Related papers: Remarks on QFT in the Coordinate Space
In this work, the second-quantized version of the spatial-coordinate operator, known as the Newton-Wigner-Pryce operator, is explicitly given w.r.t. the massless scalar field. Moreover, transformations of the conformal group are calculated…
Generators of the super-Poincar\'e algebra in the non-(anti)commutative superspace are represented using appropriate higher-derivative operators defined in this quantum superspace. Also discussed are the analogous representations of the…
In standard quantum field theory, the one-particle states are classified by the unitary representations of the Poincar\'e group, whereas the causal fields' classification employs the finite-dimensional (non-unitary) representations of the…
We have obtained propagators in the position space as an expansion over Landau levels for the charged scalar particle, fermion, and massive vector boson in a constant external magnetic field. The summation terms in the resulting expressions…
For any massless, irreducible representation of the covering of the proper, orthochronous Poincar\'e group we construct covariant, free quantum fields that generate the representation space from the vacuum and are localized in semi-infinite…
We construct the algebra of operators acting on the Hilbert spaces of Quantum Mechanics for systems of $N$ identical particles from the field operators acting in the Fock space of Quantum Field Theory by providing the explicit relation…
We present an in-depth investigation of the ${\rm SL}(2,\mathbb{R})$ momentum space describing point particles coupled to Einstein gravity in three space-time dimensions. We introduce different sets of coordinates on the group manifold and…
In this work we analyze complex scalar fields using a new framework where the object of noncommutativity $\theta^{\mu\nu}$ represents independent degrees of freedom. In a first quantized formalism, $\theta^{\mu\nu}$ and its canonical…
In standard quantum field theory, the one-particle states are classified by unitary representations of the Poincar\'e group, whereas the causal fields' classification employs the finite dimensional (non-unitary) representations of the…
We present a field theoretical model of point-form dynamics which exhibits resonance scattering. In particular, we construct point-form Poincar\'e generators explicitly from field operators and show that in the vector spaces for the…
An extension of the Poincar\'e group with half-integer spin generators is explicitly constructed. We start discussing the case of three spacetime dimensions, and as an application, it is shown that hypergravity can be formulated so as to…
By separating the gluon field into physical and pure-gauge components, the usual Poincar\'e subalgebra for an interacting system can be reconciled with gauge-invariance when decomposing the total rotation and translation generators of QCD…
Starting from the instant form of relativistic quantum dynamics for a system of interacting fields, where amongst the ten generators of the Poincare group only the Hamiltonian and the boost operators carry interactions, we offer an…
Successful applications of a conceptually novel setup of Quantum Field Theory, that accounts for all subtheories of the Standard Model (QED, Electroweak Interaction and Higgs, Yang-Mills and QCD) and beyond (Helicity 2), call for a…
We present a new set of massless Poincar\'e group operators Hermitian with respect to the $ 1 / r $ inner product space, which have quasi-plane wave energy-momentum eigenfunctions having velocity $ c $ along their axis of propagation. These…
Using the method of canonical group quantization, we construct the angular momentum operators associated to configuration spaces with the topology of (i) a sphere and (ii) a projective plane. In the first case, the obtained angular momentum…
Wigner's irreducible positive energy representations of the Poincare group are often used to give additional justifications for the Lagrangian quantization formalism of standard QFT. Here we study another more recent aspect. We explain in…
In this work, we systematically derive explicit expressions for the Poincar\'e Group generators on arbitrary-rank tensors and spinor-tensors in $D=3+1$ and $D=2+1$ spacetimes, thus generalizing previous works in the literature for the…
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…
We investigate how fields transform under the Poincar\'e group in nonrelativistic effective field theories of QCD. In constructing these transformations, we rely only on symmetries and field redefinitions to limit the number of allowed…