Related papers: How to commute
Commutation or anticommutation relations quantized at equal instant time and commutation or anticommutation relations quantized at equal light-front time cannot be transformed into each other. While they would thus appear to describe…
It has been known for a long time that there are two non-trivial possibilities for the relative commutation relations between a set of $m$ parafermions and a set of $n$ parabosons. These two choices are known as ``relative parafermion…
We introduce a concise quantum operator formula for bosonization in which the Lie group structure appears in a natural way. The connection between fermions and bosons is found to be exactly the connection between Lie group elements and the…
Complete sets of commutation relations for arbitrary pairs of quantum minors are computed, with explicit coefficients in closed form.
We use the light-front machinery to study the behavior of a relativistic free particle and obtain the quantum commutation relations from the classical Poisson brackets. We argue that the usual projection onto the light-front coordinates for…
In a minimalistic view, the use of noncommutative coordinates can be seen just as a way to better express non-local interactions of a special kind: 1-particle solutions (wavefunctions) of the equation of motion in the presence of an…
In quantum field theory the creation and annihilation operators that are located at the points in 3-momentum space have commutation relations that are conserved under the action of a $U({\infty})$ group. Here it is shown how to define an…
Commutation or anticommutation relations quantized at equal instant time and commutation or anticommutation relations quantized at equal light-front time not only cannot be transformed into each other, they take completely different forms.…
The symmetrization postulate asserts that the state of particular species of particles can only be of one permutation symmetry type: symmetric for bosons and antisymmetric for fermions. We report some experimental results showing that pairs…
One of the traditional ways of introducing bosons and fermions is through creation-annihilation algebras. Historically, these have been associated with emission and absorption processes at the quantum level and are characteristic of the…
The commutation relations of the composite fields are studied in the 3, 2 and 1 space dimensions. It is shown that the field of an atom consisting of a nucleus and an electron fields satisfies, in the space-like asymptotic limit, the…
The theoretical description of interacting fermions in one spatial dimension is simplified by the fact that the low energy excitations can be described in terms of bosonic degrees of freedom. This fermion-boson transmutation (FBT) which…
The momentum of a free massive particle, invariant under translation, thereby realizes a trivial representation of the translation group. By allowing nontrivial reps of translations, momentum changes with translation, a recipe for force.…
The commutation relations of the composite fields are studied in the 3, 2 and 1 space dimensions. It is shown that the field of an atom consisting of a nucleus and an electron fields satisfies, in the space-like asymptotic limit, the…
We compare light-front quantization and instant-time quantization both at the level of operators and at the level of their Feynman diagram matrix elements. At the level of operators light-front quantization and instant-time quantization…
Modifications of a free quantum field calculation using translation-related concepts and general translation representations yield quantum fields for massive particles that as a consequence follow the classical trajectories of…
We derive the relativistic transformation laws for the annihilation operators of the scalar field, the massive spin-1 vector field, the electromagnetic field and the spinor field. The technique developed here involves straightforward…
Bosonic quantum conversion systems can be modeled by many-particle single-mode Hamiltonians describing a conversion of $n$ molecules of type A into $m$ molecules of type B and vice versa. These Hamiltonians are analyzed in terms of…
The work contains a detailed investigation of free neutral (Hermitian) or charged (non-Hermitian) scalar fields and the describing them (system of) Klein-Gordon equation(s) in momentum picture of motion. A form of the field equation(s) in…
While single boson entanglement is known to be equivalent to standard non-identical particle entanglement, the use of fermionic entanglement is constrained by a parity superselection rule. Nevertheless we show that within the framework of…