Related papers: On the Fermionic Sector of Quantum Holonomy Theory
We extend the recently developed kinematical framework for diffeomorphism invariant theories of connections for compact gauge groups to the case of a diffeomorphism invariant quantum field theory which includes besides connections also…
Entanglement in finite and semi-infinite free Fermionic chains is studied. A parallel is drawn with the analysis of time and band limiting in signal processing. It is shown that a tridiagonal matrix commuting with the entanglement…
Quantum theory can be formulated with certain non-Hermitian Hamiltonians. An anti-linear involution, denoted by PT, is a symmetry of such Hamiltonians. In the PT-symmetric regime the non-Hermitian Hamiltonian is related to a Hermitian one…
We study the Hamiltonian formulation of SU(2) Yang-Mills theory with staggered fermions in a (2+1)-dimensional small lattice system. We construct a gauge-invariant and finite-dimensional Hilbert space for the theory by applying the…
A topological quantum field theory of non-abelian differential forms is investigated from the point of view of its possible applications to description of polynomial invariants of higher-dimensional two-component links. A path-integral…
We provide geometric quantization of a completely integrable Hamiltonian system in the action-angle variables around an invariant torus with respect to the angle polarization. The carrier space of this quantization is the pre-Hilbert space…
In the present paper, we study quantum Sobolev spaces whose elements are operators of the Hilbert-Schmidt class. We construct these Sobolev spaces from the Fourier transform for operators. Next, we obtain continuous embedding theorems.…
We study quantum spin chains solvable via hidden free fermionic structures. We study the algebras behind such models, establishing connections to the mathematical literature of the so-called ``graph-Clifford'' or ``quasi-Clifford''…
Simulating quantum many-body systems is a highly demanding task since the required resources grow exponentially with the dimension of the system. In the case of fermionic systems, this is even harder since nonlocal interactions emerge due…
We introduce a three-dimensional quantum field theory with an infinite-dimensional symmetry, realized explicitly through a centrally extended affine graded Lie algebra. This symmetry is a direct three-dimensional generalization of the…
The $D=4$ supersymmetric Yang-Mills quantum mechanics with $SU(2)$ and $SU(3)$ gauge symmetry groups is studied. A numerical method to find finite matrix representation of the Hamiltonian is presented in detail. It is used to find spectrum…
I present here a new method that allows the introduction of a discrete auxiliary symmetry in a theory in such a way that the eigenvalue spectrum of the fermion functional determinant is made up of complex conjugated pairs. The method…
We quantize the interaction of gravity with Yang-Mills and spinor fields, hence offering a quantum theory incorporating all four fundamental forces of nature. Using canonical quantization we obtain solutions of the Wheeler-DeWitt equation…
The quantum-field model described by non-Hermitian, but a ${\cal PT}$-symmetric Hamiltonian is considered. It is shown by the algebraic way that the limiting of the physical mass value $m \leq m_{max}= {m_1}^2/2m_2$ takes place for the case…
A quantum theory in a finite-dimensional Hilbert space can be geometrically formulated as a proper Hamiltonian theory as explained in [2, 3, 7, 8]. From this point of view a quantum system can be described in a classical-like framework…
The action of the quantum mechanical volume operator, introduced in connection with a symmetric representation of the three-body problem and recently recognized to play a fundamental role in discretized quantum gravity models, can be given…
Quantum walks on lattices can give rise to relativistic wave equations in the long-wavelength limit, but going beyond the single-particle case has proven challenging, especially in more than one spatial dimension. We construct quantum…
Examples are given of non-Hermitian Hamiltonian operators which have a real spectrum. Some of the investigated operators are expressed in terms of the generators of the Weil-Heisenberg algebra. It is argued that the existence of an…
We show that space-time evolution of one-dimensional fermionic systems is described by nonlinear equations of soliton theory. We identify a space-time dependence of a matrix element of fermionic systems related to the {\it Orthogonality…
We present a proof that quantum Yang-Mills theory can be consistently defined as a renormalized, perturbative quantum field theory on an arbitrary globally hyperbolic curved, Lorentzian spacetime. To this end, we construct the…