Absence of neutrinos on a lattice: (I). Proof by homotopy theory

doi:10.1016/0550-3213(81)90361-8

Nuclear Physics B

Volume 185, Issue 1, 13 July 1981, Pages 20-40

https://doi.org/10.1016/0550-3213(81)90361-8 Get rights and content

Abstract

It is shown, by a homotopy theory argument, that for a general class of fermion theories on a Kogut-Susskind lattice an equal number of species (types) of left- and right-handed Weyl particles (neutrinos) necessarily appears in the continuum limit. We thus present a no-go theorem for putting theories of the weak interaction on a lattice. One of the most important consequences of our no-go theorem is that is not possible, in strong interaction models, to solve the notorious species doubling problem of Dirac fermions on a lattice in a chirally invariant way.

References (12)

S.D. Drell et al.
Phys. Rev.
(1976)
T. Banks et al.
Nucl. Phys.
(1980)
M. Peskin
Cornell University preprints CLNS-395, -396
(1976)
J. Kogut et al.
Phys. Rev.
(1975)
L. Susskind
Phys. Rev.
(1977)
K.G. Wilson
Erice lecture notes
(1975)
L.H. Karsten et al.
Nucl. Phys.
(1981)
V. Baluni et al.
Phys. Rev.
(1976)

There are more references available in the full text version of this article.

Cited by (1636)

Non-Hermitian topological magnonics
2024, Physics Reports
Dissipation in mechanics, optics, acoustics, and electronic circuits is nowadays recognized to be not always detrimental but can be exploited to achieve non-Hermitian topological phases or properties with functionalities for potential device applications, ranging from sensors with unprecedented sensitivity, energy funneling, wave isolators, non-reciprocal signal amplification, to dissipation induced phase transition. As elementary excitations of ordered magnetic moments that exist in various magnetic materials, magnons are the information carriers in magnonic devices with low-energy consumption for reprogrammable logic, non-reciprocal communication, and non-volatile memory functionalities. Non-Hermitian topological magnonics deals with the engineering of dissipation and/or gain for non-Hermitian topological phases or properties in magnets that are not achievable in the conventional Hermitian scenario, with associated functionalities cross-fertilized with their electronic, acoustic, optic, and mechanic counterparts, such as giant enhancement of magnonic frequency combs, magnon amplification, (quantum) sensing of the magnetic field with unprecedented sensitivity, magnon accumulation, and perfect absorption of microwaves. In this review article, we address the unified approach in constructing magnonic non-Hermitian Hamiltonian, introduce the basic non-Hermitian topological physics, and provide a comprehensive overview of the recent theoretical and experimental progress towards achieving distinct non-Hermitian topological phases or properties in magnonic devices, including exceptional points, exceptional nodal phases, non-Hermitian magnonic SSH model, and non-Hermitian skin effect. We emphasize the non-Hermitian Hamiltonian approach based on the Lindbladian or self-energy of the magnonic subsystem but address the physics beyond it as well, such as the crucial quantum jump effect in the quantum regime and non-Markovian dynamics. We provide a perspective for future opportunities and challenges before concluding this article.
Topological nodal-point phononic systems
2024, Matter
Topological phonons in materials are associated with specific atomic lattice vibrations around the terahertz frequency ranges, offering a rich platform for studying various boson-related quasiparticles. Recently, researchers in topological physics have prioritized the search for materials that exhibit topological phonons. This review focuses on topological nodal-point phononic systems in three dimensions. On the one hand, the review highlights the classification, symmetry conditions, material realizations, unique properties, and potential applications of these topological nodal-point systems. On the other hand, it summarizes our guidelines for predicting such materials in three and two dimensions. This review can serve as a scholarly survey of recent developments in topological nodal-point phononic systems over the past 5 years as well as a guide for achieving other and designing new topological nodal-point phononic states in the future. It will undoubtedly benefit academic communities interested in materials science and condensed matter physics.
QCD running couplings and effective charges
2024, Progress in Particle and Nuclear Physics
We discuss our present knowledge of $α_{s}$ , the fundamental running coupling or effective charge of Quantum Chromodynamics (QCD). A precise understanding of the running of $α_{s} (Q^{2})$ at high momentum transfer, $Q$ , is necessary for any perturbative QCD calculation. Equally important, the behavior of $α_{s}$ at low $Q^{2}$ in the nonperturbative QCD domain is critical for understanding strong interaction phenomena, including the emergence of mass and quark confinement. The behavior of $α_{s} (Q^{2})$ at all momentum transfers also provides a connection between perturbative and nonperturbative QCD phenomena, such as hadron spectroscopy and dynamics. We first sketch the origin of the QCD coupling, the reason why its magnitude depends on the scale at which hadronic phenomena are probed, and the resulting consequences for QCD phenomenology. We then summarize latest measurements in both the perturbative and nonperturbative domains. New theory developments include the derivation of the universal nonperturbative behavior of $α_{s} (Q^{2})$ from both the Dyson–Schwinger equations and light-front holography. We also describe theory advances for the calculation of gluon and quark Schwinger functions in the nonperturbative domain and the relation of these quantities to $α_{s}$ . We conclude by highlighting how the nonperturbative knowledge of $α_{s}$ is now providing a parameter-free determination of hadron spectroscopy and structure, a central and long-sought goal of QCD studies.
Noncentrosymmetric two-dimensional Weyl semimetals in porous Si/Ge structures
2024, Journal of Physics Condensed Matter
Path integral approach to quantum anomalies in interacting models
2024, Physical Review B
Chiral Gauge Theory at the Boundary between Topological Phases
2024, Physical Review Letters

View all citing articles on Scopus

View full text

Absence of neutrinos on a lattice: (I). Proof by homotopy theory

Abstract

Phys. Rev.

Nucl. Phys.

Cornell University preprints CLNS-395, -396

Phys. Rev.

Phys. Rev.

Erice lecture notes

Nucl. Phys.

Phys. Rev.