Related papers: Quantum Theory, Noncommutativity and Heuristics
We study the perturbative unitarity of noncommutative scalar field theories. Field theories with space-time noncommutativity do not have a unitary S-matrix. Field theories with only space noncommutativity are perturbatively unitary. This…
We analyze, starting from first principles, the quantization of field theories, in order to find out to which problems a noncommutative time would possibly lead. We examine the problem in the interaction picture (Tomonaga-Schwinger…
We consider the role of Lorentz symmetry in noncommutative field theory. We find that a Lorentz-violating standard-model extension involving ordinary fields is general enough to include any realisitc noncommutative field theory as a subset.…
We consider the $\mathcal{PT}$-symmetric quantum field theory on the noncommutative spacetime with angular twist and construct its pseudo-Hermitian interpretation. We explore the differences between internal and spatial parities in the…
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…
Over the past five years, there has been significant progress on the problem of quantization of diffeomorphism covariant field theories with {\it local} degrees of freedom. The absence of a background space-time metric in these theories…
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this…
With the present trend in experimental particle physics of probing yet shorter distances and with the requirement on the theoretical side of renormalizability, conformal invariance becomes an attractive symmetry for particle interactions.…
For classical field theories with probabilistic initial conditions the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial…
We consider two model field theories on a noncommutative plane that have smooth commutative limits. One is the single-component fermion theory with quartic interaction that vanishes identically in the commutative limit. The other is a…
We argue that the conventional quantum field theory in curved spacetime has a grave drawback: The canonical commutation relations for quantum fields and conjugate momenta do not hold. Thus the conventional theory should be denounced and the…
We expect quantum field theories for matter to acquire intricate corrections due to their coupling to quantum fluctuations of the gravitational field. This can be precisely worked out in 3d quantum gravity: after integrating out quantum…
Trying to connect a fundamentally non-commutative spacetime with the conservative perturbative approach to quantum gravity, we are led to the natural question: are non-commutative geometrical effects already present in the regime where…
We analyse in detail the quantization of a simple noncommutative model of spontaneous symmetry breaking in zero dimensions taking into account the noncommutative setting seriously. The connection to the counting argument of Feyman diagrams…
We discuss some properties of noncommutative supersymmetric field theories which do not involve gauge fields. We concentrate on the renormalizability issue of these theories.
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
(Anti)causal boundary conditions being imposed on the (seemingly) Hermitian Quantum Theory (HQT) as described in standard textbooks lead to an (Anti)Causal Quantum Theory ((A)CQT) with an indefinite metric. Therefore, an (anti)causal…
We consider a scalar quantum field theory, in which the interaction takes the form of a field cutoff; the energy diverges to infinity whenever the value of the field at some point falls outside a finite interval. In a simple…
These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key…
It is shown that the violation of unitarity observed in space/time noncommutative field theories is due to an improper definition of quantum field theory on noncommutative spacetime.