相关论文: The Reeh-Schlieder Property for the Dirac Field on…

We study the Dirac--Klein-Gordon system in $1+2$ spacetime dimensions. We show global existence of the solutions, as well as sharp time decay and linear scattering. One key advance is that we provide the first asymptotic stability result…

A generalization of the Dirac field equation in three-dimensional Minkowski space-time to the case of the $\bar{SL}(3,R)$ $\subset$ $\bar{SA}(3,R)$ symmetry is considered. Constraints that ensure a correct physical interpretation of the…

We describe a Riemannian space class where the second Dirac operator arises and prove that the operator is always equivalent to a standard Dirac one. The particle state in this gravitational field is degenerate to some extent and we…

Let S(x) be a massless scalar quantum field which lives on the three-dimensional hyperboloid $xx= (x^0)^2-(x^1)^2-(x^2)^2-(x^3)^2=-1.$ The classical action is assumed to be $(\hbar=1=c)(8\pi e^2)^{-1}\int dx g^{ik}\partial_i S\partial_k S$,…

We show that a relativistic version of Schrodinger cat states, here called Dirac cat states, can be built in relativistic Landau levels when an external magnetic field couples to a relativistic spin 1/2 charged particle. Under suitable…

On a static spacetime, the solutions of the Dirac equation are generated by a time-independent Hamiltonian. We study this Hamiltonian and characterize the split into positive and negative energy. We use it to find explicit expressions for…

We study a formal extension of the Dirac equation in the framework of a non-commutative two-sheeted space-time. It is shown that this approach naturally extends the classical Dirac theory by doubling the number of fermionic states, which…

We generalize the original derivation of transparent, static Schroedinger potentials by Kay and Moses, to obtain a large class of time-dependent transparent Dirac potentials in one spatial dimension. They contain all known transparent…

The tetrad gauge invariant theory of the free Dirac field in two special moving charts of the de Sitter spacetime is investigated pointing out the operators that commute with the Dirac one. These are the generators of the symmetry…

Quantum field theory on curved spacetimes lacks an obvious distinguished vacuum state. We review a recent no-go theorem that establishes the impossibility of finding a preferred state in each globally hyperbolic spacetime, subject to…

There are constructed exact solutions of the quantum-mechanical Dirac equation for a spin S=1/2 particle in Riemannian space of constant negative curvature, hyperbolic Lobachevsky space, in presence of an external magnetic field, analogue…

We establish the Kato-type smoothing property, i.e., global-in-time smoothing estimates with homogeneous weights, for the Schr\"odinger equation on Riemannian symmetric spaces of non-compact type and general rank. These form a rich class of…

We prove the global well-posedness of the so-called hyperbolic relaxation of the Cahn-Hilliard-Oono equation in the whole space R^3 with the non-linearity of the sub-quintic growth rate. Moreover, the dissipativity and the existence of a…

We consider supersymmetric quantum mechanical systems in arbitrary dimensions on curved spaces with nontrivial gauge fields. The square of the Dirac operator serves as Hamiltonian. We derive a relation between the number of supercharges…

We characterise the homogeneous and isotropic gauge invariant and quasifree states for free Dirac quantum fields on Robertson-Walker spacetimes in any even dimension. Using this characterisation, we construct adiabatic vacuum states of…

We study a model of two scalar fields with a hyperbolic field space and show that it reduces to a single-field Dirac-Born-Infeld (DBI) model in the limit where the field space becomes infinitely curved. We apply the de Sitter swampland…

Superpartner correspondence of states of colored particle in external chromomagnetic field given by non-commuting constant vector potentials is determined. Squared Dirac equation for this particle is solved exactly and explicit expressions…

The structure of 29-dimensional extended real Clifford-Dirac algebra, which has been introduced in our paper Phys. Lett. A, 2011, 375, 2479, is considered in brief. Using this algebra, the property of Fermi-Bose duality of the Dirac…

We study non-interacting automorphic quantum scalar fields with positive mass in two-dimensional de Sitter space. We find that there are no Hadamard states which are de Sitter invariant except in the periodic case, extending the result of…

We review the mathematically rigorous formulation of the quantum theory of a linear field propagating in a globally hyperbolic spacetime. This formulation is accomplished via the algebraic approach, which, in essence, simultaneously admits…