Absence of neutrinos on a lattice

Nielsen, Holger Bech; Ninomiya, M.

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

Cited by 1,582 publications

(1,057 citation statements)

References 5 publications

Supporting

Mentioning

1,030

Contrasting

Unclassified

Order By: Relevance

“…In particular, when the Dirac equation is naively discretized, one faces the fermion doubling problem. Instead of one physical fermion, one encounters additional 2 d − 1 species [81]. In his original formulation of lattice QCD, Wilson has explicitly removed the unwanted doubler fermions by giving them a large mass at the order of the cut-off 1 a .…”

Section: Lattice Fermions Hopping In a Classical Electromagnetic Backmentioning

confidence: 99%

Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories

2013

View full text Add to dashboard Cite

Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, Abelian U(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev's toric code is a Z(2) lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge theory of the strong interactions between quarks and gluons, is nonperturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real-time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should allow us to address very challenging problems, ranging from confinement and deconfinement, or chiral symmetry breaking and its restoration at finite baryon density, to color superconductivity and the real-time evolution of heavy-ion collisions, first in simpler model gauge theories and ultimately in QCD.

show abstract

Section: Lattice Fermions Hopping In a Classical Electromagnetic Backmentioning

confidence: 99%

Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories

2013

View full text Add to dashboard Cite

show abstract

“…For our purpose of establishing the desired connection to a sigma-model it is most convenient to evaluate these expressions in position space. Here the matrix B −1 is block diagonal and explicitly given by 10) where the notation (Φ * n ) 0 = Φ 0 n , (Φ * n ) i = −Φ i n was used andB was defined in eq. (2.9).…”

Section: Jhep09(2007)041mentioning

confidence: 99%

“…Within this model an exact lattice chiral symmetry can be established while suppressing the fermion doublers at the same time. This is possible despite of the Nielsen-Ninomiya theorem [10], since the established lattice chiral symmetry is not the continuum chiral symmetry itself, but recovers the latter symmetry only in the continuum limit. We consider here a Higgs-Yukawa model including only the two heaviest fermions, i.e.…”

Section: Introductionmentioning

confidence: 99%

The phase structure of a chirally invariant lattice Higgs-Yukawa model for small and for large values of the Yukawa coupling constant

Gerhold¹,

Jansen²

2007

J. High Energy Phys.

View full text Add to dashboard Cite

We consider a chirally invariant lattice Higgs-Yukawa model based on the Neuberger overlap operator D (ov) . As a first step towards the eventual determination of Higgs mass bounds we study the phase diagram of the model analytically in the large N flimit. We present an expression for the effective potential at tree-level in the regime of small Yukawa and quartic coupling constants and determine the order of the phase transitions. In the case of strong Yukawa couplings the model effectively becomes an O(4)-symmetric nonlinear σ-model for all values of the quartic coupling constant. This leads to the existence of a symmetric phase also in the regime of large values of the Yukawa coupling constant. On finite and small lattices, however, strong finite volume effects prevent the expectation value of the Higgs field from vanishing thus obscuring the existence of the symmetric phase at strong Yukawa couplings.

show abstract

“…Because the lattice itself provides a gauge-invariant regularization, any system that can be realized on the lattice cannot be anomalous. That this is true follows immediately from fermion doubling [17]. For example, a purely 2+1d lattice system of fermions with relativistic dispersion necessarily contains an even number of (low energy) Dirac fermions in the absence of P and T breaking.…”

mentioning

confidence: 99%

Topological insulators avoid the parity anomaly

Mulligan

Burnell

2013

Phys. Rev. B

View full text Add to dashboard Cite

The surface of a 3+1d topological insulator hosts an odd number of gapless Dirac fermions when charge conjugation and time-reversal symmetries are preserved. Viewed as a purely 2+1d system, this surface theory would necessarily explicitly break parity and time-reversal when coupled to a fluctuating gauge field. Here we explain why such a state can exist on the boundary of a 3+1d system without breaking these symmetries, even if the number of boundary components is odd. This is accomplished from two complementary perspectives: topological quantization conditions and regularization. We first discuss the conditions under which (continuous) large gauge transformations may exist when the theory lives on a boundary of a higher-dimensional spacetime. Next, we show how the higher-dimensional bulk theory is essential in providing a parity-invariant regularization of the theory living on the lower-dimensional boundary or defect.

show abstract

Absence of neutrinos on a lattice

Cited by 1,582 publications

References 5 publications

Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories

Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories

The phase structure of a chirally invariant lattice Higgs-Yukawa model for small and for large values of the Yukawa coupling constant

Topological insulators avoid the parity anomaly

Contact Info

Product

Resources

About