Related papers: Reducible field quantization (II): Electrons
Theories which have been used to describe the quantized electromagnetic field interacting with a nonlinear dielectric medium are either phenomenological or derived by quantizing the macroscopic Maxwell equations. Here we take a different…
Fermion-number fractionalization without breaking of time-reversal symmetry was recently demonstrated for a field theory in $(2+1)$-dimensional space and time that describes the couplings between massive Dirac fermions, a complex-valued…
Free quantum field theories on curved backgrounds are discussed via three explicit examples: the real scalar field, the Dirac field and the Proca field. The first step consists of outlining the main properties of globally hyperbolic…
Consider a formally self-adjoint first order linear differential operator acting on pairs (2-columns) of complex-valued scalar fields over a 4-manifold without boundary. We examine the geometric content of such an operator and show that it…
In the free case, it is possible to define quantum fields which describe particles with integer or half-integer spin larger than one. It is shown that particles with integer spin must have Bose statistic and particles with half-integer-spin…
The commutation relations for bosons are field independent, and can be reliably inferred from the definition of creation and annihilation operators. Here, the commutation relations are assumed known, and the quantum electrodynamics…
Starting from a Lagrangian, the electromagnetic field is quantized in the presence of a body rotating along its axis of symmetry. Response functions and fluctuation-dissipation relations are obtained. A general formula for rotational…
It is shown how the theory of the fields can be constructed in a consistent way in quantized spaces. All constructions are connected with unitary irreducible representations of real forms of six dimensional rotation algebras O(1,5), O(2,4),…
Motivated by some well-known results in the phase space description of quantum optics and quantum information theory, we aim to describe the formalism of quantum field theory by explicitly considering the holomorphic representation for a…
A concise discussion of a 3+1-dimensional derivative coupling model, in which a massive Dirac field couples to the four-gradient of a massless scalar field, is given in order to elucidate the role of different concepts in quantum field…
The notion that the electromagnetic field is quantised is usually inferred from observations such as the photoelectric effect and the black-body spectrum. However accounts of the quantisation of this field are usually mathematically…
Drawing inspiration from Dirac's work on functions of non commuting observables, we develop a fresh approach to phase space descriptions of operators and the Wigner distribution in quantum mechanics. The construction presented here is…
A four-dimensional photon polarization space, such that gives a different interpretation of the ladder operators for the time-like degree comparing to the Gupta-Bleuler formulation is presented. This interpretation, coming from the…
A field-theoretical space-time position operator can be properly introduced for the Dirac field, it plays the role of a generalized Noether charge associated with a local symmetry, and its second-quantized form shows that quantum fields…
It is shown that relative coordinate and momentum of coherent electron pair have the meaning of observables with the help of quadrupole and magnetic moments. Distributions of quadrupole terms of scalar potential are shown. These…
We consider the bosonic Fock space over the Hilbert space of transversal vector fields in three dimensions. This space carries a canonical representation of the group of rotations. For a certain class of operators in Fock space we show that…
We construct a mathematical version of quantum field theory. It assigns to a multidimensional variational principle an associative algebra which is a quantization of the Poisson algebra of classical field theory observables. For free scalar…
We introduce a reduced model for a real sector of complexified Ashtekar gravity that does not correspond to a subset of Einstein's gravity but for which the programme of canonical quantization can be carried out completely, both, via the…
In a classical Hamiltonian theory with second class constraints the phase space functions on the constraint surface are observables. We give general formulas for extended observables, which are expressions representing the observables in…
Considering a fluctuating scalar field on momentum space, some relativistic statistical field theories are constructed. A Hilbert space of observables is then constructed from functionals of the fluctuating scalar field with an inner…