# Deformation quantization of covariant fields

@article{Dito2002DeformationQO, title={Deformation quantization of covariant fields}, author={Giuseppe Dito}, journal={arXiv: Quantum Algebra}, year={2002} }

After sketching recent advances and subtleties in classical relativistically covariant field theories, we give in this short Note some indications as to how the deformation quantization approach can be used to solve or at least give a better understanding of their quantization.

## 9 Citations

### STATES AND REPRESENTATIONS IN DEFORMATION QUANTIZATION

- Psychology
- 2005

In this review we discuss various aspects of representation theory in deformation quantization starting with a detailed introduction to the concepts of states as positive functionals and the GNS…

### Quantization: Deformation and/or Functor?

- Mathematics
- 2005

After a short presentation of the difference in motivation between the Berezin and deformation quantization approaches, we start with a reminder of Berezin’s view of quantization as a functor…

### A ug 2 00 4 States and representations in deformation quantization

- Mathematics
- 2008

In this review we discuss various aspects of representation theory in deformation quantization starting with a detailed introduction to the concepts of states as positive functionals and the GNS…

### Some reflections on mathematicians’ views of quantization

- Mathematics
- 2007

We start with a short presentation of the difference in attitude between mathematicians and physicists even in their treatment of physical reality, and look at the paradigm of quantization as an…

### Deformation Quantization: From Quantum Mechanics to Quantum Field Theory

- Physics
- 2006

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…

### Convergence of star products: From examples to a general framework

- MathematicsEMS Surveys in Mathematical Sciences
- 2019

It is argued that one of the most important remaining problems is the question of convergence, and different approaches found in the literature so far are discussed.

### O ct 2 00 6 Deformation Quantization : From Quantum Mechanics to Quantum Field Theory

- Physics
- 2008

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…

## References

SHOWING 1-10 OF 16 REFERENCES

### An example of cancellation of infinities in the star-quantization of fields

- Business
- 1993

Within the *-quantization framework, it is shown how to remove some of the divergences occurring in theλø24-theory by introducing aλ-dependent *-product cohomologically equivalent to the normal…

### Star-product approach to quantum field theory: The free scalar field

- Physics
- 1990

The star-quantization of the free scalar field is developed by introducing an integral representation of the normal star-product. A formal connection between the Feynman path integral in the…

### Deformation Quantization: Genesis, Developments and Metamorphoses

- Mathematics
- 2002

We start with a short exposition of developments in physics and mathematics that preceded, formed the basis for, or accompanied, the birth of deformation quantization in the seventies. We indicate…

### Linearization of relativistic nonlinear wave equations

- Mathematics
- 1980

Some linearization theorems for relativistic nonlinear wave equations are formulated and proved. Examples are discussed and the physical meaning of such a linearization is sketched. Finally, some…

### Formal linearization of nonlinear massive representations of the connected Poincaré group

- Mathematics
- 1984

Let U1 be an arbitrary finite direct sum of unitary irreducible representations, each of positive (mass)2, of the connected Poincare group P0=R4⊗SL(2,C). It is proved that each nonlinear…

### Initial Data for Non-Linear Evolution Equations and Differentiable Vectors of Group Representations

- Mathematics
- 1995

Regularity properties of non-linear Lie algebra representations are defined. These properties are satisfied in examples given by evolution equations. We prove that this regularity implies that the…

### Methods of modern mathematical physics. III. Scattering theory

- Physics, Mathematics
- 1979

Topics covered include: overview; classical particle scattering; principles of scattering in Hilbert space; quantum scattering; long range potentials; optical and acoustical scattering; the linear…

### On global solutions of the Maxwell-Dirac equations

- Mathematics
- 1987

We prove, for the Maxwell-Dirac equations in 1+3 dimensions, that modified wave operators exist on a domain of small entire test functions of exponential type and that the Cauchy problem, inR+×R3,…

### Complex Analysis on Infinite Dimensional Spaces

- Mathematics
- 1999

Polynomials * Duality Theory for Polynomials * Holomorphic Mappings Between Locally Convex Spaces * Decompositions of Holomorphic Functions * Riemann Domains * Holomorphic Extensions.

### Wave operators and analytic solutions for systems of non-linear Klein-Gordon equations and of non-linear Schrödinger equations

- Mathematics
- 1985

We consider, in a 1+3 space time, arbitrary (finite) systems of nonlinear Klein-Gordon equations (respectively Schrödinger equations) with an arbitrary local and analytic non-linearity in the unknown…