Related papers: Minimal Doubling Fermion and Hermiticity

QCD is expected to have a rich phase structure. It is empirically known to be difficult to access low temperature and nonzero chemical potential $\mu$ regions in lattice QCD simulations. We address this issue in a lattice QCD with the use…

In non-Hermitian scattering problems the behavior of the transmission probability is very different from its Hermitian counterpart; it can exceed unity or even be divergent, since the non-Hermiticity can add or remove the probability to and…

The species doubling problem of the lattice fermion is resolved by introducing hopping interactions that mix left- and right-handed fermions around the momentum boundary. Approximate chiral symmetry is realized on the lattice. The deviation…

We introduce hermiticity as a new symmetry and show that when starting with a model which is Hermitian in the classical level, quantum corrections can break hermiticity while the theory stay physically acceptable. To show this, we…

We find that a broken PT-symmetry operator when interacts with suitable Hermitian operator, new system becomes completely un-broken PT symmetry. Further on varying the contribution of Hermiticity one can delay or control the broken…

The Feshbach-type reduction of the Hilbert space to the physically most relevant "model" subspace is suggested as a means of a formal unification of the standard quantum mechanics with its recently proposed PT symmetric modification. The…

A condition to have a real spectrum for a non-Hermitian Hamiltonian is given. As special cases, it is shown that the condition is reduced to Hermiticity and PT symmetric conditions.

For thermodynamics studies it is desirable to simulate two degenerate flavors and retain at least a remnant of the chiral symmetry. Staggered fermions can achieve this at the cost of rooting the determinant. Rooting can be avoided using…

Non-Hermitian quantum field theories are a promising tool to study open quantum systems. These theories preserve unitarity if PT-symmetry is respected, and in that case an equivalent Hermitian description exists via the so-called Dyson map.…

We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields.…

We investigate the connection between pseudo-Hermitian and Hermitian descriptions for a lattice, which consists of a set of isomorphic pseudo-Hermitian clusters. We show that such non-Hermitian systems can act as Hermitian systems. This is…

In recent reports, suggestions have been put forward to the effect that parity and time-reversal (PT) symmetry in quantum mechanics is incompatible with causality. It is shown here, in contrast, that PT-symmetric quantum mechanics is fully…

The local reggeon field theory is studied perturbatively taking advantage of the PT symmetry in the Hamiltonian formulation. In the lowest non trivial order we show that the pomeron interactions renormalize the slope. In the same order we…

We study perturbative quantum gravity in the first-order tetrad formalism. The lowest order action corresponds to Einstein-Cartan plus a parity-odd term, and is known in the literature as the Holst action. The coupling constant of the…

We study the Non-Hermitian quantum mechanics for the discrete system. This paper gives an exact analytic single-particle solution for an $N$-site tight-binding chain with two conjugated imaginary potentials $\pm i\gamma $ at two end sites,…

We construct a fermionic lattice model containing interacting spin-$\frac{1}{2}$ fermions with an $O(4)$ symmetry. In addition the model contains a $\mathbb{Z}_2$ chiral symmetry which prevents a fermion mass term. Our model is motivated by…

Lattice chiral perturbation theory is developed for Karsten-Wilczek fermions, a variant of minimally doubled fermions. As a first step, we consider the n\"aive fermionic field on lattice without its doubler. Once the symmetries of the…

PT-symmetric quantum theory was originally proposed with the aim of extending standard quantum theory by relaxing the Hermiticity constraint on Hamiltonians. However, no such extension has been formulated that consistently describes states,…

Using the method of continuous constructive renormalization group around the Fermi surface, it is proved that a jellium two-dimensional interacting system of Fermions at low temperature $T$ remains analytic in the coupling constant…

We present a purely diagrammatic derivation of the dual fermion scheme [Phys. Rev. B 77 (2008) 033101]. The derivation makes particularly clear that a similar scheme can be developed for an arbitrary reference system provided it has the…