# Cylindrical Wigner Measures

@article{Falconi2016CylindricalWM, title={Cylindrical Wigner Measures}, author={Marco Falconi}, journal={Documenta Mathematica}, year={2016} }

In this paper we study the semiclassical behavior of quantum states acting on the C*-algebra of canonical commutation relations, from a general perspective. The aim is to provide a unified and flexible approach to the semiclassical analysis of bosonic systems. We also give a detailed overview of possible applications of this approach to mathematical problems of both axiomatic relativistic quantum field theories and nonrelativistic many body systems. If the theory has infinitely many degrees of…

## 12 Citations

### Concentration of cylindrical Wigner measures

- MathematicsCommunications in Contemporary Mathematics
- 2018

In this paper, we aim to characterize the cylindrical Wigner measures associated to regular quantum states in the Weyl C*-algebra of canonical commutation relations. In particular, we provide…

### Magnetic Schrödinger operators as the quasi-classical limit of Pauli–Fierz-type models

- Mathematics, PhysicsJournal of Spectral Theory
- 2019

We study the quasi-classical limit of the Pauli-Fierz model: the system is composed of finitely many non-relativistic charged particles interacting with a bosonic radiation field. We trace out the…

### A pr 2 01 7 CONCENTRATION OF CYLINDRICAL WIGNER MEASURES

- Mathematics
- 2017

. In this note we aim to characterize the cylindrical Wigner mea- sures associated to regular quantum states in the Weyl C*-algebra of canonical commutation relations. In particular, we provide…

### Entanglement of classical and quantum short-range dynamics in mean-field systems

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### Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit

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- 2017

We study the quasi-classical limit of a quantum system composed of finitely many nonrelativistic particles coupled to a quantized field in Nelson-type models. We prove that, as the field becomes…

### Ground State Properties in the Quasi-Classical Regime

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- 2020

We study the ground state energy and ground states of systems coupling non-relativistic quantum particles and force-carrying Bose fields, such as radiation, in the quasi-classical approximation. The…

### Microscopic Derivation of Time-dependent Point Interactions

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We study the dynamics of the three-dimensional Frohlich polaron -- a quantum particle coupled to a bosonic field -- in the quasi-classical regime, i.e., when the field is very intense and the…

### Classical dynamics generated by long-range interactions for lattice fermions and quantum spins

- PhysicsJournal of Mathematical Analysis and Applications
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### Classical limits of unbounded quantities by strict quantization

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This paper extends the tools of C*-algebraic strict quantization toward analyzing the classical limits of unbounded quantities in quantum theories. We introduce the approach first in the simple case…

### Quasi-Classical Dynamics

- Physics
- 2019

We study quantum particles in interaction with a force-carrying field, in the quasi-classical limit. This limit is characterized by the field having a very large number of excitations (it is…

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In this paper, we aim to characterize the cylindrical Wigner measures associated to regular quantum states in the Weyl C*-algebra of canonical commutation relations. In particular, we provide…

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We study the quasi-classical limit of a quantum system composed of finitely many nonrelativistic particles coupled to a quantized field in Nelson-type models. We prove that, as the field becomes…