Related papers: Quantization In Finite Volumes Using Symplectic Qu…
Working in relativistic quantum field theory, we derive the quantization condition satisfied by coupled two- and three-particle systems of identical scalar particles confined to a cubic spatial volume with periodicity $L$. This gives the…
First of all we shortly illustrate how the symplectic quantization scheme [Gradenigo and Livi, 2021] can be applied to a relativistic field theory with self-interaction. Taking inspiration from the stochastic quantization method by Parisi…
New features of a previously introduced Group Approach to Quantization are presented. We show that the construction of the symmetry group associated with the system to be quantized (the "quantizing group") does not require, in general, the…
Bosonic quantum fields can be simulated with `quantum software' in phase-space. The positive-P, Wigner and Q-function phase-space methods are reviewed. Initial quantum states and boundaries for infinite domains are considered in detail. The…
Canonical quantization relies on Cartesian, canonical, phase-space coordinates to promote to Hermitian operators, which also become the principal ingredients in the quantum Hamiltonian. While generally appropriate, this procedure can also…
An operator-valued quantum phase space formula is constructed. The phase space formula of Quantum Mechanics provides a natural link between first and second quantization, thus contributing to the understanding of quantization problem. By…
We present here the first lattice simulation of symplectic quantization, a new functional approach to quantum field theory which allows to define an algorithm to numerically sample the quantum fluctuations of fields directly in Minkowski…
In this article we propose a `second quantization' scheme especially suitable to deal with non-trivial, highly symmetric phase spaces, implemented within a more general Group Approach to Quantization, which recovers the standard Quantum…
Quantum computing may offer the opportunity to simulate strongly-interacting field theories, such as quantum chromodynamics, with physical time evolution. This would give access to Minkowski-signature correlators, in contrast to the…
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 of finite systems. Then we apply this…
Algebraic quantization has been applied on the class of globally hyperbolic spacetime for many decades, leading to remarkable results. Nonetheless, the presence of a boundary calls for a separate treatment, since, in general, it breaks…
Free noncommutative fields constitute a natural and interesting example of constrained theories with higher derivatives. The quantization methods involving constraints in the higher derivative formalism can be nicely applied to these…
The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion of a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for…
A midi-superspace model is a field theory obtained by symmetry reduction of a parent gravitational theory. Such models have proven useful for exploring the classical and quantum dynamics of the gravitational field. I present 3 recent…
Pure gravitational plane waves are considered as a special case of spacetimes with two commuting spacelike Killing vector fields. Starting with a midisuperspace that describes this kind of spacetimes, we introduce gauge-fixing and symmetry…
We describe the symplectic reduction construction for the physical phase space in gauge theory and apply it for the BF theory. Symplectic reduction theorem allows us to rewrite the same phase space as a quotient by the gauge group action,…
We describe in detail the implementation of the relativistic three-neutron finite-volume quantization condition derived in Ref. [1]. In particular, we show how the complications due to Wigner rotations acting on spins are included, and…
A semiclassical approach is used to obtain Lorentz covariant expressions for the form factors between the kink states of a quantum field theory with degenerate vacua. Implemented on a cylinder geometry it provides an estimate of the…
The coordinate-free formulation of canonical quantization, achieved by a flat-space Brownian motion regularization of phase-space path integrals, is extended to a special class of closed first-class constrained systems that is broad enough…
We describe quantization schemes for scalar field cosmology in the metric variables with fundamental discreteness imposed with a lattice. The variables chosen for quantization determine the lattice, and each lattice produces distinct…