| Peer-Reviewed

Chiral Symmetry Breaking and Quark Mass Generation of Fermions

Received: 30 December 2021     Accepted: 18 January 2022     Published: 11 March 2022
Views:       Downloads:
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), 2022. 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.
Cite This Article
  • APA Style

    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

    Copy | Download

    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

    Copy | Download

    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

Author Information
  • Department of Physics, JIS College of Engineering, Kalyani, India

  • Sections