it has the specific property of coordinate independence and is governed by geometry. It has been pointed out that this formulation is equivalent to the geometric quantization where the Hermitian line bundle takes a significant role. Also it has been shown that this procedure has its relevance in the quantization of a fermionin the framework of Nelson’s stochastic quantization procedurewhen a spinning particle is endowed with an internal degree of freedom through a direction vector (vortex line) which is topologically equivalent to a magnetic flux line. In view of this specific feature of the role of magnetic field in all these formulations of quantization procedure it is expected that the peculiar property of entanglement in quantum mechanics has its relevance with the magnetic flux associated with the quantization procedure. In a seminal paper Berry has shown that when a quantum particle moves in a closed path in a parameter space it attains a geometric phase apart from the dynamical phase. It is here argued that as the Berry phase is related to chiral anomalyentanglement leads to topological mass generation through this anomaly. It is pointed out thatwhen a spin 1 state is considered to be an entangled system of two spin 1/2 states, the maximallyentangled state corresponds to the longitudinal component and gives rise to mass leading to gaugesymmetry breaking.

Published in	Engineering Physics (Volume 6, Issue 1)
DOI	10.11648/j.ep.20220601.11
Page(s)	1-4
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), 2024. Published by Science Publishing Group

Keywords

Berry Phase, Chiral Anomaly, Berry Phase, Quantization, Topological Mass Generation, Gauge Symmetry, Entanglement

References

[1]	Banerjee, D. & Bandyopadhyay, P. (1992). Topological aspects of a fermion, chiral anomaly, and Berry phase. J. Math. Phys., 33, 990. https://doi.org/10.1063/1.529752.
[2]	Roy, A. & Bandyopadhyay, P. Topological aspects of a fermion and the chiral anomaly.(1989). J. Math. Phys., 30, 2366. https://doi.org/10.1063/1.528566.
[3]	Bandyopadhyay, P. & Hajra, K. (1987). Stochastic quantization of a Fermi field: Fermions as solitons. J. Math. Phys., 28, 711. https://doi.org/10.1063/1.527606.
[4]	Bandyopadhyay, P. (2000). Topological Aspects of Chiral Anomaly, Origin of Mass and Electroweak Theory. Int. J. Mod. Phys. A, 15 4107. DOI: 10.1142/S0217751X00002972.
[5]	Bandyopadhyay, P. (2010). The geometric phase and the spin-statistics relation. Proc. Roy. Soc. (London) A, 466 2917. https://www.jstor.org/stable/20779285.
[6]	Berry, M. V. & Robbins, J. M. (1997). In distinguishability for quantum particles: spin, statistics and the geometric phase. Proc. Roy. Soc. (London) A 453, 1771. https://doi.org/10.1098/rspa.1997.0096.
[7]	Goswami, G. & Bandyopadhyay, P. (1997). Fermion doubling on a lattice and topological aspects of chiral anomaly. J. Math. Phys., 38, 4451. https://doi.org/10.1063/1.532136.
[8]	Bandyopadhyay, P. (2000). Conformal field theory, quantum group and berry phase. Int. J. Mod. Phys. A, 15, 1415. https://doi.org/10.1142/S0217751X0000063X.
[9]	Bandyopadhyay, P. (2011). Anisotropic spin system, quantized Dirac monopole and the Berry phase. Proc. Roy. Soc. (London) A, 467, 427. doi: 10.1098/rspa.2010.0266.
[10]	Goswami, G. & and Bandyopadhyay, P. (1995). Spin system, gauge theory, and renormalization group equation. J. Math. Phys. 34,749. https://doi.org/10.1063/1.530218.
[11]	Bandyopadhyay, P. (2017) and (2010). The geometric phase and the spin-statistics relation. Proc. Roy. Soc (Londan) A. 466. https://doi.org/10.1098/rspa.2010.0042.
[12]	Roy, S. Singha. (2017). DNA Molecule as a Spin System and the Symmetric Top Model. Theoretical Physics, 2, Number 3, 141. DOI: 10.22606/TP.2017.23005.
[13]	Roy, A. & Bandyopadhyay, P. (1989). Topological aspects of a fermion and the chiral anomaly. J. Math. Phys. 30, 2366. https://doi.org/10.1063/1.528566.
[14]	Bandyopadhyay, A., Chatterjee, P. & Bandyopadhyay, P. (1986). SL (2, C) Gauge theory, N=1 Supergravity and Torsion. Gen. Rel. Grav 18, 1293. DOI: 10.1007/BF00763446.
[15]	Roy, S. Singha. & Bandyopadhyay, P. (2018). Quantum perspective on the localized strand separation and cyclization of DNA double helix. Phys. Lett. A 382, 1973. 10.1016/j.physleta.2018.04.048.
[16]	Milman, P. & Mosseri, D. (2003). Topological Phase for Entangled Two-Qubit States. Phys. Rev. Lett., 90, 230403. https://doi.org/10.1103/PhysRevLett.90.230403.
[17]	Bandyopadhyay, P. (2009). Topological mass generation, electroweak symmetry breaking and baryogenesis. Mod. Phys. Lett. A, 24, 703. https://doi.org/10.1142/S0217732309028643.
[18]	Nelson, P. (1999). Transport of torsional stress in DNA. Proc. Natl. Acad. Sci (USA) 96, 14342. https://doi.org/10.1073/pnas.96.25.14342.

