# From Quantum Field Theory to Quantum Mechanics

@inproceedings{Sa2021FromQF, title={From Quantum Field Theory to Quantum Mechanics}, author={Nuno Barros e S'a and Cl'audio Gomes}, year={2021} }

We construct the algebra of operators acting on the Hilbert spaces of Quantum Mechanics for systems of N identical particles from the field operators acting in the Fock space of Quantum Field Theory by providing the explicit relation between the position and momentum operators acting in the former spaces and the field operators acting on the latter. This is done in the context of the non-interacting Klein-Gordon field. It may not be possible to extend the procedure to interacting field theories… Expand

#### Figures from this paper

#### References

SHOWING 1-10 OF 18 REFERENCES

Obtaining the non-relativistic quantum mechanics from quantum field theory: issues, folklores and facts

- Physics
- The European Physical Journal C
- 2018

Given the classical dynamics of a non-relativistic particle in terms of a Hamiltonian or an action, it is relatively straightforward to obtain the non-relativistic quantum mechanics (NRQM) of the… Expand

On the Dirac Theory of Spin 1/2 Particles and Its Non-Relativistic Limit

- Physics
- 1950

By a canonical transformation on the Dirac Hamiltonian for a free particle, a representation of the Dirac theory is obtained in which positive and negative energy states are separately represented by… Expand

Localized States in Quantum Field Theory

- Physics
- 2017

Localized states in relativistic quantum field theories are usually considered as problematic, because of their seemingly strange (non covariant) behavior under Lorentz transformations, and because… Expand

Localizable Particles in the Classical Limit of Quantum Field Theory

- Physics, Mathematics
- 2021

A number of arguments purport to show that quantum field theory cannot be given an interpretation in terms of localizable particles. We show, in light of such arguments, that the classical ~ → 0… Expand

Quantum Field Theory and the Standard Model

- Physics
- 2013

Providing a comprehensive introduction to quantum field theory, this textbook covers the development of particle physics from its foundations to the discovery of the Higgs boson. Its combination of… Expand

Covariant Position Operators, Spin, and Locality

- Physics
- 1965

A manifestly covariant formalism is developed suitable for a discussion of position operators for relativistic systems. It is shown that the rest-frame center of mass and the frame-dependent center… Expand

Reeh-Schlieder Meets Newton-Wigner

- 2002

The Reeh-Schlieder theorem asserts the vacuum and certain other states to be spacelike superentangled relative to local fields. This motivates an inquiry into the physical status of various concepts… Expand

Introduction to quantum field theory

- Physics
- 1995

Even the uninitiated will know that Quantum Field Theory cannot be introduced systematically in just four lectures. I try to give a reasonably connected outline of part of it, from second… Expand

The Newton-Wigner and Wightman localization of the photon

- Mathematics
- 1996

A quantum theory of the photon is developed in a natural manner. Newton-Wigner and Wightman demonstrated that the photon could not be strictly localized according to natural criteria. These… Expand

Pauli And The Spin-Statistics Theorem

- Physics
- 1998

Discovery of the exclusion principle discovery of the electron spin Bose-Einstein statistics identical particle wave functions Fermi-Dirac statistics quantum field theory anticommunication for F-D… Expand