Related papers: Reducible field quantization (II): Electrons
In this article we study the quantization of a free real scalar field on a class of noncommutative manifolds, obtained via formal deformation quantization using triangular Drinfel'd twists. We construct deformed quadratic action functionals…
Properties of the magnetic translation operators for a charged particle moving in a crystalline potential and a uniform magnetic field show that it is necessary to consider all inequivalent irreducible projective representations of the the…
In this paper the quantization of the 2$+$1-dimensional gravity couplet to the massless Dirac field is carried out. The problem is solved by the application of the new Dynamic Quantization Method [1,2]. It is well-known that in general…
The anti self-adjoint operators of imaginary coordinate and momentum, together with the self-adjoint operators of real coordinate, momentum, energy and time are used in construction of the quantum field theory in operator form. This…
Free electromagnetic fields, satisfying Maxwell's equations with no charges and electric currents, can be described by complex vector fields. In the standard formulation with fields sharply dependent on position and time, one obtains…
It is shown that the hypercomplex Dirac equation describes the system of connected fields: 4-scalar, 4-pseudoscalar, 4-vector, 4-pseudo-vector and antisymmetric 4-tensor second rank field. If mass is assumed to be zero this system splits…
Magnetic effects on free electron systems have been studied extensively in the context of spin-to-orbital angular momentum conversion. Starting from the Dirac equation, we derive a fully relativistic expression for the energy of free…
We construct the spectral decomposition of field operators in bosonic quantum field theory as a limit of a strongly continuous family of positive-operator-valued measure decompositions. The latter arise from integrals over families of…
The physical meaning of the operators is not reducible to the intrinsic relations of the quantum system, since unitary transformations can find other operators satisfying the exact same relations. The physical meaning is determined…
Quantum fields are generally taken to be operator-valued distributions, linear functionals of test functions into an algebra of operators; here the effective dynamics of an interacting quantum field is taken to be nonlinearly modified by…
We formulate quantum mechanics in the two-dimensional torus without using position operators. We define an algebra with only momentum operators and shift operators and construct irreducible representation of the algebra. We show that it…
Quantum spaces with $\frak{su}(2)$ noncommutativity can be modelled by using a family of $SO(3)$-equivariant differential $^*$-representations. The quantization maps are determined from the combination of the Wigner theorem for $SU(2)$ with…
In this article, the axioms presented in the first one are reformulated according to the special theory of relativity. Using these axioms, quantum mechanic's relativistic equations are obtained in the presence of electromagnetic fields for…
By introducing a doublet of electromagnetic four dimensional vector potentials, we set up a manifestly Lorentz covariant and SO(2) duality invariant classical field theory of electric and magnetic charges. In our formulation one does not…
The theory of free relativistic fields is shown to arise in a unified manner from higher-order, configuration-space, irreducible representations of the Poincar\'e group. A de Sitter subalgebra, in the massive case, and a Poincar\'e…
A concise discussion of the 3-dimensional irreducible (1,0) and (0,1) representations of the restricted Lorentz group and their application to the description of the electromagnetic field is given. It is shown that a mass term is in…
Using carefully chosen projections, we consider different Carroll limits of relativistic Dirac fermions in any spacetime dimensions. These limits define Carroll fermions of two types: electric and magnetic. The latter type transforms as a…
The hypothesis is suggested that the equation for the Dirac free wave field is, in fact, a group-theoretical relation describing propagation of specific microscopic deviations of space geometry from the euclidean one (closed topological…
Irreducibility of the set of quantum field operators has been proved in noncommutative quantum field theory in the general case when time does not commute with spatial variables.
The Dirac constraint formalism is applied to the d(d>2) dimensional Einstein-Hilbert action when written in first order form, using the metric density and affine connection as independent fields. Field equations not involving time…