Related papers: Anomalous dimension in semiclassical gravity
We have investigated some issues relevant for the possibility to construct physical theories on the $\kappa$-Minkowski noncommutative spacetime. The notion of field in $\kappa$-Minkowski has been introduced by generalizing the Weyl…
In this paper, we analyze the relativistic and nonrelativistic energy spectra (fermionic Landau levels) for the noncommutative quantum Hall effect with anomalous magnetic moment in the conical G\"odel-type spacetime in (2+1)-dimensions,…
Quantum group Fourier transform methods are applied to the study of processes on noncommutative Minkowski spacetime $[x^i,t]=\imath\lambda x^i$. A natural wave equation is derived and the associated phenomena of {\it in vacuo} dispersion…
We study field theories on spaces with additional compact noncommutative dimensions. As an example, we study \phi^3 on R^{1,3}\times T^{2}_\theta using perturbation theory. The infrared divergences in the noncompact theory give rise to…
There ought to exist a reformulation of quantum mechanics which does not refer to an external classical spacetime manifold. Such a reformulation can be achieved using the language of noncommutative differential geometry. A consequence which…
It is by now well established that the momentum space dual to the non-commutative $\kappa$-Minkowski space is a submanifold of de Sitter space. It has been noticed recently that field theories built on such momentum space suffer from a…
Noncommutative geometry is a mathematical framework that expresses the structure of space-time in terms of operator algebras. By using the tools of quantum mechanics to describe the geometry, noncommutative space-times are expected to give…
A framework is proposed that allows to write down field theories with a new energy scale while explicitly preserving Lorentz invariance and without spoiling the features of standard quantum field theory which allow quick calculations of…
We compute the heat kernel for the Laplacians of symmetric transverse traceless fields of arbitrary spin on the $AdS$ background in even number of dimensions using the group theoretic approach introduced in \cite{Gopakumar:2011qs} and apply…
The non perturbative construction of quantum field models with nontrivial scattering in arbitrary dimension $d$ of the underlying Minkowski space-time is much more simple in the framework of quantum field theory with indefinite metric than…
A fundamental spacetime scale in the universe leads to noncommutative spacetime and thence to a modified energy - momentum dispersion relation or equivalently to a modification of Lorentz symmetry as shown by the author and others. This…
We generalize the formulation of non-commutative quantum mechanics to three dimensional non-commutative space. Particular attention is paid to the identification of the quantum Hilbert space in which the physical states of the system are to…
The theory of quantum gravity, in which tetrads emerge as the bilinear combinations of the fermionic field, suggests that in general relativity the interval $ds$ is dimensionless. Several other approaches to quantum gravity, including the…
We study the possible phase transitions between (2+1)-dimensional abelian Chern-Simons theories. We show that they may be described by non-unitary rational conformal field theories with c_eff = 1. As an example we choose the fractional…
Extending the commutator algebra of quantum $\kappa$-Poincar\'e symmetry to the whole of the phase space, and assuming that this algebra is to be covariant under action of deformed Lorentz generators, we derive the transformation properties…
We study properties of a scalar quantum field theory on two-dimensional noncommutative space-times. Contrary to the common belief that noncommutativity of space-time would be a key to remove the ultraviolet divergences, we show that field…
Well-defined nonlinear deformations of free quantum fields are introduced as manifestly Poincar\'e invariant scaling and resonance properties of non-dynamical scale models in Minkowski space, instead of introducing nonlinear dynamical…
A noncommutative geometric generalisation of the quantum field theoretical framework is developed by generalising the Heisenberg commutation relations. There appear nonzero minimal uncertainties in positions and in momenta. As the main…
The concept of a particle is ambiguous in quantum field theory. It is generally agreed that particles depend not only on spacetime, but also on coordinates used to parametrise spacetime points. One of us has in contrast proposed a…
The positive energy theorem precludes the possibility of Minkowski flat space decaying by any mechanism. In certain circumstances, however, large quantum fluctuations of the gravitational field could arise---not only at the Planck scale,…