Related papers: Perturbative Algebraic Field Theory, and Deformati…
Entanglement has long been the subject of discussion by philosophers of quantum theory, and has recently come to play an essential role for physicists in their development of quantum information theory. In this paper we show how the…
The classical limit of quantum q-oscillators suggests an interpretation of the deformation as a way to introduce non linearity. Guided by this idea, we considered q-fields, the partition fumction, and compute a consequence on specific heat…
A model of 3-dimensional topological quantum field theory is rigorously constructed. The results are applied to an explicit formula for deformation quantization of any finite-dimensional Lie bialgebra over the field of complex numbers. This…
We study some basic quantum confinement effects through investigation a deformed harmonic oscillator algebra. We show that spatial confinement effects on a quantum harmonic oscillator can be represented by a deformation function within the…
When the symmetry of a physical theory describing a finite system is deformed by replacing its Lie group by the corresponding quantum group, the operators and state function will lie in a new algebra describing new degrees of freedom. If…
A new formalism for the perturbative construction of algebraic quantum field theory is developed. The formalism allows the treatment of low dimensional theories and of non-polynomial interactions. We discuss the connection between the…
Foundations of the formal series $*$ -- calculus in deformation quantisation are discussed. Several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced. The notion of nonnegativity…
The Jacobian conjecture is an old unsolved problem in mathematics, which has been unsuccessfully attacked from many different angles. We add here another point of view pertaining to the so called formal inverse approach, that of…
The invariance of physical observables under redefinitions of the quantum fields is a well-known and important property of quantum field theory. We study perturbative field redefinitions in effective theories, paying special attention to…
A noncommutative and non-anticommutative quantum field theory is formulated in a superspace, in which the superspace coordinates satisfy noncommutative and non-anticommutative relations. A perturbative scalar field theory is investigated in…
The perturbative approach to quantum field theory using retarded functions is extended to noncommutative theories. Unitarity as well as quantized equations of motion are studied and seen to cause problems in the case of space-time…
We examine deformed Poincar\'e algebras containing the exact Lorentz algebra. We impose constraints which are necessary for defining field theories on these algebras and we present simple field theoretical examples. Of particular interest…
The aim of this paper is to give a basic overview of Deformation Quantization (DQ) to physicists. A summary is given here of some of the key developments over the past thirty years in the context of physics, from quantum mechanics to…
We argue that the quantized non-Abelian gauge theory can be obtained as the infrared limit of the corresponding classical gauge theory in a higher dimension. We show how the transformation from classical to quantum field theory emerges and…
We elaborate the generalizations of the approach to gauge-invariant deformations of the gauge theories developed in our previous work [1]. In the given paper we construct the exact transformations defying the gauge-invariant deformed theory…
We describe the deformed E.T. quantization rules for kappa-deformed free quantum fields, and relate these rules with the kappa-deformed algebra of field oscillators.
Deformation quantization (sometimes called phase-space quantization) is a formulation of quantum mechanics that is not usually taught to undergraduates. It is formally quite similar to classical mechanics: ordinary functions on phase space…
Studies of geometrical theories suggest that fundmental problems of quantization arise from the disparate usage of displacement operators. These may be the source of a concealed inconsistency in the accepted formalism of quantum physics.…
Interpretational problems with quantum mechanics can be phrased precisely by only talking about empirically accessible information. This prompts a mathematical reformulation of quantum mechanics in terms of classical mechanics. We survey…
The quantization of the gravitational field is discussed within the exact uncertainty approach. The method may be described as a Hamilton-Jacobi quantization of gravity. It differs from previous approaches that take the classical…