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To make sense of quantum field theory in an arbitrary (globally hyperbolic) curved spacetime, the theory must be formulated in a local and covariant manner in terms of locally measureable field observables. Since a generic curved spacetime…
We consider massive scalar field theory on static four-dimensional space-times with horizons. We study the near horizon behaviour of the quantum expectation values of the stress-energy tensor operator for thermal state with generic…
The preparation of thermal equilibrium states is important for the simulation of condensed-matter and cosmology systems using a quantum computer. We present a method to prepare such mixed states with unitary operators, and demonstrate this…
In it's usual presentation, classical mechanics appears to give time a very special role. But it is well known that mechanics can be formulated so as to treat the time variable on the same footing as the other variables in the extended…
We interpret, in the realm of relativistic quantum field theory, the tangential operator given by Coleman, Mandula as an appropriate coordinate operator. The investigation shows that the operator generates a Snyder-like noncommutative…
We review the present status of gauge theories built on various quantum space-times described by noncommutative space-times. The mathematical tools and notions underlying their construction are given. Different formulations of gauge theory…
I introduce in kappa-Minkowski noncommutative spacetime the basic tools of quantum differential geometry, namely bicovariant differential calculus, Lie and inner derivatives, the integral, the Hodge-star and the metric. I show the relevance…
We characterize all Gaussian dynamical semigroups in continuous variables quantum systems of n-bosonic modes which have a thermal Gibbs state as a stationary solution. This is performed through an explicit relation between the diffusion and…
In two-dimensional space a subtle point that for the case of both space-space and momentum-momentum noncommuting, different from the case of only space-space noncommuting, the deformed Heisenberg-Weyl algebra in noncommutative space is not…
In this work quantum physics in noncommutative spacetime is developed. It is based on the work of Doplicher et al. which allows for time-space noncommutativity. The Moyal plane is treated in detail. In the context of noncommutative quantum…
Some skeptical arguments on the physical reality of quantum states are given. First, I argue that the algebraic formalism of quantum field theory in curved spacetime (algebraic QFTCS, AQFTCS) leads to such a skepticism. Of course we have…
Thermal quantum field theories are expected to obey a relativistic KMS condition, which replaces both the relativistic spectrum condition of Wightman quantum field theory and the KMS condition, which characterises equilibrium states in…
Thermodynamic formalism for rotating black holes, characterized by noncommutative and quantum corrections, is constructed. From a fundamental thermodynamic relation, equations of state and thermodynamic response functions are explicitly…
We study parity-time-symmetric non-Hermitian quantum systems at finite temperature, where the Boltzmann distribution law fails to hold. To characterize their abnormal physical properties, a new quantum statistics theory (the so-called…
We revisit the notion of quantum Lie algebra of symmetries of a noncommutative spacetime, its elements are shown to be the generators of infinitesimal transformations and are naturally identified with physical observables. Wave equations on…
A novel approach to the Hamiltonian formulation of quantum field theory at finite temperature is presented. The temperature is introduced by compactification of a spatial dimension. The whole finite-temperature theory is encoded in the…
We discuss scalar quantum field theories in a Lorentz-invariant three-dimensional noncommutative space-time. We first analyze the one-loop diagrams of the two-point functions, and show that the non-planar diagrams are finite and have…
We give a brief account of the description of the standard model in noncommutative geometry as well as the thermal time hypothesis, questioning their relevance for quantum gravity.
The density operator for a quantum system in thermal equilibrium with its environment depends on Planck's constant, as well as the temperature. At high temperatures, the Weyl representation, that is, the thermal Wigner function, becomes…
We wish to report here on a recent approach to the non-commutative calculus on $q$-Minkowski space which is based on the reflection equations with no spectral parameter. These are considered as the expression of the invariance (under the…