Related papers: The Problem of Constructing the Current Operators …
It is shown that in the general case the canonical construction of the current operators in quantum field theory does not render a bona fide vector field since Lorentz invariance is violated by Schwinger terms. We argue that the…
In this work we develop a re-formulation of quantum field theory through the more general weighted Lorentz invariant measures that the definition of quantum fields allows; this approach provides finite answers for the long-live problems of…
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…
An unstable field theory is what we obtain when we linearise the equations of an interacting field theory near an unstable state. Theories of this kind are adopted to model the onset of spontaneous symmetry breakings, when the fields are…
Noncommutative field theories with commutator of the coordinates of the form $[x^{\mu},x^{\nu}]=i \Lambda_{\quad \omega}^{\mu \nu}x^{\omega}$ are studied. Explicit Lorentz invariance is mantained considering $\Lambda $ a Lorentz tensor. It…
We study a class of perturbative scalar quantum field theories where dynamics is characterized by Lorentz-invariant or Lorentz-breaking non-local operators of fractional order and the underlying spacetime has a varying spectral dimension.…
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…
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
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…
Background: Phenomenological Poincar\'e invariant quantum mechanical models can provide an efficient description of the dynamics of strongly interacting particles that is consistent with spectral and scattering observables. These models are…
We use tools from non-standard analysis to formulate the building blocks of quantum field theory within the framework of categorical quantum mechanics. Building upon previous work, we construct an object of *Hilb having quantum fields as…
In classical Lorentz-invariant field theories, localized soliton solutions necessarily break translation symmetry. In the corresponding quantum field theories, the position is quantized and, if the theory is not compactified, they have…
It is shown that the joint measurements of some physical variables corresponding to commuting operators performed on pre- and post-selected quantum systems invariably disturb each other. The significance of this result for recent proofs of…
Conserved operator quantities in quantum field theory can be defined via the Noether theorem in the Lagrangian formalism and as generators of some transformations. These definitions lead to generally different conserved operators which are…
Quantum field theory is assumed to be gauge invariant. However it is well known that when certain quantities, such as the vacuum current, are calculated the results are not gauge invariant. The non-gauge invariant terms have to be removed…
An analysis of the Schwinger's action principle in Lagrangian quantum field theory is presented. A solution of a problem contained in it is proposed via a suitable definition of a derivative with respect to operator variables. This results…
The algebra of observables associated with a quantum field theory is invariant under the connected component of the Lorentz group and under parity reversal, but it is not invariant under time reversal. If we take general covariance…
For the current realization of the affine quantum groups, a simple comultiplication for the quantum current operators was given by Drinfeld. With this comultiplication, we study the zeros and poles of the quantum current operators and…
A structural explanation of the coupling constants in the standard model, i.e the fine structure constant and the Weinberg angle, and of the gauge fixing contributions is given in terms of symmetries and representation theory. The coupling…
Non-trivial solutions in string field theory may lead to the spontaneous breaking of Lorentz invariance and to new tensor-matter interactions. It is argued that requiring the contribution of the vacuum expectation values of Lorentz tensors…