Chiral anomaly in Weyl systems: No violation of classical conservation laws

Morawetz, Klaus

doi:10.1016/j.physleta.2019.01.042

Cited by 3 publications

(2 citation statements)

References 42 publications

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“…From the asymmetry of F µν it follows that ∂ µ (j µ + i µ ) = 0, i.e., the current j µ + i µ is conserved. This is analogous to what happens with the chiral anomaly in Weyl systems, where the anomalous term can be rewritten as a current that satisfies the classical balance equation [13,14].…”

Section: Introductionmentioning

confidence: 82%

Quantum Uncertainty and Energy Flux in Extended Electrodynamics

Minotti

Modanese

2021

Quantum Reports

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In quantum theory, for a system with macroscopic wavefunction, the charge density and current density are represented by non-commuting operators. It follows that the anomaly I=∂tρ+∇·j, being essentially a linear combination of these two operators in the frequency-momentum domain, does not admit eigenstates and has a minimum uncertainty fixed by the Heisenberg relation ΔNΔϕ≃1, which involves the occupation number and the phase of the wavefunction. We give an estimate of the minimum uncertainty in the case of a tunnel Josephson junction made of Nb. Due to this violation of the local conservation of charge, for the evaluation of the e.m. field generated by the system it is necessary to use the extended Aharonov–Bohm electrodynamics. After recalling its field equations, we compute in general form the energy–momentum tensor and the radiation power flux generated by a localized oscillating source. The physical requirements that the total flux be positive, negative or zero yield some conditions on the dipole moment of the anomaly I.

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Section: Introductionmentioning

confidence: 82%

Quantum Uncertainty and Energy Flux in Extended Electrodynamics

Minotti

Modanese

2021

Quantum Reports

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“…Only exclusively one of them can be made normal. [ 67 ] The rate of chirality (5) can be rewritten explicitly either according to (3) in a non‐conservative form

\partial_{t} n_{5} + \nabla \cdot j = \frac{e^{2}}{2 π^{2} ℏ^{2}} E \cdot B

or by an anomalous current in a conservative form [ 68 ]

\partial_{t} n_{5} + \nabla \cdot (j + {boldj}_{anom}) = 0

…”

Section: Introductionmentioning

confidence: 99%

Exploring Anomalies by Many‐Body Correlations

Morawetz

2021

Physica Status Solidi (b)

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The quantum anomaly is written alternatively into a form violating conservation laws or as non‐gauge invariant currents seen explicitly on the example of chiral anomaly. By reinterpreting the many‐body averaging, the connection to Pauli–Villars regularization is established which gives the anomalous term a new interpretation as arising from quantum fluctuations by many‐body correlations at short distances. This is exemplified using an effective many‐body quantum potential which realizes quantum Slater sums by classical calculations. It is shown that these quantum potentials avoid the quantum anomaly but approach the same anomalous result by many‐body correlations. Consequently, quantum anomalies might be a shortcut way of single‐particle field theory to account for many‐body effects. This conjecture is also supported since the chiral anomaly can be derived by a completely conserving quantum kinetic theory. A measure for the quality of quantum potentials is suggested to describe these quantum fluctuations in the mean energy. The derived quantum potentials might be used to describe quantum simulations in classical terms.

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Weyl systems: anomalous transport normally explained

Morawetz

2019

Eur. Phys. J. B

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The chiral kinetic theory is derived from exact spinor mean field equations without symmetrybreaking terms for large classes of SU(2) systems with spin-orbit coupling. The influence of the Wigner function's off-diagonal elements is worked out. The decoupling of the diagonal elements renormalizes the drift according to Berry connection which is found as an expression of the meanfield, spin-orbit coupling and magnetic field. As special limit, Weyl systems are considered. The anomalous term ∼ EB in the balance of the chiral density appears consequently by an underlying conserving theory. The experimental observations of this term and the anomalous magneto-transport in solid-sate physics usually described by chiral kinetic theory are therefore not a unique signal for mixed axial-gravitational or triangle anomaly and no signal for the breaking of Lorentz-invariance. The source of the anomalous term is by two thirds the divergence of Berry curvature at zero momentum which can be seen as Dirac monopole and by one third the Dirac sea at infinite momentum. During the derivation of the chiral kinetic theory this source by the Dirac sea is transferred exclusively to the Dirac monopole due to the projection of the spinor Wigner functions to the chiral basis. The dynamical result is shown to suppress the anomalous term by two thirds. 75.76.+j, 05.60.Gg. 47.70.Nd,51.10.+y,

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Chiral anomaly in Weyl systems: No violation of classical conservation laws

Abstract: The anomalous term ∼ EB in the balance of the chiral density can be rewritten as quantum current in the classical balance of density. Therefore it does not violate classical conservation laws as it is claimed to be caused by quantum fluctuations.

Cited by 3 publications

References 42 publications

Quantum Uncertainty and Energy Flux in Extended Electrodynamics

Quantum Uncertainty and Energy Flux in Extended Electrodynamics

Exploring Anomalies by Many‐Body Correlations

Weyl systems: anomalous transport normally explained

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