Related papers: Path Integral Quantization of Noncommutative Compl…
Guided by idealized but soluble nonrenormalizable models, a nontraditional proposal for the quantization of covariant scalar field theories is advanced, which achieves a term-by-term, divergence-free perturbation analysis of interacting…
The in-in path integral of a scalar field propagating in a fixed background is formulated in a suitable function space. The free kinetic operator, whose inverse gives the propagators of the in-in perturbation theory, becomes essentially…
A recent proposal to connect the loop quantization with the spin foam model for cosmology via the path integral is hereby adapted to the case of mechanical systems within the framework of the so called polymer quantum mechanics. The…
In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to…
The renormalization of effective potential for the noncommutative scalar field theory is investigated to the two-loop approximation. It is seen that the nonplanar diagram does not appear in the one-loop potential. However, nonplanar diagram…
We consider the propagation of both fully coherent and partially coherent complex scalar fields, through linear shift-invariant imaging systems. The state of such imaging systems is characterized by a countable infinity of aberration…
The quantization of noncommutative scalar field theory is studied from the matrix model point of view, exhibiting the significance of the eigenvalue distribution. This provides a new framework to study renormalization, and predicts a phase…
We investigate the incorporation of space noncommutativity into field theory by extending to the spectral continuum the minisuperspace action of the quantum mechanical harmonic oscillator propagator with an enlarged Heisenberg algebra. In…
We study radial waves in (2+1)-dimensional noncommutative scalar field theory, using operatorial methods. The waves propagate along a discrete radial coordinate and are described by finite series deformations of Bessel-type functions. At…
The symmetry properties of a proposal to go beyond relativistic quantum field theory based on a modification of the commutation relations of fields are identified. Poincar\'e invariance in an auxiliary spacetime is found in the Lagrangian…
We formulate Feynman path integral on a non commutative plane using coherent states. The propagator for a free particle exhibits UV cut-off induced by the parameter of non commutativity.
In this work, we study the Quantum Field Theory version of the higher derivative Pais-Uhlenbeck oscillator. We quantize canonically this system and construct its Fock space, as well as study its path integral. We demonstrate that the…
In this work we analyze complex scalar fields using a new framework where the object of noncommutativity $\theta^{\mu\nu}$ represents independent degrees of freedom. In a first quantized formalism, $\theta^{\mu\nu}$ and its canonical…
We formulate the coherent state path integral on a two dimensional noncommutative plane using the fact that noncommuative quantum mechanics can be viewed as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on…
Very high energy physics needs a coherent description of the four fundamental forces. Non-commutative geometry is a promising mathematical framework which already allowed to unify the general relativity and the standard model, at the…
In this paper, we revise the concept of noncommutative vector fields introduced previously in Ref. [1,2], extending the framework, adding new results and clarifying the old ones. Using appropriate algebraic tools certain shortcomings in the…
We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment…
The quantum correlations of scalar fields are examined as a power series in derivatives. Recursive algebraic equations are derived and determine the amplitudes; all loop integrations are performed. This recursion contains the same…
We study free scalar field theory on flat spacetime using a background independent (polymer) quantization procedure. Specifically we compute the propagator using a method that takes the energy spectrum and position matrix elements of the…
Non-commutative Euclidean scalar field theory is shown to have an eigenvalue sector which is dominated by a well-defined eigenvalue density, and can be described by a matrix model. This is established using regularizations of R^{2n}_\theta…