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Subhamoy Singha Roy. (2022). Chiral Symmetry Breaking and Quark Mass Generation of Fermions. Engineering Physics, 6(1), 1-4. https://doi.org/10.11648/j.ep.20220601.11

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ACS Style

Subhamoy Singha Roy. Chiral Symmetry Breaking and Quark Mass Generation of Fermions. Eng. Phys. 2022, 6(1), 1-4. doi: 10.11648/j.ep.20220601.11

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AMA Style

Subhamoy Singha Roy. Chiral Symmetry Breaking and Quark Mass Generation of Fermions. Eng Phys. 2022;6(1):1-4. doi: 10.11648/j.ep.20220601.11

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@article{10.11648/j.ep.20220601.11,
  author = {Subhamoy Singha Roy},
  title = {Chiral Symmetry Breaking and Quark Mass Generation of Fermions},
  journal = {Engineering Physics},
  volume = {6},
  number = {1},
  pages = {1-4},
  doi = {10.11648/j.ep.20220601.11},
  url = {https://doi.org/10.11648/j.ep.20220601.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ep.20220601.11},
  abstract = {It has been shown earlier that the measure of entanglement between two nearest neighbor spins ina spin system given by concurrence is related to the Berry phase acquired by the ground state whenit evolves in a closed path. The significant aspect of this quantization procedure is that it has the specific property of coordinate independence and is governed by geometry. It has been pointed out that this formulation is equivalent to the geometric quantization where the Hermitian line bundle takes a significant role. Also it has been shown that this procedure has its relevance in the quantization of a fermionin the framework of Nelson’s stochastic quantization procedurewhen a spinning particle is endowed with an internal degree of freedom through a direction vector (vortex line) which is topologically equivalent to a magnetic flux line. In view of this specific feature of the role of magnetic field in all these formulations of quantization procedure it is expected that the peculiar property of entanglement in quantum mechanics has its relevance with the magnetic flux associated with the quantization procedure. In a seminal paper Berry has shown that when a quantum particle moves in a closed path in a parameter space it attains a geometric phase apart from the dynamical phase. It is here argued that as the Berry phase is related to chiral anomalyentanglement leads to topological mass generation through this anomaly. It is pointed out thatwhen a spin 1 state is considered to be an entangled system of two spin 1/2 states, the maximallyentangled state corresponds to the longitudinal component and gives rise to mass leading to gaugesymmetry breaking.},
 year = {2022}
}

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TY  - JOUR
T1  - Chiral Symmetry Breaking and Quark Mass Generation of Fermions
AU  - Subhamoy Singha Roy
Y1  - 2022/03/11
PY  - 2022
N1  - https://doi.org/10.11648/j.ep.20220601.11
DO  - 10.11648/j.ep.20220601.11
T2  - Engineering Physics
JF  - Engineering Physics
JO  - Engineering Physics
SP  - 1
EP  - 4
PB  - Science Publishing Group
SN  - 2640-1029
UR  - https://doi.org/10.11648/j.ep.20220601.11
AB  - It has been shown earlier that the measure of entanglement between two nearest neighbor spins ina spin system given by concurrence is related to the Berry phase acquired by the ground state whenit evolves in a closed path. The significant aspect of this quantization procedure is that it has the specific property of coordinate independence and is governed by geometry. It has been pointed out that this formulation is equivalent to the geometric quantization where the Hermitian line bundle takes a significant role. Also it has been shown that this procedure has its relevance in the quantization of a fermionin the framework of Nelson’s stochastic quantization procedurewhen a spinning particle is endowed with an internal degree of freedom through a direction vector (vortex line) which is topologically equivalent to a magnetic flux line. In view of this specific feature of the role of magnetic field in all these formulations of quantization procedure it is expected that the peculiar property of entanglement in quantum mechanics has its relevance with the magnetic flux associated with the quantization procedure. In a seminal paper Berry has shown that when a quantum particle moves in a closed path in a parameter space it attains a geometric phase apart from the dynamical phase. It is here argued that as the Berry phase is related to chiral anomalyentanglement leads to topological mass generation through this anomaly. It is pointed out thatwhen a spin 1 state is considered to be an entangled system of two spin 1/2 states, the maximallyentangled state corresponds to the longitudinal component and gives rise to mass leading to gaugesymmetry breaking.
VL  - 6
IS  - 1
ER  -

