Related papers: Fermions in odd space-time dimensions: back to bas…
Unconventional lattice fermions with high degeneracies beyond Weyl and Dirac fermions have attracted intensive attention in recent years. In this paper, attention is drawn to the pseudospin-1 Maxwell fermions and the $(2+1)$ dimensional…
We revisit the conformal anomaly for a Weyl fermion in four dimensions that has generated some debate recently. We employ a perturbative expansion for the metric around Minkowski space, dimensional regularization and a Breitenlohner--Maison…
Using the method of finite differences a scheme is proposed to solve exactly the Klein-Gordon and Dirac free field equations, in a (1+1)-dimensional lattice. The hamiltonian of the Dirac field is translational invariant, hermitian, avoids…
We study the implications of non-invertible chiral symmetry in a four-dimensional U(1) gauge theory coupled to massless fermions with electromagnetic $SL(2,\mathbb{Z})$ duality. This is done by deriving the Adler-Bell-Jackiw anomaly of…
We study boundary states for Dirac fermions in d=1+1 dimensions that preserve Abelian chiral symmetries, meaning that the left- and right-moving fermions carry different charges. We derive simple expressions, in terms of the fermion charge…
For the gamma-pion interaction, the perturbative expansion of the effective chiral Lagrangian (chi-PT) can be limited to terms quartic in momenta and masses (O(p4)), or to higher order. The abnormal intrinsic parity (chiral anomaly)…
We define chiral fermions in the presence of non-trivial gravitational and gauge background fields in the framework of locally covariant field theory. This allows to straightforwardly compute the chiral anomalies on non-compact Lorentzian…
In a Hamiltonian formalism we study chiral symmetry for lattice Fermions formulated in terms of Shockley surface states bound to a wall in an extra spatial dimension. For hadronic physics this provides a natural scheme for taking quark…
A generalized Lagrangian for the description of hadronic matter based on the linear $SU(3)_L \times SU(3)_R$ $\sigma$-model is proposed. Besides the baryon octet, the spin-0 and spin-1 nonets, a gluon condensate associated with broken scale…
The vacuum polarization due to chiral fermions on a 4--dimensional Euclidean lattice is calculated according to the overlap prescription. The fermions are coupled to weak and slowly varying background gauge and Higgs fields, and the…
The realization of global symmetries can depend on the geometry of the underlying space. In particular, compactification can lead to spontaneous breaking of such symmetries. Four-dimensional QCD with fundamental representation fermions…
We present a derivation of the recently discovered duality between the free massless (2+1)-dimensional Dirac fermion and QED$_3$. Our derivation is based on a regularized lattice model of the Dirac fermion and is similar to the more…
The most general theory of gravity in d-dimensions which leads to second order field equations for the metric has [(d-1)/2] free parameters. It is shown that requiring the theory to have the maximum possible number of degrees of freedom,…
Boundary conditions for a massless Dirac fermion in 2+1 dimensions where the space is a half-plane are discussed in detail. It is argued that linear boundary conditions that leave the Hamiltonian Hermitian generically break $C$ $P$ and $T$…
We calculate the electron self-energy in a magnetized QED plasma to the leading perturbative order in the coupling constant and to the linear order in an external magnetic field. We find that the chiral asymmetry of the normal ground state…
In this work we present symmetry transformations relating bosons to fermions which cannot be represented as a supersymmetric algebra. We present a symmetry transformation relating a complex scalar and a fermion in four dimensions and…
We investigate the emergence of geometric phases in chiral transformations within gauge theories coupled to fermions. We begin by analyzing the Schwinger model in (1+1) dimensions, where chiral symmetry is explicitly modified due to the…
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…
Three aspects of symmetry structure of lattice chiral fermion in the overlap formalism are discussed. By the weak coupling expansion of the overlap Dirac operator, the axial anomaly associated to the chiral transformation proposed by…
We consider a matrix space based on the spin degree of freedom, describing both a Hilbert state space, and its corresponding symmetry operators. Under the requirement that the Lorentz symmetry be kept, at given dimension, scalar symmetries,…