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Chiral Symmetry Breaking and Quark Mass Generation of Fermions

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.

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

APA Style

Subhamoy Singha Roy. (2022). Chiral Symmetry Breaking and Quark Mass Generation of Fermions. Engineering Physics, 6(1), 1-4.

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

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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