Chiral Anomaly of Kogut-Susskind Fermion in the (3+1)-dimensional Hamiltonian formalism
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arXiv
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| Format: | Preprint |
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2025
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| author | Aoki, Shoto Kikukawa, Yoshio Takemoto, Toshinari |
| author_facet | Aoki, Shoto Kikukawa, Yoshio Takemoto, Toshinari |
| contents | We consider Kogut-Susskind fermions (also known as staggered fermions) in a $(3+1)$-dimensional Hamiltonian formalism and examine a chiral transformation and its associated chiral anomaly. The Hamiltonian of the massless Kogut-Susskind fermion has symmetry under the shift transformations in each space direction $S_k \, (k=1,2,3)$, and the product of the three shift transformations in particular (the odd shifts in general) may be regarded as a unitary discrete chiral transformation, modulo two-site translations. The hermitian part of the transformation kernel $Γ= i S_1 S_2 S_3$ can define an axial charge as $Q_A = (1/2)\sum_x χ^\dagger(x) \left(Γ+Γ^\dagger \right)χ(x)$, which is non-onsite, nonquantized, and commutative with the vector charge, analogous to $\tilde{Q}_A = (1/2) \sum_n ( χ^\dagger_n χ_{n+1} + χ^\dagger_{n+1} χ_{n} )$ for the $(1+1)$ dimensional Kogut-Susskind fermion. However, our $Q_A$ cannot be expressed in terms of any quantized charges in a generalized Onsager algebra. Although $Q_A$ does not commute with the fermion Hamiltonian in general when coupled to background link gauge fields, we show that they become commutative for a class of $U(1)$ link configurations carrying nontrivial magnetic and electric fields. We then verify numerically that the vacuum expectation value of $Q_A$ satisfies the anomalous conservation law of axial charge in the continuum two-flavor theory under an adiabatic evolution of the link gauge field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06198 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chiral Anomaly of Kogut-Susskind Fermion in the (3+1)-dimensional Hamiltonian formalism Aoki, Shoto Kikukawa, Yoshio Takemoto, Toshinari High Energy Physics - Lattice Strongly Correlated Electrons High Energy Physics - Theory We consider Kogut-Susskind fermions (also known as staggered fermions) in a $(3+1)$-dimensional Hamiltonian formalism and examine a chiral transformation and its associated chiral anomaly. The Hamiltonian of the massless Kogut-Susskind fermion has symmetry under the shift transformations in each space direction $S_k \, (k=1,2,3)$, and the product of the three shift transformations in particular (the odd shifts in general) may be regarded as a unitary discrete chiral transformation, modulo two-site translations. The hermitian part of the transformation kernel $Γ= i S_1 S_2 S_3$ can define an axial charge as $Q_A = (1/2)\sum_x χ^\dagger(x) \left(Γ+Γ^\dagger \right)χ(x)$, which is non-onsite, nonquantized, and commutative with the vector charge, analogous to $\tilde{Q}_A = (1/2) \sum_n ( χ^\dagger_n χ_{n+1} + χ^\dagger_{n+1} χ_{n} )$ for the $(1+1)$ dimensional Kogut-Susskind fermion. However, our $Q_A$ cannot be expressed in terms of any quantized charges in a generalized Onsager algebra. Although $Q_A$ does not commute with the fermion Hamiltonian in general when coupled to background link gauge fields, we show that they become commutative for a class of $U(1)$ link configurations carrying nontrivial magnetic and electric fields. We then verify numerically that the vacuum expectation value of $Q_A$ satisfies the anomalous conservation law of axial charge in the continuum two-flavor theory under an adiabatic evolution of the link gauge field. |
| title | Chiral Anomaly of Kogut-Susskind Fermion in the (3+1)-dimensional Hamiltonian formalism |
| topic | High Energy Physics - Lattice Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2511.06198 |