Related papers: The Fermionic Signature Operator and Space-Time Sy…
We construct the coherent states in the sense of Gilmore and Perelomov for the fermionic Fock space. Our treatment is from the outset adapted to the infinite-dimensional case. The fermionic Fock space becomes in this way a reproducing…
Time-symmetric quantum mechanics can be described in the usual Weyl--Wigner--Moyal formalism (WWM) by using the properties of the Wigner distribution, and its generalization, the cross-Wigner distribution. The use of the latter makes clear…
With the concept of "discrete space-time" the space-time continuum is resolved into discrete points at the scale of the Planck length. We postulate with the "principle of the fermionic projector" that physical equations must be formulated…
The compatibility between the general relativity and the mathematical property that the space-times are embedded manifolds are further examined. In particular we study the uniqueness of the signature of the embedding space for a given…
A signature changing spacetime is one where an initially Riemannian manifold with Euclidean signature evolves into the Lorentzian universe we see today. This concept is motivated by problems in causality implied by the isotropy and…
Different quantum mechanical operators can correspond to the same classical quantity. Hermitian operators differing only by operator ordering of the canonical coordinates and momenta at one moment of time are the most familiar example.…
We explore new aspects of internal fermionic shifting symmetries, present in physical systems such as free Dirac spinors and p-form tensor-spinor fields. We propose a novel procedure to gauge these global symmetries, which also introduces a…
We provide an alternative view of the efficient classical simulatibility of fermionic linear optics in terms of Slater determinants. We investigate the generic effects of two-mode measurements on the Slater number of fermionic states. We…
Requiring physical consistency in a classical flat spacetime geometrisation of fermions is shown to suggest the introduction of torsion. A resulting simple model for that torsion produces a localised quantum-like particle as a solution of a…
The classical procedures which define the relativistic notion of space-time can be implemented in the framework of Quantum Field Theory. Only relying on the conformal symmetries of field propagation, time-frequency transfer and localization…
A total position operator $X$ in the position representation is derived for lattice fermionic systems with periodic boundary conditions. The operator is shown to be Hermitian, the generator of translations in momentum space, and its time…
We consider invariance of the action of N=1 supersymmetric theories under the change of sign of the fermionic co-ordinate in superspace. We show that the R-parity can be realized as a special implementation of this symmetry. Other…
Spatial symmetries occur in combination with temporal symmetries in a wide range of physical systems in nature, including time-periodic quantum systems typically described by the Floquet formalism. In this context, groups formed by…
Tomographic probability representation is introduced for fermion fields. The states of the fermions are mapped onto probability distribution of discrete random variables (spin projections). The operators acting on the fermion states are…
Self-similar spacetimes are of importance to cosmology and to gravitational collapse problems. We show that self-similarity or the existence of a homothetic Killing vector field for spherically symmetric spacetimes implies the separability…
I describe the interplay between Minkowski and Euclidean signature gamma matrices, Majorana fermions, and discrete and continuous symmetries in all spacetime dimensions.
Extending our previous construction in the sine-Gordon model, we show how to introduce two kinds of fermionic screening operators, in close analogy with conformal field theory with c<1.
Within the scope of a spherically symmetric space-time we study the role of different types of matter in the formation of different configurations with spherical symmetries. Here we have considered matter with barotropic equation of state,…
We set up the Dirac equation in a Friedmann-Robertson-Walker geometry and separate the spatial and time variables. In the case of a closed universe, the spatial dependence is solved explicitly, giving rise to a discrete set of solutions. We…
Considering homogeneous four-dimensional space-time geometries within real projective geometry provides a mathematically well-defined framework to discuss their deformations and limits without the appearance of coordinate singularities. On…