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Author Information

Subhamoy Singha Roy

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

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Subhamoy Singha Roy. (2022). Chiral Symmetry Breaking and Quark Mass Generation of Fermions. Engineering Physics, 6(1), 1-4. https://doi.org/10.11648/j.ep.20220601.11

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ACS Style

Subhamoy Singha Roy. Chiral Symmetry Breaking and Quark Mass Generation of Fermions. Eng. Phys. 2022, 6(1), 1-4. doi: 10.11648/j.ep.20220601.11

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AMA Style

Subhamoy Singha Roy. Chiral Symmetry Breaking and Quark Mass Generation of Fermions. Eng Phys. 2022;6(1):1-4. doi: 10.11648/j.ep.20220601.11

Copy | Download

@article{10.11648/j.ep.20220601.11,
  author = {Subhamoy Singha Roy},
  title = {Chiral Symmetry Breaking and Quark Mass Generation of Fermions},
  journal = {Engineering Physics},
  volume = {6},
  number = {1},
  pages = {1-4},
  doi = {10.11648/j.ep.20220601.11},
  url = {https://doi.org/10.11648/j.ep.20220601.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ep.20220601.11},
  abstract = {It has been shown earlier that the measure of entanglement between two nearest neighbor spins ina spin system given by concurrence is related to the Berry phase acquired by the ground state whenit evolves in a closed path. The significant aspect of this quantization procedure is that it has the specific property of coordinate independence and is governed by geometry. It has been pointed out that this formulation is equivalent to the geometric quantization where the Hermitian line bundle takes a significant role. Also it has been shown that this procedure has its relevance in the quantization of a fermionin the framework of Nelson’s stochastic quantization procedurewhen a spinning particle is endowed with an internal degree of freedom through a direction vector (vortex line) which is topologically equivalent to a magnetic flux line. In view of this specific feature of the role of magnetic field in all these formulations of quantization procedure it is expected that the peculiar property of entanglement in quantum mechanics has its relevance with the magnetic flux associated with the quantization procedure. In a seminal paper Berry has shown that when a quantum particle moves in a closed path in a parameter space it attains a geometric phase apart from the dynamical phase. It is here argued that as the Berry phase is related to chiral anomalyentanglement leads to topological mass generation through this anomaly. It is pointed out thatwhen a spin 1 state is considered to be an entangled system of two spin 1/2 states, the maximallyentangled state corresponds to the longitudinal component and gives rise to mass leading to gaugesymmetry breaking.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Chiral Symmetry Breaking and Quark Mass Generation of Fermions
AU  - Subhamoy Singha Roy
Y1  - 2022/03/11
PY  - 2022
N1  - https://doi.org/10.11648/j.ep.20220601.11
DO  - 10.11648/j.ep.20220601.11
T2  - Engineering Physics
JF  - Engineering Physics
JO  - Engineering Physics
SP  - 1
EP  - 4
PB  - Science Publishing Group
SN  - 2640-1029
UR  - https://doi.org/10.11648/j.ep.20220601.11
AB  - It has been shown earlier that the measure of entanglement between two nearest neighbor spins ina spin system given by concurrence is related to the Berry phase acquired by the ground state whenit evolves in a closed path. The significant aspect of this quantization procedure is that it has the specific property of coordinate independence and is governed by geometry. It has been pointed out that this formulation is equivalent to the geometric quantization where the Hermitian line bundle takes a significant role. Also it has been shown that this procedure has its relevance in the quantization of a fermionin the framework of Nelson’s stochastic quantization procedurewhen a spinning particle is endowed with an internal degree of freedom through a direction vector (vortex line) which is topologically equivalent to a magnetic flux line. In view of this specific feature of the role of magnetic field in all these formulations of quantization procedure it is expected that the peculiar property of entanglement in quantum mechanics has its relevance with the magnetic flux associated with the quantization procedure. In a seminal paper Berry has shown that when a quantum particle moves in a closed path in a parameter space it attains a geometric phase apart from the dynamical phase. It is here argued that as the Berry phase is related to chiral anomalyentanglement leads to topological mass generation through this anomaly. It is pointed out thatwhen a spin 1 state is considered to be an entangled system of two spin 1/2 states, the maximallyentangled state corresponds to the longitudinal component and gives rise to mass leading to gaugesymmetry breaking.
VL  - 6
IS  - 1
ER  -

Copy | Download