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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…
The paper provides three main definitions of the Cartesian photon position operator based on: boost generator, the transversality condition and the helicity operator. In each case, the correctness of the definition and Hermitianness of the…
We consider the world-line quantisation of a system invariant under the symmetries of reciprocal relativity. Imposition of the first class constraint, the generator of local time reparametrisations, on physical states enforces…
We present a new approach to the definition of optical helicity in a medium. Our approach resolves the problem that duality transformations which simultaneously combine $\mathbf{E}$ with $\mathbf{H}$ and $\mathbf{D}$ with $\mathbf{B}$ are…
The photon wave equation proposed in terms of the Riemann-Silberstein vector is derived from a first-order Dirac/Weyl-type action principle. It is symmetric w.r.t. duality transformations, but the associated Noether quantity vanishes.…
The non-relativistic hydrogen atom and the Zwanziger problem have the same dynamical symmetry for bound and scattering states.We show that this is also true for a Hilbert space which is non-commutative in co-ordinates. The group structure…
The Pauli equations describing electron (hole) dynamics in 2D Dirac-like intrinsic semiconductors in external (impurity) scalar potential and for inhomogeneous lattice distortions are obtained within second quantization approach. We show…
Contents 1. Creation and annihilation operators for the system of indistinguishable particles 1.1 The permutation group and the states of a system of indistinguishable particles 1.2 Dimension of the Hilbert space of a system of…
There has been an extended debate regarding the existence of a spin-orbital decomposition of the angular momentum of photons and other massless particles. It was recently shown that there are both geometric and topological obstructions…
It is shown that the components of Pryce's spin operator of Dirac's theory are $SU(2)$ generators of a representation carried by the space of Pauli's spinors determining the polarization of the plane wave solutions of Dirac's equation.…
We revisit the construction of the Hilbert space of non-relativistic particles moving in three spatial dimensions. This is given by the space of sections of a line bundle that can in general be topologically non-trivial. Such bundles are…
We tested in the framework of quantum mechanics the consequences of a noncommutative (NC from now on) coordinates. We restricted ourselves to 3D rotationally invariant NC configuration spaces with dynamics specified by the Hamiltonian H =…
In this work we extend the definition of asymptotic multi-particle states of the $S$-matrix, beyond the direct products of one-particle states. We identify new quantum numbers which we call pairwise helicities, or $q_{ij}$, associated with…
We present a derivation of a position operator for a massive field with spin $1/2$, expressed in a representation-independent form of the Poincar\'e group. Using the recently derived Lorentz-covariant field spin operator, we obtain a…
Working within the framework of Loop Quantum Gravity (LQG), we construct a set of three operators suitable for identifying coordinate-like quantities on a spin-network configuration. In doing so, we rely on known properties of operators for…
The missed particle-antiparticle degrees of freedom are retrieved and the corresponding particle-antiparticle intrinsic space are introduced to study the dynamical symmetry of the Dirac particle. As a result, the particle-antiparticle…
We identify momentum/helicity probability amplitudes for the photon and find their relativistic transformation properties. We also find their behaviour under space inversion and time reversal. The discussion begins with a review of the…
We prove the possibility of existence of stationary bound states of spin-half particles in the Reissner-Nordstroem gravitational field using a self-conjugate Hamiltonian with a flat scalar product of wave functions. Bound states of Dirac…
In this work, we derive from first principles the relativistic wave equation of massless particles of arbitrary helicity. We start from unitary projective irreducible representations of the restricted Poincar\'e group. We define a weaker…
The dynamics of a spin--1/2 neutral particle possessing electric and magnetic dipole moments interacting with external electric and magnetic fields in noncommutative coordinates is obtained. Noncommutativity of space is interposed in terms…