相关论文: A Note on the Real Fermionic and Bosonic quadratic…
We study some properties of quadratic forms with values in a field whose underlying vector spaces are endowed with the structure of right vector spaces over a division ring extension of that field. Some generalized notions of isotropy,…
It is shown that the equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of conformally "curved" space-time. This shows that it is possible to formulate quantum…
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…
A method is developed for realizing entanglement and general second quantized fermionic and bosonic fields in the framework of the fermionic projector.
We review a recently proposed SuperGeometric (SG) approach to Quantum Field Theories (QFTs) that allow for scalar-fermion field transformations in a manifestly reparameterisation covariant manner. By adopting natural choices for the…
It is shown that supersymmetric integrable models in two dimensions, both relativistic (i.e. super-Toda type theories) and non-relativistic (reductions of super-KP hierarchies) can be associated to general Poisson-brackets structures given…
In this paper we give a unified framework for the construction of complex valued harmonic morphisms from the real, complex and quaternionic Grassmannians and their non-compact duals. This gives a positive answer to the corresponding open…
We describe the fermionic and bosonic Fock representation of the Lie super-algebra of endomorphisms of the exterior algebra of the ${\mathbb Q}$-vector space of infinite countable dimension, vanishing at all but finitely many basis…
We show that the metric operator for a pseudo-supersymmetric Hamiltonian that has at least one negative real eigenvalue is necessarily indefinite. We introduce pseudo-Hermitian fermion (phermion) and abnormal phermion algebras and provide a…
The relevance in Physics of non-Hermitian operators with real eigenvalues is being widely recognized not only in quantum mechanics but also in other areas, such as quantum optics, quantum fluid dynamics and quantum field theory. %stochastic…
We establish that the recently discovered fermionic T-duality can be viewed as a canonical transformation in phase space. This requires a careful treatment of constrained Hamiltonian systems. Additionally, we show how the canonical…
A Symmetry between bosonic coordinates and some Grassmannian-type coordinates is presented. Commuting two of these Grassmannian-type variables results in an arbitrary phase (not just a minus sign). This symmetry is also realised at the…
The introduction of operator states and of observables in various fields of quantum physics has raised questions about the mathematical structures of the corresponding spaces. In the framework of third quantization it had been conjectured…
We extend all cohomological invariants of similarity classes of quadratic forms to anti-hermitian forms over a quaternion algebra. This uses the fact that such invariants can be lifted to Witt invariants, which can be described as…
It was recently argued that quantum field theories possess one-form and higher-form symmetries, labelled `generalized global symmetries.' In this paper, we describe how those higher-form symmetries can be understood mathematically as…
We show that a dynamical supersymmetry can appear in a purely fermionic system. This ``supersymmetry without bosons" is constructed by application of a recently introduced boson-fermion Dyson mapping from a fermion space to a space…
Dualities provide deep insight into physics by relating two seemingly distinct theories. Here we propose and elaborate on a novel duality between bosonic and fermionic theories in four spacetime dimensions. Starting with a Euclidean lattice…
The widely used large-scale diagonalization method using harmonic oscillator basis functions (an instance of the Rayleigh-Ritz method, also called a spectral method, configuration-interaction method, or ``exact diagonalization'' method) is…
A new procedure to diagonalize quadratic Hamiltonians is introduced. We show that one can find a unitary transformation such that the transformed quadratic Hamiltonian is diagonal but still written in terms of the original position and…
We study differential calculus on h-deformed bosonic and fermionic quantum space. It is shown that the fermionic quantum space involves a parafermionic variable as well as a classical fermionic one. Further we construct the classical…