Related papers: Quantum Loop Representation for Fermions coupled t…
A new density matrix and corresponding quantum kinetic equations are introduced for fermions undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). A central element in our derivation…
In this paper is considered relativistic quantum field theory expressed by elementary units of quantum information as they are considered as fundamental entity of nature by Carl Friedrich von Weizsaecker. Through quantization of a Weyl…
Loop quantum cosmology is an application of recent developments for a non-perturbative and background independent quantization of gravity to a cosmological setting. Characteristic properties of the quantization such as discreteness of…
In this paper we regard the dynamics obtained from Fermat principle as begin the classical theory of light. We (first-)quantize the action and show how close we can get to the Maxwell theory. We show that Quantum Geometric Optics is not a…
This course of lectures has been taught for several years at the Lomonosov Moscow State University; its modified version in 2021 is read in the Zhejiang University (Hangzhou), in the framework of summer school on quantum computing. The…
Quantum-mechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group. Any linear representation of a finite…
This paper extends earlier work on quantum theory representations of natural numbers N, integers I, and rational numbers Ra to describe a space of these representations and transformations on the space. The space is parameterized by 4-tuple…
We discuss canonical transformations in Quantum Field Theory in the framework of the functional-integral approach. In contrast with ordinary Quantum Mechanics, canonical transformations in Quantum Field Theory are mathematically more subtle…
We consider a matrix space based on the spin degree of freedom, describing both a Hilbert state space, and its corresponding symmetry operators. Under the requirement that the Lorentz symmetry be kept, at given dimension, scalar symmetries,…
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
In this paper we construct explicitly natural (from the geometrical point of view) Fock space representations (contragradient Verma modules) of the quantized enveloping algebras. In order to do so, we start from the Gauss decomposition of…
A reasonable quantum information theory for fermions must respect the parity super-selection rule to comply with the special theory of relativity and the no-signaling principle. This rule restricts the possibility of any quantum state to…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
We use the idea of the symmetry between the spacetime coordinates x^\mu and the energy-momentum p^\mu in quantum theory to construct a momentum space quantum gravity geometry with a metric s_{\mu\nu} and a curvature P^\lambda_{\mu\nu\rho}.…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
This series of lectures gives a simple and self-contained introduction to the non-perturbative and background independent loop approach of canonical quantum gravity. The Hilbert space of kinematical quantum states is constructed and a…
An one-parameter regularization freedom of the Hamiltonian constraint for loop quantum gravity is analyzed. The corresponding spatially flat, homogenous and isotropic model includes the two well-known models of loop quantum cosmology as…
We introduce a certain type of representations for the quantum Teichmuller space of a punctured surface, which we call local representations. We show that, up to finitely many choices, these purely algebraic representations are classified…
We study the coupling of massive fermions to the quantum mechanical dynamics of spacetime emerging from the spinfoam approach in three dimensions. We first recall the classical theory before constructing a spinfoam model of quantum gravity…
Simulating fermionic systems on a quantum computer requires representing fermionic states using qubits. The complexity of many simulation algorithms depends on the complexity of implementing rotations generated by fermionic…